euclaise/TinyCoT · Datasets at Hugging Face

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$$\left( 9\times 11+11\times 2+13\times 3 \right)\div 16=10$$．	a	TAL-SCQ5K	其中$$9$$岁的有$$11$$人，$$11$$岁的有$$2$$人，$$13$$岁的有$$3$$人，那么这$$16$$个小朋友的平均年龄是． a) $$10$$岁 b) $$10.5$$岁 c) $$11$$岁 d) $$11.5$$岁
A fortress is a military stronghold, which implies that it is very strong.	Yes	FLUTE	Consider the statement "My words sounded strong .". Based on this "My words sounded like an impenetrable fortress ." a true statement? Yes, no, or I don't know?
£$$20 \div 50p=40$$.	(E)	TAL-SCQ5K	Abigail is saving $$50$$p each week. How many weeks will she take to save £$$20$$? (A) $$20$$ (B) $$25$$ (C) $$30$$ (D) $$35$$ (E) $$40$$
The question tells us that Sally is not sitting at either end. This leaves three possible positions for Sally, which we will call positions $$2$$, $$3$$ and $$4$$ from the left-hand end. Were Sally to sit in place $$2$$, neither Dolly nor Kelly could sit in places $$1$$ or $$3$$ as they cannot sit next to Sally and, since Elly must sit to the right of Dolly, there would be three people to fit into places $$4$$ and $$5$$ which is impossible. Similarly, were Sally to sit in place $$3$$, Dolly could not sit in place $$2$$ or $$4$$ and the question also tells us she cannot sit in place $$1$$ so Dolly would have to sit in place $$5$$ making it impossible for Elly to sit to the right of Dolly. However, were Sally to sit in place $$4$$, Dolly could sit in place $$2$$, Kelly in place $$1$$, Molly (who cannot sit in place $$5$$) in place $$3$$ leaving Elly to sit in place $$5$$ at the right-hand end.	e	TAL-SCQ5K	Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next to her. Who is sitting at the far right end? Options: a) Molly　 b) Dolly　 c) Sally　 d) Kelly　 e) Elly
因为，在四边形中，两个最大的内角的和大于等于$$180{}^{}\circ $$，所以，凸$$n$$边形（$$n\geqslant 4$$）中，两个最大的内角和也大于等于$$180{}^{}\circ $$，同时小于$$360{}^{}\circ $$，设两个最大的内角的和为$$k{}^{}\circ $$，则$$1100+180\leqslant 1100+k=(n-2)\times 180 ~\textless{} ~1100+360$$，所以$$7\frac{1}{9}\leqslant n-2 ~\textless{} ~8\frac{1}{9}$$，$$9\frac{1}{9}\leqslant n ~\textless{} ~10\frac{1}{9}$$，$$n=10$$．故选$$\text{D}$$．	d	TAL-SCQ5K	凸$$n$$边形（$$n\geqslant 4$$）中，不算两个最大的内角，其余内角的和为$$1100{}^{}\circ $$，则$$n$$等于． a) $$12$$ b) $$11$$ c) $$10$$或$$9$$ d) $$10$$
Having to work all the time and never getting a break cannot be seen as a good thing because it means that someone is overworked and stressed.	Yes	FLUTE	Context: It's been getting to me lately that I'm constantly working and never get a break. Hypothesis: It's been totally fine with me lately that I'm always working and never get a break Is the hypothesis incorrect? (Yes, no, or unknown)?
两正方形的面积差$$=A{{P}^{2}}-{{\left( 1-AP \right)}^{2}}=2AP-1$$，由题意$$\left\textbar{} 2AP-1 \right\textbar=\frac{1}{2}$$，则有 $$\begin{cases}2AP-1=\frac{1}{2},\Rightarrow AP=\frac{3}{4} 2AP-1=-\frac{1}{2},\Rightarrow AP=\frac{1}{4} \end{cases}$$．故选$$\text{A}$$．	(a)	TAL-SCQ5K	$$P$$是线段$$AB$$上的一点，$$AB=1$$，以$$AP$$和$$BP$$为边分别作两个正方形，当这两个正方形的面积的差的绝对值为$$\frac{1}{2}$$时，$$AP$$的长是． (a) $$\frac{1}{4}$$或$$\frac{3}{4}$$ (b) $$\frac{1}{3}$$或$$\frac{2}{3}$$ (c) $$\frac{1}{5}$$或$$\frac{4}{5}$$ (d) $$\frac{2}{7}$$或$$\frac{5}{7}$$
$$A$$能被$$5$$整除，个位就是$$0$$或$$5$$，$$A$$加$$1$$得$$B$$ 是$$8$$的倍数，个位不能是$$1$$，故只能是$$6$$，$$B$$再加$$1$$得$$C$$ 是$$9$$的倍数，个位数字是$$7$$，$$C$$的个位只能由$$3\times 9=27$$得来．假设$$C=3\times 9=27$$，则$$B=26$$，$$26$$不能被$$8$$整除；故排除；假设$$C=13\times 9=127$$，则$$B=126$$，$$126$$不能被$$8$$整除；故排除；假设$$C=23\times 9=207$$，则$$B=206$$，$$206$$不能被$$8$$整除；故排除；假设$$C=33\times 9=297$$，则$$B=296$$，$$296\div 8=37$$，且$$295\div 5=59$$；因此，最小$$A=295$$，$$B=296$$，$$C=297$$，三个数的和为：$$295+296+297=888$$．故选$$888$$．	(4)	TAL-SCQ5K	$$A$$, $$B$$ and $$C$$ are three consecutive numbers that are divisible by $$5$$, $$8$$ and $$9$$ respectively. The smallest possible sum of these three numbers is ． $$A$$、$$B$$、$$C$$是三个连续数，分别可被$$5$$、$$8$$及$$9$$整除．此三个数最小的和是~\uline{~~~~~~~~~~}~． Options: (1) $$555$$ (2) $$666$$ (3) $$777$$ (4) $$888$$ (5) $$999$$
With higher frequencies, the microwaves also have more energy.	[b]	quartz	Tim adjusted his microwave so that it was at a higher frequency. This resulted in the waves inside the microwave to have Options: [a] less energy [b] more energy.
People who litter often think that they won't get caught or that it doesn't matter because there's already trash on the ground but it's actually really inconsiderate and drives other people crazy	Yes	FLUTE	Given the statement "I really hate seeing people throw trash on the street like if it was a natural thing to do", is the statement "It drives me crazy when people think it's okay to litter on the street like it has no consequences" is true? - Yes - No - I don't know
对比发现，小$$O$$与小$$Y$$说的矛盾，相互对立，则小$$O$$与小$$Y$$必一对一错，则小$$M$$说假话，则小$$M$$会开车，选$$\text{B}$$．	2	TAL-SCQ5K	小$$Y$$、小$$M$$、小$$O$$、小$$T$$四人中只有$$1$$人会开车．小$$Y$$说：``我会开''．小$$M$$说：``我不会开''．小$$O$$说：``小$$Y$$不会开''．小$$T$$什么也没说．已知小$$Y$$、小$$M$$、小$$O$$三人只有一人说了真话．会开车的是谁？ 1. 小$$Y$$ 2. 小$$M$$ 3. 小$$O$$ 4. 小$$T$$
A year is 12 months, so Elias spends 4 * 12 = $48 per year on bars of soap. In two years, he spends 2 * 48 = $96 on bars of soap.	96	gsm8k	Elias uses a bar of soap every month. If each bar of soap costs $4, how much does he spend on bars of soap in two years?
It is natural to feel angry when ones parents are making decisions that will directly impact the person's life without even taking their opinion into account	No	FLUTE	Consider the statement "I had a huge conflict with my parents about moving to another country and I was simply enraged to have them trying to control my life.". Is the statement "I was so mad when my parents were trying to control my life and deciding where to move without even consulting me" false? Yes/no/unknown
Losing the chance to buy a property one was interested in because someone else put in an offer before them would not make anyone thrilled but rather disappointed.	Yes	FLUTE	Given the statement "I was trying to buy a piece of property that had came up on the market, but someone put in a offer quicker than I did and it was sold already.", is the statement "I am thrilled that I lost the chance to buy the property because someone put in a offer quicker than I did" wrong? - Yes - No - Unknown
If Rehana is currently 25 years old, she will be 25+5=30 in five years. Rehana will be three times as old as Phoebe in five years, meaning Phoebe will be 30/3=10 years old in five years. Currently, Phoebe is 10-5=5 years old. 3/5 of Phoebe's age now is 3/5*5=3 years, which is Jacob's age.	3	gsm8k	In five years, Rehana will be three times as old as Phoebe. If Rehana is currently 25 years old, and Jacob, Rehana's brother, is 3/5 of Phoebe's current age, how old is Jacob now?
Rose is $$150\rm cm$$ tall. Quentin is $$10 \rm cm$$ taller than Rose, so Quentin is $$160 \rm cm$$ tall. Sam is $$4 \rm cm$$ shorter than Rose, so Sam is $$146 \rm cm$$ tall. Their average height is $$ (150+160+146)\div3 =152 \rm cm$$.	[3]	TAL-SCQ5K	Rose is $$150\rm cm$$ tall. Rose\textquotesingle s older brother Quentin is $$10 \rm cm$$ taller than Rose is. Rose\textquotesingle s younger brother Sam is $$4 \rm cm$$ shorter than Rose is. What is the average of the heights of Rose, Sam, and Quentin? Options: [1] $$148\rm cm$$ [2] $$150\rm cm$$ [3] $$152\rm cm$$ [4] $$154\rm cm$$
The garden produced 237 potatoes - 60 = 177 cucumbers. The garden produced 177 cucumbers * 2 peppers/cucumber = 354 peppers. The garden produced 237 potatoes + 177 cucumbers + 354 peppers = 768 vegetables.	768	gsm8k	A garden produced 237 potatoes, 60 fewer cucumbers and twice as many peppers than the cucumbers. How many vegetables did the garden produce?
$$\left( 甲，乙\right)=1$$，则甲、乙互质；$$\left(乙，丙 \right)=$$质数；$$\left(甲，丙 \right)=$$质数的平方，最小的质数的平方为$$4$$，$$\therefore $$丙最小：$$3\times ~4=12$$，甲：$$4$$，乙$$3$$．$$12+4+3=19$$．	1	TAL-SCQ5K	甲、乙、丙三个非零自然数满足：甲和乙的最大公因数恰有$$1$$个因数，乙和丙的最大公因数恰有$$2$$个因数，丙和甲的最大公因数恰有$$3$$个因数．那么，甲、乙、丙三数之和的最小值是~\uline{~~~~~~~~~~}~（中上） 1) $$19$$ 2) $$20$$ 3) $$21$$ 4) $$22$$
By AM-GM, \[\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge 3 \sqrt[3]{\frac{a}{b} \cdot \frac{b}{c} \cdot \frac{c}{a}} = 3.\]Equality occurs when $a = b = c,$ so the minimum value is $3.$	$3$	competition-math	Let $a,$ $b,$ and $c$ be positive real numbers. Find the minimum value of \[\frac{a}{b} + \frac{b}{c} + \frac{c}{a}.\]
Gravity is a pull which all matter exerts on all other matter, the more mass, the stronger the pull.	[a]	quartz	A big planet has a _____ pull of gravity than a small planet. [a] stronger [b] weaker
由$$a+b+ab+1=(a+1)(b+1)$$得，每次操作前和操作后，黑板上的每个数加$$1$$后的乘积不变，设经过$$99$$次操作后黑板上剩下的数为$$x$$，则$$x+1=(1+1)( \frac{1}{2}+1)(\frac{1}{3}+1)\cdots (\frac{1}{100}+1)$$，解得$$x=100$$．	C	TAL-SCQ5K	✩✩✩✩✩黑板上写有$$1$$，$$\frac{1}{2}$$，$$\cdots$$，$$\frac{1}{100}$$共$$100$$个数字，每次操作先从黑板上的数中选取两个数$$a$$，$$b$$，然后删去$$a$$，$$b$$，并在黑板上写上数$$a+b+ab$$，则经过$$99$$次操作后黑板上剩下的数是． Options: A: $$2012$$ B: $$101$$ C: $$100$$ D: $$99$$
To bring up the rear means to move last in a group of people.	True	FLUTE	Context: "Besides, I can do a lot more damage with a sheath of arrows than she can with two axes, so I'm the best one to follow behind." Claim: "Besides, I can do a lot more damage with a sheath of arrows than she can with two axes, so I'm the best one to bring up the rear." Considering the context, is the claim true, false, or unknown?
Fear and anxiety are not feelings that anyone would want to feel and so being excited about the potential of being shot near one's house is definitely not warranted.	Yes	FLUTE	Consider the statement "I am terrified that someone got shot near my house the other day.". Is the statement "I am excited that somebody was just shot near my house and it could happen to me too" false? Yes/no/unknown
Since $100=33\cdot3+1$, the first $100$ letters are $33$ copies of the $3$ letters $ABC$ followed by an $A$. The $100$th letter is $A$.	$A$	competition-math	What is the 100th letter in the pattern ABCABCABC...?
Travel between the three stations takes 2+2 = 4 hours The total time for the journey is 4*60 = 240 minutes. If Kira takes a 30-minute break, her journey takes 240+30 = 270 minutes	270	gsm8k	Three train stations are 2 hours apart from one another. Kira travels from the first station to the third, taking a 30 minutes break at the second station. What's the total time, in minutes, that Kira takes to travel between the first and third station?
Suppose that Cici will be $x$ years old $4$ years later, Linda will be $$(x+11)$$ years old. $x+(x+11)=37$, so $x=13$. Thus, Linda will be $13+11=24$ years old $3$ years later.	(C)	TAL-SCQ5K	When Cici was born, Linda was $11$ years old. The sum of their ages $4$ years later will be $37$. How old will be Linda $3$ years later? Options: (A) $$12$$ (B) $$22$$ (C) $$24$$ (D) $$26$$
Not on your life is used to refuse very firmly to do something, but in this context they are willingly giving up his possessions.	No	FLUTE	Given the statement "All they wanted were his - of course!.", is the statement "All they wanted were his - not on your life!" is true? - Yes - No - I don't know
With a higher the concentration of hydrogen ions, a solution is more acidic and has a lower pH.	(b)	quartz	James wants to create a solution that is less acidic than others, so his concentration of hydrogen ions will be (a) higher (b) lower
Countries with more industry produce more hazardous wastes than those with little industry.	a lot of	quartz	If your country has a lot of industry it likely has _____ hazardous waste. * a lot of * not so much
It is very rude and unprofessional to just dump work on someone's desk without any prior warning or discussion so it is understandable to get mad in that situation	Yes	FLUTE	Consider the staetement "A coworker mad me very mad one day by slamming a large order of work on my desk and basically demanding that I do it.". Based on this statement, is "I got so mad one day when my coworker threw a large order of work on my desk and basically demanded that I do it" a true statement? Yes/no/unknown
Two pairs of sneakers cost 2 x $100 = $200. So, Leonard spent $50 + $200 = $250. Two pairs of jeans cost 2 x $50 = $100. Thus, Michael spent $100 + $100 = $200. Therefore, they spent a total of $250 + $200 = $450 in all.	450	gsm8k	Leonard and his brother Michael bought presents for their father. Leonard bought a wallet at $50 and two pairs of sneakers at $100 each pair, while Michael bought a backpack at $100 and two pairs of jeans at $50 each pair. How much did they spend in all?
The chest of drawers sold for half as much as the treadmill, for a price of $100/2= $50. The television sold for three times what he earned for the treadmill, for a price of $100*3= $300. For the three items, he raised $100+$50+$300 = $450. If $450 is 75% of the total sum of money that Toby made at the garage sale, then the total amount is $450 / (75/100) = $600.	600	gsm8k	Toby held a garage sale to raise money to support friends who have lost their jobs. Of all the items that he sold during the garage sale, three of the items he sold made up 75% of the total amount of sales money he earned. He sold a treadmill for $100, a chest of drawers for half as much as he made for selling the treadmill, and he sold a television for three times what he earned for selling the treadmill. What is the total sum of money, in dollars, that Toby made at the garage sale?
First find how many text messages he sent on Tuesday: 220 messages / 2 = 110 messages Then find how many text messages he sent Wednesday-Friday: 50 messages/day * 3 days = 150 messages Then add up all the messages he sent to find the total: 110 messages + 150 messages + 220 messages = 480 messages Then divide that number by the number of days to find the average number of messages he sent per day: 480 messages / 5 days = 96 messages/day	96	gsm8k	Jason sent 220 text messages on Monday, half as many text messages on Tuesday, and 50 text messages each day Wednesday through Friday. How many text messages did he send on average during those five days?
There are 168 hours in a week. The entire Ugly Betty series is 85 hours long.	Yes	strategyqa	Would a week be enough time to watch every episode of Ugly Betty?
Pizza is an Italian food. Anchovies are occasionally used as a pizza topping.	Yes	strategyqa	Are anchovies associated with Italian food?
When your brain senses that your body temperature is increasing, it sends messages to the blood vessels in the skin to increase in diameter.	[A]	quartz	The blood vessels near the top of the skin do what when it's warm? [A] enlarge [B] contract
Jose can earn $3 x 8 = $24 per day for kids. He charges $3 x 2 = $6 per adult. So, he can earn $6 x 10 = $60 per day for adults. Jose earns $60 + $24 = $84 per day for kids and adults. Therefore, he can earn $84 x 7 = $588 per week.	588	gsm8k	Jose owns a swimming pool. He charges $3 for kids and twice that amount for adults. If 8 kids and 10 adults swim in his swimming pool per day, how much money will he earn per week?
Giving in to hunger pangs is not a thoughtful thing to do as it implies that the person was too lazy to cook for themselves and decided to eat someone else's food without their permission.	No	FLUTE	Consider the staetement "I was really hungry today and ate my roomates leftovers.". Based on this statement, is "I felt so thoughtful about giving in to my hunger pangs and eating my roommates leftovers" a true statement? Yes/no/unknown
一共赛了$$4\times (4-1)\div2=6$$场，每人各有$$3$$场比赛，因为甲，乙，丙三人胜的场数相同，若甲，乙，丙各胜$$1$$场，则丁胜$$6-1\times3=3$$场，即丁全胜，不合题意（甲胜了丁）．若甲，乙，丙各胜$$2$$场，则丁胜$$6-2\times3=0$$场，即丁全输，符合题意．所以，丁胜了$$0$$场．故选$$\text{A}$$．	(1)	TAL-SCQ5K	甲、乙、丙、丁比赛羽毛球，每两人要赛一场．结果甲胜了丁，并且甲、乙、丙三人胜得场数相同．丁胜了场． (1) $$0$$场 (2) $$1$$场 (3) $$2$$场 (4) $$3$$场
Enrico was able to sell the 30-kilogram rooster for 30 x 0.50 = $15. And he was able to sell the 40-kilogram rooster for 40 x 0.50= $20. Therefore, he was able to earn $20 + $15 = $35.	35	gsm8k	Enrico owns a rooster farm, he sells each rooster for $0.50 per kilogram. He was able to sell a 30-kilogram rooster and a 40-kilogram rooster, how much money was he able to earn?
Chandler and Lucy can eat 23 + 19 = 42 apples per week. Therefore, they have to order 42 x 4 = 168 apples for a month.	168	gsm8k	Chandler can eat a total of 23 apples and Lucy can eat a total of 19 apples per week. If the farmer only delivers 1 time per month, how many apples do they have to order for a month?
$$a\star b=\underbrace{(a+b)}\_{\rm{tens}} \underbrace{(a-b)}\_{\rm{ones}}$$	3	TAL-SCQ5K	An operator $$\star$$ acts on two numbers to give the following outcomes: $$3\star2=51$$ $$5\star3=82$$ $$6\star1=75$$ $$9\star4=135$$ What is $$7\star5$$ equal to? 1) $$112$$ 2) $$121$$ 3) $$122$$ 4) $$212$$ 5) None of the above
Bigger atoms have more electrons.	Quentin's	quartz	Evan has a 10 meter atom model. Quentin has a 20 meter atom model. Whose atom would probably have more electrons if they are different elements to the same scale? Options: * Evan's * Quentin's
If the number of candies was 300, and 40% percent were sour, then there were 40/100*300 =120 sour candies. The number of good candies was 300-120=180 The number of people who received candy is Henley, 1+ 2 brothers = 3 people if they divided the good candies equally, each person got 180/3 = 60 candies.	60	gsm8k	Henley bought 300 candies and shared them with her two brothers. However, they realized 40% of them were sour, and they had to separate those out. If they then shared the good candies equally, how many candies did each get?
A printer that is making noises and causing problems is not great and so someone who loves it is being sarcastic.	No	FLUTE	Consider the statement "This new printer really grinds my gears!!!". Based on this "This new printer is soooo great and I absolutely love how it's grinding on my nerves." a true statement? Yes, no, or I don't know?
With a higher the concentration of hydrogen ions, a solution is more acidic and has a lower pH.	[B]	quartz	A small container that has 100 hydrogen ions is sitting near a larger container that has 2 hydrogen ions. The solution in the larger container is Options: [A] more acidic [B] less acidic.
As more resistors are added in series, the total resistance of the circuit increases.	[A]	quartz	John was building a circuit in the electrical room when he noticed something. The more resistors he removed, the level of resistance would [A] Decrease [B] Increase
The rider travels for $$13$$ hours over $$60$$ rides, which is anaverage time of $$\frac{13}{60}$$ of an hour per ride, hence $$13$$ minutes.	$$13$$ minutes	TAL-SCQ5K	A city has a bicycle hire scheme where it is possible to hire a bicycle for short journeys. Last year I hired a bicycle $$60$$ times and rode for $$13$$ hours altogether. For how long on average did I hire the bicycle on each ride? - $$13$$ minutes - $$23$$ minutes - $$39$$ minutes - $$47$$ minutes - $$73$$ minutes
When Jerry reads 30 pages on Saturday, he would be remaining with 93-30 = 63 pages. After reading an additional 20 pages on Sunday, he would be remaining with 63 – 20 = 43 pages.	43	gsm8k	Jerry has an interesting novel he borrowed from a friend to read over the weekend. The book has 93 pages. On Saturday, he reads 30 pages. On Sunday, he goes to church and comes back, sits down, and reads 20 pages of the book. How many pages are remaining before Jerry can finish the book?
$(x+y)-(x-y)=2y$ $(2x+3y)+(-2x-y)=2x+3y-2x-y=2y$ $(3x-2y)+(-3x+4y)=3x-2y-3x+4y=2y$ $(x-y)+(-x+y)=x-y-x+y=0$	[D]	TAL-SCQ5K	After simplying the following expressions, which one is different from others? [A] $(x+y)-(x-y)$ [B] $(2x+3y)+(-2x-y)$ [C] $(3x-2y)+(-3x+4y)$ [D] $(x-y)+(-x+y)$
For babysitting, Jolene raises 4 x $30 = $120. For car washing, she raises 5 x $12 = $60. So far, she has raised $120 + $60 = $180.	180	gsm8k	Jolene wants to raise some money to buy a bicycle. She babysits for 4 families for $30 each. She also washes 5 neighbors’ cars for $12 each. How much did she raise so far?
Machines make work easier by increasing the amount of force that is applied, increasing the distance over which the force is applied, or changing the direction in which the force is applied.	A	quartz	Kate makes a machine that is very unproductive, and it gets work done slowly, because it uses force in amounts that are A: lesser B: greater
Temujin was the birth name of Genghis Khan. Genghis Khan founded the Mongol Empire which was the largest land empire in world history. Charlemagne, King of the Franks, conquered most of Western Europe. At its peak, the Mongol Empire had 110 million people. Charlemagne's empire had around 20 million people at its height.	No	strategyqa	Would Temujin hypothetically be jealous of Charlemagne's conquests?
Roberta's bag costs $45 - $17 = $28. Roberta spend $28 / 4 = $7 on lunch. Roberta spend 45 + 28 + 7 = 80 in total. Roberta has $158 - 80 = $78 left.	78	gsm8k	Roberta takes $158 with her on a shopping trip to the mall. She spends $45 on new shoes, $17 less on a new bag, and a quarter of the price of the bag for lunch. How much money does she have left after these purchases?
算式中的分母是裂项计算的最基本形式，但分子比较复杂，我们可以从前几项找找规律： $$\frac{{{1}^{2}}+{{2}^{2}}}{1\times 2}=\frac{5}{2}=2\frac{1}{2}$$，$$\frac{{{2}^{2}}+{{3}^{2}}}{2\times 3}=\frac{13}{6}=2\frac{1}{6}$$，$$\frac{{{3}^{2}}+{{4}^{2}}}{3\times 4}=\frac{25}{12}=2\frac{1}{12}$$．我们发现一规律：每一项减去$$2$$后，分子就变成了$$1$$．再来试试最后一项：$$\frac{{{19}^{2}}+{{20}^{2}}}{19\times 20}=\frac{761}{380}=2\frac{1}{380}$$，也满足这个规律，这是为什么呢？观察每一项的分子和分母，我们发现分子的每个加数都与分母大小接近，可以做如下变形： $$\frac{{{19}^{2}}+{{20}^{2}}}{19\times 20}=\frac{19\times \left( 20-1 \right)+20\times \left( 19+1 \right)}{19\times 20}$$ $$=\frac{19\times 20\times 2+\left( 20-19 \right)}{19\times 20}$$ $$=2+\frac{1}{19\times 20}$$．算式中的每一项都能像上面一样进行变形，再结合分数裂差，所以：原式$$=2\frac{1}{1\times 2}+2\frac{1}{2\times 3}+\cdots +2\frac{1}{19\times 20}$$ $$=2\times 19+\frac{1}{1\times 2}+\frac{1}{2\times 3}+\cdots +\frac{1}{19\times 20}$$ $$=38+1-\frac{1}{20}$$ $$=38\frac{19}{20}$$．	(3)	TAL-SCQ5K	计算：$$\frac{{{1}^{2}}+{{2}^{2}}}{1\times 2}+\frac{{{2}^{2}}+{{3}^{2}}}{2\times 3}+\cdots +\frac{{{18}^{2}}+{{19}^{2}}}{18\times 19}+\frac{{{19}^{2}}+{{20}^{2}}}{19\times 20}$$=~\uline{~~~~~~~~~~}~ Options: (1) $$37\frac{19}{20}$$ (2) $$28\frac{19}{20}$$ (3) $$38\frac{19}{20}$$
To be under fire means to be subject to intense criticism or judgment, but the headline states that the local celebrities are not receiving any criticism or judgment.	No	FLUTE	Given the statement "The headline read, local celebrities not receiving any criticism or judgment.", what is the statement "The headline read, local celebrities under fire." true? - Yes - No - Unknown
$$P$$和$$Q$$一天可以完成$$\frac{1}{2}$$，$$Q$$和$$R$$一天可以完成$$\frac{1}{4}$$，$$P$$和$$R$$一天可以完成$$\frac{1}{2.4}=\frac{5}{12}$$，则三人一天一共可以完成$$\frac{1}{2}\times \left( \frac{1}{2}+\frac{1}{4}+\frac{5}{12} \right)=\frac{7}{12}$$，$$P$$的工作效率为$$\frac{7}{12}-\frac{1}{4}=\frac{1}{3}$$，因此$$P$$单独做需要$$3$$天完成.	(1)	TAL-SCQ5K	$$P$$和$$Q$$共做一事$$2$$天可完成，$$Q$$和$$R$$共做此事$$4$$天可完成，$$P$$和$$R$$共做此事$$2.4$$天可完成，$$P$$一人做完此事完成的天数是( )天. Options: (1) $$3$$ (2) $$8$$ (3) $$12$$ (4) $$6$$
It comes $4+4=8$ when we count Amy twice. The number of all singing students is $4+4-1=7$	c	TAL-SCQ5K	Several students are singing in a line. Amy is the fourth one from the left. From the right, Amy is the fourth too. How many students are singing? (adapted from $$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$5$$) a. $5$ b. $6$ c. $7$ d. $8$ e. $9$
甲每分钟行驶路程的$$\frac{1}{30}$$，乙每分钟行驶路程的$$\frac{1}{40}$$．设$$x$$分钟后，甲追上乙，由题意，得$$\frac{x}{30}=\frac{x+5}{40}$$，解得$$x=15$$．答：甲出发后的第$$15$$分钟，追上乙．	d	TAL-SCQ5K	甲、乙两人沿同一路线骑车（匀速）从$$A$$站到$$B$$站，甲要用$$30$$分钟，乙要用$$40$$分钟．如果乙比甲早出发$$5$$分钟去$$B$$站，则甲追上乙时，是甲出发后的第（~ ）． Options: a) $$12$$分钟 b) $$13$$分钟 c) $$14$$分钟 d) $$15$$分钟
The movie that is being replayed 6 times takes 1.5 x 6 = 9 hours. The advertisements before the start of the movie take 20 x 6 = 120 minutes in all. One hundred twenty minutes is equal to 120/60 = 2 hours. Thus, the movie theater operates for 9 + 2 = 11 hours each day.	11	gsm8k	A movie that's 1.5 hours long is being replayed 6 times in one movie theater each day. There is a 20-minute advertisement before the start of the movie. How long, in hours, does the movie theater operate each day?
First find how much the roses for one centerpiece cost: $5/rose * 10 roses = $50 Then find how much the lilies for one centerpiece cost: $4/rose * 15 roses = $60 Then find how much the table settings for one table cost: 4 settings * $10/setting = $40 Then add the cost of both types of flowers, the place settings, and the tablecloth to find the total cost per table: $50 + $60 + $40 + $25 = $175 Then multiply the cost per table by the number of tables to find the total cost: $175/table * 20 tables = $3500	3500	gsm8k	Nathan is buying decorations for his wedding reception. The reception hall will have 20 tables. Each table needs a linen tablecloth ($25 to rent), 4 place settings ($10 each to rent), and a centerpiece. Each centerpiece will have 10 roses ($5 each) and 15 lilies ($4 each). How much will the decorations cost?
Raccoons are often considered to be dirty animals and so finding one dead inside a shed would likely make someone feel disgusted	No	FLUTE	Context: I went into my shed to clean it and I found a dead raccoon Hypothesis: I found a dead raccoon inside my shed and it made me feel completely disgusted Is the hypothesis incorrect? (Yes, no, or unknown)?
Smaller tributary glaciers, like tributary streams, flow into the main glacier in their own shallower U-shaped valleys.	[2]	quartz	What would happen to the size of the valley created by a tributary stream if the size of the stream were to be increased? [1] the valley would be shallower [2] the valley would be deeper
At higher temperatures, particles of reactants have more energy, so they move faster. They are more likely to bump into one another and to collide with greater force.	faster	quartz	When something gets very hot does it move slower faster
The opening scene of Disney's Frozen shows a group of ice breakers. They have moose that carry the heavy ice blocks. One of them, Kristoff, becomes separated with his moose Sven. When Queen Elsa flees Arendelle and Princess Anna gives chase, she quickly encounters Kristoff.	Yes	strategyqa	Are moose used for work near the kingdom of Arendelle?
The second drink was 2/12=1/6 the size of the first drink So it had 1/63=1/2 the caffeine That means it had 1/2250=125 grams of caffeine So the total amount of caffeine he drank was 125+250=375 grams So he consumed 375*2=750 grams of caffeine for the day	750	gsm8k	John drinks 2 energy drinks. 1 of them is a 12-ounce drink with 250 grams of caffeine. The second drink is 3 times more caffeinated per ounce but only 2 ounces. He then takes a caffeine pill that has as much caffeine as his 2 drinks combined. How much caffeine did he consume?
First of all, we know that $\|ab\|=\|a\|\cdot \|b\|$, so \[\left\|\left(3 + \sqrt{7}i\right)^3\right\|=\left\|3 + \sqrt{7} i\right\|^3\]We also find that \[\left\|3 +\sqrt{7}i\right\|=\sqrt{\left(3\right)^2+\left(\sqrt{7}\right)^2}=\sqrt{16}=4\]Therefore, our answer is $4^3=64$.	$64$	competition-math	Find \[\left\|\left(3 + \sqrt{7}i\right)^3\right\|\]
A radio transmitter located in the Eiffel Tower. This transmitter jammed German radio communications. This hindrance in German radio communications contributing to the Allied victory at the First Battle of the Marne.	Yes	strategyqa	Did Eiffel Tower contribute to a war victory?
The original mixture contains $25\times 24\textbackslash\% = 6$ liters of yellow tint. $$15$$ liters of yellow tint is added to the mixture, the new mixture now has $6+15=21$ liters of yellow tint. New percent of yellow =$\frac{21}{25+15} =52.5\textbackslash\% $	A	TAL-SCQ5K	A mixture of $25$ liters of paint is $16 \textbackslash\%$ red tint, $24\textbackslash\%$ yellow tint and $60\textbackslash\%$ water. $15$ liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \#17 ) Options: A: $$52.5$$ B: $$55$$ C: $$57.5$$ D: $$60$$
Most people are disgusted by bugs and finding them in large numbers in your new apartment is definitely no exception	Yes	FLUTE	Given the statement "When I moved into my apartment it was full of bugs", is the statement "I was so disgusted when I moved into my apartment and found it crawling with bugs." is true? - Yes - No - I don't know
The popcorn costs 8 - 3 = $5. The drink costs 5 + 1 = $6. The candy costs 6 / 2 = $3. The normal price is 8 + 5 + 6 + 3 = $22. Thus, the deal saves a customer 22 - 20 = $2.	2	gsm8k	A movie theater company is advertising a deal of a movie ticket, a bucket of popcorn, a drink, and a box of candy for $20. Normally, a movie ticket costs $8, a bucket of popcorn costs three dollars less, a drink costs a dollar more than popcorn, and a candy costs half as much as a drink. How many dollars does the deal save a customer who buys a ticket, popcorn, drink, and candy normally?
On the 2nd week, Paul halved the first week's sugar, therefore he used 24/2 = 12 cups The third week, Paul used 12/2 = 6 cups The fourth week, he used 6/2 = 3 cups	3	gsm8k	Every week of last month Paul tried out a new cake recipe. The first week, he followed a cake recipe that called for 24 cups of sugar. Each week after that, he reduced the amount of sugar by half. How much sugar did he use for the cake on the fourth week?
Elizabeth spends 6*2 = 12 dollars on pens. Elizabeth has 20-12 = 8 dollars to spend on pencils. Elizabeth can buy 8/1.6 = 5 pencils.	5	gsm8k	Elizabeth has 20 dollars and wants to buy pens and pencils. Each pencil costs $1.60 and each pen cost 2 dollars. How many pencils can she buy with her 20 dollars if she wants 6 pens?
16 jars are exactly twice the number of clay pots made by the craftsman, meaning there are 16/2=8 clay pots If each jar has 5 marbles, the total number of marbles in the jars is 516=80 Each of the clay pots also has 35=15 marbles. The total number of marbles in the 8 clay pots is 15*8=120 There are a total of 120+80=200 marbles.	200	gsm8k	A craftsman makes 16 jars. This is exactly twice the number of clay pots he made. If each jar has 5 marbles and each clay pot has three times as many, how many marbles are there?
No one should feel proud when their partner gets drunk and starts behaving in an embarrassing way because it is not a good thing.	No	FLUTE	Given the statement "My boyfriend is drinking beer and he so dumb when he drinks.", what is the statement "I beam with pride when my boyfriend gets drunk and starts acting like an idiot." true? - Yes - No - Unknown
one sentence is saying that the silence was so overwhelming that it felt like it was crushing the person where as another sentence is saying that the person found comfort in the silence and that the moment passed by quickly.	Yes	FLUTE	Given the statement "Silence was comfort, the moment had arrived.", is the statement "Silence was crushing, I knew the moment had arrived." wrong? - Yes - No - Unknown
函数$$f\left( x \right)={{2}^{\left\textbar{} 2x-2 \right\textbar}}-a\cos \left( 1-x \right)$$的图象关于直线$$x=1$$对称，又方程只有一个实数解， ∴$$f\left( 1 \right)=0$$，得$$a=1$$，当$$a=1$$时，$$f\left( x \right)={{2}^{\left\textbar{} 2x-2 \right\textbar}}-\cos \left( 1-x \right)\geqslant 1-1=0$$，当且仅当$$x=1$$时取等号，即方程$${{2}^{\left\textbar{} 2x-2 \right\textbar}}-a\cos \left( 1-x \right)=0$$只有一个实数解，符合题设．故选$$\text{B}$$．	$$a=1$$	TAL-SCQ5K	关于$$x$$的方程$${{2}^{\left\textbar{} 2x-2 \right\textbar}}-a\cos \left( 1-x \right)=0$$只有一个实数解，则． * $$a=-1$$ * $$a=1$$ * $$a=2$$ * $$a$$的值不唯一
If he was wrong, it meant going back to the drawing board, or starting the planning process all over again, but in this sentence it would mean not having to start over.	No	FLUTE	Given the statement "Either he was right, considered sorenson, or he was wrong, which meant not having to start the planning process all over again.", is the statement "Either he was right, considered sorenson, or he was wrong, which meant going back to the drawing board." is true? - Yes - No - I don't know
The Los Angeles Memorial Sports Arena had a capacity of 16,740 people. Coachella has had attendance numbers in excess of 99.000 people. Coachella relies on an outdoor set up to accommodate the massive crowds.	Yes	strategyqa	Was Los Angeles Memorial Sports Arena hypothetically inadequate for hosting Coachella?
Gravity is a pull which all matter exerts on all other matter, the more mass, the stronger the pull.	weaker	quartz	A small planet has a _____ pull of gravity than a small planet. * stronger * weaker
A CEO is a high-level executive who is typically very wealthy, so living like one would not be poverty-stricken	Yes	FLUTE	Consider the statement "I live poverty-stricken". Is the statement "I live like a CEO with diamond-studded sneakers." false? Yes/no/unknown
To change hands means to pass from one owner to another, and in this sentence money or assets are about to be transferred.	Yes	FLUTE	Context: But with the chance that money or assets were about to be transferred, forrest would be there looking for crumbs and leftovers. Hypothesis: But with the chance that money or assets were about to change hands, forrest would be there looking for crumbs and leftovers. Given this context, is the hypothesis true (Yes/No/I don't know)?
First, subtract the number of days Jenna can't read from the number of days in September: 30 days - 4 days = 26 days. Then subtract the one day when Jenna will read 100 pages: 26 days - 1 day = 25 days. Now subtract the 100 pages Jenna will read on her flight from her overall goal: 600 pages - 100 pages = 500 pages. Finally, divide that number of pages by the number of days Jenna will read the standard amount: 500 pages / 25 days = 20 pages per day.	20	gsm8k	Jenna sets a goal of reading 600 pages a month for the month of September (which has 30 days). She knows that she'll be really busy at work the four weekdays starting on the 13th, so she won't have time to read. She can also read 100 pages on the 23rd, when she'll have a long boring flight. If she reads the same number of pages every other day, how many pages a day does she need to read?
If $$20$$ years ago Allen was half as old as he is today, then today he is $$40$$. Thus, $$10$$ years ago he was $$30$$.	b	TAL-SCQ5K	If $$20$$ years ago Allen was half as old as he is today, how old was he $$10$$ years ago? a. $$20$$ b. $$30$$ c. $$40$$ d. $$50$$
February mornings are cold since it is the middle of winter so skin can't be warm	No	FLUTE	Context: My skin was warm Hypothesis: My skin was like a february morning. Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
Basketball games consist of four quarters. Tom\textquotesingle s scoring at the end of the third quarter implies that there is one quarter left, which is equivalent to 1/4 of the entire game.	[A]	TAL-SCQ5K	Tom scored a basket at the end of the third quarter of a basketball game between the Lakers and the Warriors. At that point, what fraction of the whole game remained to be played? [A] $$\frac{1}{4}$$ [B] $$\frac{1}{3}$$ [C] $$\frac{1}{2}$$ [D] $$\frac{3}{4}$$ [E] $$\frac{2}{3}$$
The smaller bags each have 100/2=50 gold coins each So in total, they have 50*2=100 coins So he found 100+100=200 coins So he finds 200/8=25 coins an hour	25	gsm8k	Jim spends 8 hours scuba diving. In that time he finds a treasure chest with 100 gold coins in it. He also finds 2 smaller bags that have half as much gold each. How much gold does he find per hour?
A quart is 32 ounces so this jar is 32-2=30 ounces James uses 3*.5=1.5 ounces a day So it last 30/1.5=20 day	20	gsm8k	James buys a jar of hot sauce. Each serving is .5 ounces. He uses 3 servings every day. if the container is 2 ounces less than 1 quart how many days will it last?
It's unfortunate when someone doesn't get promoted at work even though they deserved it, but sometimes these things just happen and it can feel like pure luck was the deciding factor	Yes	FLUTE	Context: I never got the chance to get promoted at work even though all my colleagues did Hypothesis: I was never lucky enough to get promoted at work even though all my colleagues did Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
To take it on the chin means to receive the full brunt of something, which in this context is the situation.	No	FLUTE	Consider the statement "Oh well, nothing I can do about it, just accept the situation and move on.". Is the statement "Oh well, nothing I can do about it, just take it on the chin and move on." false? Yes/no/unknown
$(19\times6+26)\div7=140\div7=20$ pages.	$$20$$	TAL-SCQ5K	Eddie finished reading a story book last week. He read an average of $19$ pages per day for the first six days of the week and $26$ pages on the last day. How many pages on average did Eddie read per day? - $$26$$ - $$20$$ - $$13$$ - $$6$$
A branch jutting from a tree is quite thin, so the simile is indicating that the person's nose is quite thin as well.	Yes	FLUTE	Context: His nose was rather narrow Hypothesis: His nose was like a branch jutting from a tree. Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
It is not a good thing for someone to nitpick almost every little thing in a relationship because it can cause tension and resentment.	False	FLUTE	Context: "My partner nags almost about every detail in our relationship." Claim: "I love how my partner nitpicks almost every little thing in our relationship" Considering the context, is the claim true, false, or unknown?
The idiom better late than never means that the delayed occurrence or achievement of something is better than it not happening at all.	Yes	FLUTE	Consider the statement "It's better that this happened even though it's delayed, Danny said behind them.". Based on this "Well, better late than never,danny said behind them." a true statement? Yes, no, or I don't know?
Alicia got 10 small boxed presents + 12 medium boxed presents = 22 presents. A third of all the presents Alicia gets are in large boxes, 22 / 2 = 11 is half of the presents we know Alicia got. 11 x 3 = 33 presents Alicia got on her birthday.	33	gsm8k	Alicia had a wonderful birthday party where she got lots of presents. 10 of the presents were in small boxes. 12 of the presents were in medium boxes. A third of all the presents she is given are in large boxes. How many presents did Alicia get for her birthday?
It is unlikely that someone would be thrilled when a friend gets something good while they do not and instead, this implies that the person is jealous.	No	FLUTE	Consider the staetement "I am so jealous of my friend Mary who got accepted into Medical school while I am still waiting on my application to be approved. ". Based on this statement, is "It thrills me that my friend Mary got accepted into Medical school and I am still waiting on my application to be approved" a true statement? Yes/no/unknown
Chicken feed is a small amount of money, but this sentence describes the inheritance making Jonathan/Elliott's look like a very large amount of money.	Yes	FLUTE	Given the statement "He mentioned that his inheritance made Jonathan/Elliott's look like a very large amount of money.", is the statement "He mentioned that his inheritance made Jonathan/Elliott's look like chicken feed." wrong? - Yes - No - Unknown
The college application process is very competitive and often people who don't get accepted into their first choice school can feel scared and anxious about the future	Yes	FLUTE	Given the statement "I hated waiting each day to see if a college acceptance letter came in", is the statement "I was scared every day to see if a college acceptance letter would come in the mail" is true? - Yes - No - I don't know
She wants to send a dozen carnations that cost $4/dz to each of her 5 teachers, so 45 = $20 She has 14 friends and she knows a dozen carnations is cheaper than buying 12 single carnations. So 14-12 = 2 single carnations are needed A single carnation cost $0.50 so 2.50 = $1.00 All total she will spend 20+4+1 = $25.00 on carnations	25	gsm8k	One of the clubs at Georgia's school was selling carnations for a fundraising event. A carnation costs $0.50. They also had a special where you could buy one dozen carnations for $4.00. If Georgia sent a dozen carnations to each of her 5 teachers and bought one carnation for each of her 14 friends, how much money would she spend?
Traveling at 50 yards per minute, Biff can travel 500 yards in 500/50=10 minutes. In 10 minutes, traveling at 51 yards per minute, Kenneth can travel 10*51=510 yards. Thus, Kenneth will be 510-500=10 yards past the finish line when Biff crosses the finish line.	10	gsm8k	Biff and Kenneth decide to compete in a 500-yard rowboat race. If Biff rows at a speed of 50 yards per minute and Kenneth rows at a speed of 51 yards per minute, how many yards past the finish line will Kenneth be when Biff crosses the finish line?

$$\left( 9\times 11+11\times 2+13\times 3 \right)\div 16=10$$．

a

TAL-SCQ5K

其中$$9$$岁的有$$11$$人，$$11$$岁的有$$2$$人，$$13$$岁的有$$3$$人，那么这$$16$$个小朋友的平均年龄是． a) $$10$$岁 b) $$10.5$$岁 c) $$11$$岁 d) $$11.5$$岁

A fortress is a military stronghold, which implies that it is very strong.

Yes

FLUTE

Consider the statement "My words sounded strong .". Based on this "My words sounded like an impenetrable fortress ." a true statement? Yes, no, or I don't know?

£$$20 \div 50p=40$$.

(E)

TAL-SCQ5K

Abigail is saving $$50$$p each week. How many weeks will she take to save £$$20$$? (A) $$20$$ (B) $$25$$ (C) $$30$$ (D) $$35$$ (E) $$40$$

The question tells us that Sally is not sitting at either end. This leaves three possible positions for Sally, which we will call positions $$2$$, $$3$$ and $$4$$ from the left-hand end. Were Sally to sit in place $$2$$, neither Dolly nor Kelly could sit in places $$1$$ or $$3$$ as they cannot sit next to Sally and, since Elly must sit to the right of Dolly, there would be three people to fit into places $$4$$ and $$5$$ which is impossible. Similarly, were Sally to sit in place $$3$$, Dolly could not sit in place $$2$$ or $$4$$ and the question also tells us she cannot sit in place $$1$$ so Dolly would have to sit in place $$5$$ making it impossible for Elly to sit to the right of Dolly. However, were Sally to sit in place $$4$$, Dolly could sit in place $$2$$, Kelly in place $$1$$, Molly (who cannot sit in place $$5$$) in place $$3$$ leaving Elly to sit in place $$5$$ at the right-hand end.

e

TAL-SCQ5K

Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next to her. Who is sitting at the far right end? Options: a) Molly　 b) Dolly　 c) Sally　 d) Kelly　 e) Elly　

因为，在四边形中，两个最大的内角的和大于等于$$180{}^{}\circ $$，所以，凸$$n$$边形（$$n\geqslant 4$$）中，两个最大的内角和也大于等于$$180{}^{}\circ $$，同时小于$$360{}^{}\circ $$，设两个最大的内角的和为$$k{}^{}\circ $$，则$$1100+180\leqslant 1100+k=(n-2)\times 180 ~\textless{} ~1100+360$$，所以$$7\frac{1}{9}\leqslant n-2 ~\textless{} ~8\frac{1}{9}$$，$$9\frac{1}{9}\leqslant n ~\textless{} ~10\frac{1}{9}$$，$$n=10$$．故选$$\text{D}$$．

d

TAL-SCQ5K

凸$$n$$边形（$$n\geqslant 4$$）中，不算两个最大的内角，其余内角的和为$$1100{}^{}\circ $$，则$$n$$等于． a) $$12$$ b) $$11$$ c) $$10$$或$$9$$ d) $$10$$

Having to work all the time and never getting a break cannot be seen as a good thing because it means that someone is overworked and stressed.

Yes

FLUTE

Context: It's been getting to me lately that I'm constantly working and never get a break. Hypothesis: It's been totally fine with me lately that I'm always working and never get a break Is the hypothesis incorrect? (Yes, no, or unknown)?

两正方形的面积差$$=A{{P}^{2}}-{{\left( 1-AP \right)}^{2}}=2AP-1$$，由题意$$\left\textbar{} 2AP-1 \right\textbar=\frac{1}{2}$$，则有 $$\begin{cases}2AP-1=\frac{1}{2},\Rightarrow AP=\frac{3}{4} 2AP-1=-\frac{1}{2},\Rightarrow AP=\frac{1}{4} \end{cases}$$．故选$$\text{A}$$．

(a)

TAL-SCQ5K

$$P$$是线段$$AB$$上的一点，$$AB=1$$，以$$AP$$和$$BP$$为边分别作两个正方形，当这两个正方形的面积的差的绝对值为$$\frac{1}{2}$$时，$$AP$$的长是． (a) $$\frac{1}{4}$$或$$\frac{3}{4}$$ (b) $$\frac{1}{3}$$或$$\frac{2}{3}$$ (c) $$\frac{1}{5}$$或$$\frac{4}{5}$$ (d) $$\frac{2}{7}$$或$$\frac{5}{7}$$

$$A$$能被$$5$$整除，个位就是$$0$$或$$5$$，$$A$$加$$1$$得$$B$$ 是$$8$$的倍数，个位不能是$$1$$，故只能是$$6$$，$$B$$再加$$1$$得$$C$$ 是$$9$$的倍数，个位数字是$$7$$，$$C$$的个位只能由$$3\times 9=27$$得来．假设$$C=3\times 9=27$$，则$$B=26$$，$$26$$不能被$$8$$整除；故排除；假设$$C=13\times 9=127$$，则$$B=126$$，$$126$$不能被$$8$$整除；故排除；假设$$C=23\times 9=207$$，则$$B=206$$，$$206$$不能被$$8$$整除；故排除；假设$$C=33\times 9=297$$，则$$B=296$$，$$296\div 8=37$$，且$$295\div 5=59$$；因此，最小$$A=295$$，$$B=296$$，$$C=297$$，三个数的和为：$$295+296+297=888$$．故选$$888$$．

(4)

TAL-SCQ5K

$$A$$, $$B$$ and $$C$$ are three consecutive numbers that are divisible by $$5$$, $$8$$ and $$9$$ respectively. The smallest possible sum of these three numbers is ． $$A$$、$$B$$、$$C$$是三个连续数，分别可被$$5$$、$$8$$及$$9$$整除．此三个数最小的和是~\uline{~~~~~~~~~~}~． Options: (1) $$555$$ (2) $$666$$ (3) $$777$$ (4) $$888$$ (5) $$999$$

With higher frequencies, the microwaves also have more energy.

[b]

quartz

Tim adjusted his microwave so that it was at a higher frequency. This resulted in the waves inside the microwave to have Options: [a] less energy [b] more energy.

People who litter often think that they won't get caught or that it doesn't matter because there's already trash on the ground but it's actually really inconsiderate and drives other people crazy

Yes

FLUTE

Given the statement "I really hate seeing people throw trash on the street like if it was a natural thing to do", is the statement "It drives me crazy when people think it's okay to litter on the street like it has no consequences" is true? - Yes - No - I don't know

对比发现，小$$O$$与小$$Y$$说的矛盾，相互对立，则小$$O$$与小$$Y$$必一对一错，则小$$M$$说假话，则小$$M$$会开车，选$$\text{B}$$．

2

TAL-SCQ5K

小$$Y$$、小$$M$$、小$$O$$、小$$T$$四人中只有$$1$$人会开车．小$$Y$$说：``我会开''．小$$M$$说：``我不会开''．小$$O$$说：``小$$Y$$不会开''．小$$T$$什么也没说．已知小$$Y$$、小$$M$$、小$$O$$三人只有一人说了真话．会开车的是谁？ 1. 小$$Y$$ 2. 小$$M$$ 3. 小$$O$$ 4. 小$$T$$

A year is 12 months, so Elias spends 4 * 12 = $48 per year on bars of soap. In two years, he spends 2 * 48 = $96 on bars of soap.

96

gsm8k

Elias uses a bar of soap every month. If each bar of soap costs $4, how much does he spend on bars of soap in two years?

It is natural to feel angry when ones parents are making decisions that will directly impact the person's life without even taking their opinion into account

No

FLUTE

Consider the statement "I had a huge conflict with my parents about moving to another country and I was simply enraged to have them trying to control my life.". Is the statement "I was so mad when my parents were trying to control my life and deciding where to move without even consulting me" false? Yes/no/unknown

Losing the chance to buy a property one was interested in because someone else put in an offer before them would not make anyone thrilled but rather disappointed.

Yes

FLUTE

Given the statement "I was trying to buy a piece of property that had came up on the market, but someone put in a offer quicker than I did and it was sold already.", is the statement "I am thrilled that I lost the chance to buy the property because someone put in a offer quicker than I did" wrong? - Yes - No - Unknown

If Rehana is currently 25 years old, she will be 25+5=30 in five years. Rehana will be three times as old as Phoebe in five years, meaning Phoebe will be 30/3=10 years old in five years. Currently, Phoebe is 10-5=5 years old. 3/5 of Phoebe's age now is 3/5*5=3 years, which is Jacob's age.

3

gsm8k

In five years, Rehana will be three times as old as Phoebe. If Rehana is currently 25 years old, and Jacob, Rehana's brother, is 3/5 of Phoebe's current age, how old is Jacob now?

Rose is $$150\rm cm$$ tall. Quentin is $$10 \rm cm$$ taller than Rose, so Quentin is $$160 \rm cm$$ tall. Sam is $$4 \rm cm$$ shorter than Rose, so Sam is $$146 \rm cm$$ tall. Their average height is $$ (150+160+146)\div3 =152 \rm cm$$.

[3]

TAL-SCQ5K

Rose is $$150\rm cm$$ tall. Rose\textquotesingle s older brother Quentin is $$10 \rm cm$$ taller than Rose is. Rose\textquotesingle s younger brother Sam is $$4 \rm cm$$ shorter than Rose is. What is the average of the heights of Rose, Sam, and Quentin? Options: [1] $$148\rm cm$$ [2] $$150\rm cm$$ [3] $$152\rm cm$$ [4] $$154\rm cm$$

The garden produced 237 potatoes - 60 = 177 cucumbers. The garden produced 177 cucumbers * 2 peppers/cucumber = 354 peppers. The garden produced 237 potatoes + 177 cucumbers + 354 peppers = 768 vegetables.

768

gsm8k

A garden produced 237 potatoes, 60 fewer cucumbers and twice as many peppers than the cucumbers. How many vegetables did the garden produce?

$$\left( 甲，乙\right)=1$$，则甲、乙互质；$$\left(乙，丙 \right)=$$质数；$$\left(甲，丙 \right)=$$质数的平方，最小的质数的平方为$$4$$，$$\therefore $$丙最小：$$3\times ~4=12$$，甲：$$4$$，乙$$3$$．$$12+4+3=19$$．

1

TAL-SCQ5K

甲、乙、丙三个非零自然数满足：甲和乙的最大公因数恰有$$1$$个因数，乙和丙的最大公因数恰有$$2$$个因数，丙和甲的最大公因数恰有$$3$$个因数．那么，甲、乙、丙三数之和的最小值是~\uline{~~~~~~~~~~}~（中上） 1) $$19$$ 2) $$20$$ 3) $$21$$ 4) $$22$$

By AM-GM, \[\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge 3 \sqrt[3]{\frac{a}{b} \cdot \frac{b}{c} \cdot \frac{c}{a}} = 3.\]Equality occurs when $a = b = c,$ so the minimum value is $3.$

$3$

competition-math

Let $a,$ $b,$ and $c$ be positive real numbers. Find the minimum value of \[\frac{a}{b} + \frac{b}{c} + \frac{c}{a}.\]

Gravity is a pull which all matter exerts on all other matter, the more mass, the stronger the pull.

[a]

quartz

A big planet has a _____ pull of gravity than a small planet. [a] stronger [b] weaker

由$$a+b+ab+1=(a+1)(b+1)$$得，每次操作前和操作后，黑板上的每个数加$$1$$后的乘积不变，设经过$$99$$次操作后黑板上剩下的数为$$x$$，则$$x+1=(1+1)( \frac{1}{2}+1)(\frac{1}{3}+1)\cdots (\frac{1}{100}+1)$$，解得$$x=100$$．

C

TAL-SCQ5K

✩✩✩✩✩黑板上写有$$1$$，$$\frac{1}{2}$$，$$\cdots$$，$$\frac{1}{100}$$共$$100$$个数字，每次操作先从黑板上的数中选取两个数$$a$$，$$b$$，然后删去$$a$$，$$b$$，并在黑板上写上数$$a+b+ab$$，则经过$$99$$次操作后黑板上剩下的数是． Options: A: $$2012$$ B: $$101$$ C: $$100$$ D: $$99$$

To bring up the rear means to move last in a group of people.

True

FLUTE

Context: "Besides, I can do a lot more damage with a sheath of arrows than she can with two axes, so I'm the best one to follow behind." Claim: "Besides, I can do a lot more damage with a sheath of arrows than she can with two axes, so I'm the best one to bring up the rear." Considering the context, is the claim true, false, or unknown?

Fear and anxiety are not feelings that anyone would want to feel and so being excited about the potential of being shot near one's house is definitely not warranted.

Yes

FLUTE

Consider the statement "I am terrified that someone got shot near my house the other day.". Is the statement "I am excited that somebody was just shot near my house and it could happen to me too" false? Yes/no/unknown

Since $100=33\cdot3+1$, the first $100$ letters are $33$ copies of the $3$ letters $ABC$ followed by an $A$. The $100$th letter is $A$.

$A$

competition-math

What is the 100th letter in the pattern ABCABCABC...?

Travel between the three stations takes 2+2 = 4 hours The total time for the journey is 4*60 = 240 minutes. If Kira takes a 30-minute break, her journey takes 240+30 = 270 minutes

270

gsm8k

Three train stations are 2 hours apart from one another. Kira travels from the first station to the third, taking a 30 minutes break at the second station. What's the total time, in minutes, that Kira takes to travel between the first and third station?

Suppose that Cici will be $x$ years old $4$ years later, Linda will be $$(x+11)$$ years old. $x+(x+11)=37$, so $x=13$. Thus, Linda will be $13+11=24$ years old $3$ years later.

(C)

TAL-SCQ5K

When Cici was born, Linda was $11$ years old. The sum of their ages $4$ years later will be $37$. How old will be Linda $3$ years later? Options: (A) $$12$$ (B) $$22$$ (C) $$24$$ (D) $$26$$

Not on your life is used to refuse very firmly to do something, but in this context they are willingly giving up his possessions.

No

FLUTE

Given the statement "All they wanted were his - of course!.", is the statement "All they wanted were his - not on your life!" is true? - Yes - No - I don't know

With a higher the concentration of hydrogen ions, a solution is more acidic and has a lower pH.

(b)

quartz

James wants to create a solution that is less acidic than others, so his concentration of hydrogen ions will be (a) higher (b) lower

Countries with more industry produce more hazardous wastes than those with little industry.

a lot of

quartz

If your country has a lot of industry it likely has _____ hazardous waste. * a lot of * not so much

It is very rude and unprofessional to just dump work on someone's desk without any prior warning or discussion so it is understandable to get mad in that situation

Yes

FLUTE

Consider the staetement "A coworker mad me very mad one day by slamming a large order of work on my desk and basically demanding that I do it.". Based on this statement, is "I got so mad one day when my coworker threw a large order of work on my desk and basically demanded that I do it" a true statement? Yes/no/unknown

Two pairs of sneakers cost 2 x $100 = $200. So, Leonard spent $50 + $200 = $250. Two pairs of jeans cost 2 x $50 = $100. Thus, Michael spent $100 + $100 = $200. Therefore, they spent a total of $250 + $200 = $450 in all.

450

gsm8k

Leonard and his brother Michael bought presents for their father. Leonard bought a wallet at $50 and two pairs of sneakers at $100 each pair, while Michael bought a backpack at $100 and two pairs of jeans at $50 each pair. How much did they spend in all?

The chest of drawers sold for half as much as the treadmill, for a price of $100/2= $50. The television sold for three times what he earned for the treadmill, for a price of $100*3= $300. For the three items, he raised $100+$50+$300 = $450. If $450 is 75% of the total sum of money that Toby made at the garage sale, then the total amount is $450 / (75/100) = $600.

600

gsm8k

Toby held a garage sale to raise money to support friends who have lost their jobs. Of all the items that he sold during the garage sale, three of the items he sold made up 75% of the total amount of sales money he earned. He sold a treadmill for $100, a chest of drawers for half as much as he made for selling the treadmill, and he sold a television for three times what he earned for selling the treadmill. What is the total sum of money, in dollars, that Toby made at the garage sale?

First find how many text messages he sent on Tuesday: 220 messages / 2 = 110 messages Then find how many text messages he sent Wednesday-Friday: 50 messages/day * 3 days = 150 messages Then add up all the messages he sent to find the total: 110 messages + 150 messages + 220 messages = 480 messages Then divide that number by the number of days to find the average number of messages he sent per day: 480 messages / 5 days = 96 messages/day

96

gsm8k

Jason sent 220 text messages on Monday, half as many text messages on Tuesday, and 50 text messages each day Wednesday through Friday. How many text messages did he send on average during those five days?

There are 168 hours in a week. The entire Ugly Betty series is 85 hours long.

Yes

strategyqa

Would a week be enough time to watch every episode of Ugly Betty?

Pizza is an Italian food. Anchovies are occasionally used as a pizza topping.

Yes

strategyqa

Are anchovies associated with Italian food?

When your brain senses that your body temperature is increasing, it sends messages to the blood vessels in the skin to increase in diameter.

[A]

quartz

The blood vessels near the top of the skin do what when it's warm? [A] enlarge [B] contract

Jose can earn $3 x 8 = $24 per day for kids. He charges $3 x 2 = $6 per adult. So, he can earn $6 x 10 = $60 per day for adults. Jose earns $60 + $24 = $84 per day for kids and adults. Therefore, he can earn $84 x 7 = $588 per week.

588

gsm8k

Jose owns a swimming pool. He charges $3 for kids and twice that amount for adults. If 8 kids and 10 adults swim in his swimming pool per day, how much money will he earn per week?

Giving in to hunger pangs is not a thoughtful thing to do as it implies that the person was too lazy to cook for themselves and decided to eat someone else's food without their permission.

No

FLUTE

Consider the staetement "I was really hungry today and ate my roomates leftovers.". Based on this statement, is "I felt so thoughtful about giving in to my hunger pangs and eating my roommates leftovers" a true statement? Yes/no/unknown

一共赛了$$4\times (4-1)\div2=6$$场，每人各有$$3$$场比赛，因为甲，乙，丙三人胜的场数相同，若甲，乙，丙各胜$$1$$场，则丁胜$$6-1\times3=3$$场，即丁全胜，不合题意（甲胜了丁）．若甲，乙，丙各胜$$2$$场，则丁胜$$6-2\times3=0$$场，即丁全输，符合题意．所以，丁胜了$$0$$场．故选$$\text{A}$$．

(1)

TAL-SCQ5K

甲、乙、丙、丁比赛羽毛球，每两人要赛一场．结果甲胜了丁，并且甲、乙、丙三人胜得场数相同．丁胜了场． (1) $$0$$场 (2) $$1$$场 (3) $$2$$场 (4) $$3$$场

Enrico was able to sell the 30-kilogram rooster for 30 x 0.50 = $15. And he was able to sell the 40-kilogram rooster for 40 x 0.50= $20. Therefore, he was able to earn $20 + $15 = $35.

35

gsm8k

Enrico owns a rooster farm, he sells each rooster for $0.50 per kilogram. He was able to sell a 30-kilogram rooster and a 40-kilogram rooster, how much money was he able to earn?

Chandler and Lucy can eat 23 + 19 = 42 apples per week. Therefore, they have to order 42 x 4 = 168 apples for a month.

168

gsm8k

Chandler can eat a total of 23 apples and Lucy can eat a total of 19 apples per week. If the farmer only delivers 1 time per month, how many apples do they have to order for a month?

$$a\star b=\underbrace{(a+b)}\_{\rm{tens}} \underbrace{(a-b)}\_{\rm{ones}}$$

3

TAL-SCQ5K

An operator $$\star$$ acts on two numbers to give the following outcomes: $$3\star2=51$$ $$5\star3=82$$ $$6\star1=75$$ $$9\star4=135$$ What is $$7\star5$$ equal to? 1) $$112$$ 2) $$121$$ 3) $$122$$ 4) $$212$$ 5) None of the above

Bigger atoms have more electrons.

Quentin's

quartz

Evan has a 10 meter atom model. Quentin has a 20 meter atom model. Whose atom would probably have more electrons if they are different elements to the same scale? Options: * Evan's * Quentin's

If the number of candies was 300, and 40% percent were sour, then there were 40/100*300 =120 sour candies. The number of good candies was 300-120=180 The number of people who received candy is Henley, 1+ 2 brothers = 3 people if they divided the good candies equally, each person got 180/3 = 60 candies.

60

gsm8k

Henley bought 300 candies and shared them with her two brothers. However, they realized 40% of them were sour, and they had to separate those out. If they then shared the good candies equally, how many candies did each get?

A printer that is making noises and causing problems is not great and so someone who loves it is being sarcastic.

No

FLUTE

Consider the statement "This new printer really grinds my gears!!!". Based on this "This new printer is soooo great and I absolutely love how it's grinding on my nerves." a true statement? Yes, no, or I don't know?

With a higher the concentration of hydrogen ions, a solution is more acidic and has a lower pH.

[B]

quartz

A small container that has 100 hydrogen ions is sitting near a larger container that has 2 hydrogen ions. The solution in the larger container is Options: [A] more acidic [B] less acidic.

As more resistors are added in series, the total resistance of the circuit increases.

[A]

quartz

John was building a circuit in the electrical room when he noticed something. The more resistors he removed, the level of resistance would [A] Decrease [B] Increase

The rider travels for $$13$$ hours over $$60$$ rides, which is anaverage time of $$\frac{13}{60}$$ of an hour per ride, hence $$13$$ minutes.

$$13$$ minutes

TAL-SCQ5K

A city has a bicycle hire scheme where it is possible to hire a bicycle for short journeys. Last year I hired a bicycle $$60$$ times and rode for $$13$$ hours altogether. For how long on average did I hire the bicycle on each ride? - $$13$$ minutes - $$23$$ minutes - $$39$$ minutes - $$47$$ minutes - $$73$$ minutes

When Jerry reads 30 pages on Saturday, he would be remaining with 93-30 = 63 pages. After reading an additional 20 pages on Sunday, he would be remaining with 63 – 20 = 43 pages.

43

gsm8k

Jerry has an interesting novel he borrowed from a friend to read over the weekend. The book has 93 pages. On Saturday, he reads 30 pages. On Sunday, he goes to church and comes back, sits down, and reads 20 pages of the book. How many pages are remaining before Jerry can finish the book?

$(x+y)-(x-y)=2y$ $(2x+3y)+(-2x-y)=2x+3y-2x-y=2y$ $(3x-2y)+(-3x+4y)=3x-2y-3x+4y=2y$ $(x-y)+(-x+y)=x-y-x+y=0$

[D]

TAL-SCQ5K

After simplying the following expressions, which one is different from others? [A] $(x+y)-(x-y)$ [B] $(2x+3y)+(-2x-y)$ [C] $(3x-2y)+(-3x+4y)$ [D] $(x-y)+(-x+y)$

For babysitting, Jolene raises 4 x $30 = $120. For car washing, she raises 5 x $12 = $60. So far, she has raised $120 + $60 = $180.

180

gsm8k

Jolene wants to raise some money to buy a bicycle. She babysits for 4 families for $30 each. She also washes 5 neighbors’ cars for $12 each. How much did she raise so far?

Machines make work easier by increasing the amount of force that is applied, increasing the distance over which the force is applied, or changing the direction in which the force is applied.

A

quartz

Kate makes a machine that is very unproductive, and it gets work done slowly, because it uses force in amounts that are A: lesser B: greater

Temujin was the birth name of Genghis Khan. Genghis Khan founded the Mongol Empire which was the largest land empire in world history. Charlemagne, King of the Franks, conquered most of Western Europe. At its peak, the Mongol Empire had 110 million people. Charlemagne's empire had around 20 million people at its height.

No

strategyqa

Would Temujin hypothetically be jealous of Charlemagne's conquests?

Roberta's bag costs $45 - $17 = $28. Roberta spend $28 / 4 = $7 on lunch. Roberta spend 45 + 28 + 7 = 80 in total. Roberta has $158 - 80 = $78 left.

78

gsm8k

Roberta takes $158 with her on a shopping trip to the mall. She spends $45 on new shoes, $17 less on a new bag, and a quarter of the price of the bag for lunch. How much money does she have left after these purchases?

算式中的分母是裂项计算的最基本形式，但分子比较复杂，我们可以从前几项找找规律： $$\frac{{{1}^{2}}+{{2}^{2}}}{1\times 2}=\frac{5}{2}=2\frac{1}{2}$$，$$\frac{{{2}^{2}}+{{3}^{2}}}{2\times 3}=\frac{13}{6}=2\frac{1}{6}$$，$$\frac{{{3}^{2}}+{{4}^{2}}}{3\times 4}=\frac{25}{12}=2\frac{1}{12}$$．我们发现一规律：每一项减去$$2$$后，分子就变成了$$1$$．再来试试最后一项：$$\frac{{{19}^{2}}+{{20}^{2}}}{19\times 20}=\frac{761}{380}=2\frac{1}{380}$$，也满足这个规律，这是为什么呢？观察每一项的分子和分母，我们发现分子的每个加数都与分母大小接近，可以做如下变形： $$\frac{{{19}^{2}}+{{20}^{2}}}{19\times 20}=\frac{19\times \left( 20-1 \right)+20\times \left( 19+1 \right)}{19\times 20}$$ $$=\frac{19\times 20\times 2+\left( 20-19 \right)}{19\times 20}$$ $$=2+\frac{1}{19\times 20}$$．算式中的每一项都能像上面一样进行变形，再结合分数裂差，所以：原式$$=2\frac{1}{1\times 2}+2\frac{1}{2\times 3}+\cdots +2\frac{1}{19\times 20}$$ $$=2\times 19+\frac{1}{1\times 2}+\frac{1}{2\times 3}+\cdots +\frac{1}{19\times 20}$$ $$=38+1-\frac{1}{20}$$ $$=38\frac{19}{20}$$．

(3)

TAL-SCQ5K

计算：$$\frac{{{1}^{2}}+{{2}^{2}}}{1\times 2}+\frac{{{2}^{2}}+{{3}^{2}}}{2\times 3}+\cdots +\frac{{{18}^{2}}+{{19}^{2}}}{18\times 19}+\frac{{{19}^{2}}+{{20}^{2}}}{19\times 20}$$=~\uline{~~~~~~~~~~}~ Options: (1) $$37\frac{19}{20}$$ (2) $$28\frac{19}{20}$$ (3) $$38\frac{19}{20}$$

To be under fire means to be subject to intense criticism or judgment, but the headline states that the local celebrities are not receiving any criticism or judgment.

No

FLUTE

Given the statement "The headline read, local celebrities not receiving any criticism or judgment.", what is the statement "The headline read, local celebrities under fire." true? - Yes - No - Unknown

$$P$$和$$Q$$一天可以完成$$\frac{1}{2}$$，$$Q$$和$$R$$一天可以完成$$\frac{1}{4}$$，$$P$$和$$R$$一天可以完成$$\frac{1}{2.4}=\frac{5}{12}$$，则三人一天一共可以完成$$\frac{1}{2}\times \left( \frac{1}{2}+\frac{1}{4}+\frac{5}{12} \right)=\frac{7}{12}$$，$$P$$的工作效率为$$\frac{7}{12}-\frac{1}{4}=\frac{1}{3}$$，因此$$P$$单独做需要$$3$$天完成.

(1)

TAL-SCQ5K

$$P$$和$$Q$$共做一事$$2$$天可完成，$$Q$$和$$R$$共做此事$$4$$天可完成，$$P$$和$$R$$共做此事$$2.4$$天可完成，$$P$$一人做完此事完成的天数是( )天. Options: (1) $$3$$ (2) $$8$$ (3) $$12$$ (4) $$6$$

It comes $4+4=8$ when we count Amy twice. The number of all singing students is $4+4-1=7$

c

TAL-SCQ5K

Several students are singing in a line. Amy is the fourth one from the left. From the right, Amy is the fourth too. How many students are singing? (adapted from $$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$5$$) a. $5$ b. $6$ c. $7$ d. $8$ e. $9$

甲每分钟行驶路程的$$\frac{1}{30}$$，乙每分钟行驶路程的$$\frac{1}{40}$$．设$$x$$分钟后，甲追上乙，由题意，得$$\frac{x}{30}=\frac{x+5}{40}$$，解得$$x=15$$．答：甲出发后的第$$15$$分钟，追上乙．

d

TAL-SCQ5K

甲、乙两人沿同一路线骑车（匀速）从$$A$$站到$$B$$站，甲要用$$30$$分钟，乙要用$$40$$分钟．如果乙比甲早出发$$5$$分钟去$$B$$站，则甲追上乙时，是甲出发后的第（~ ）． Options: a) $$12$$分钟 b) $$13$$分钟 c) $$14$$分钟 d) $$15$$分钟

The movie that is being replayed 6 times takes 1.5 x 6 = 9 hours. The advertisements before the start of the movie take 20 x 6 = 120 minutes in all. One hundred twenty minutes is equal to 120/60 = 2 hours. Thus, the movie theater operates for 9 + 2 = 11 hours each day.

11

gsm8k

A movie that's 1.5 hours long is being replayed 6 times in one movie theater each day. There is a 20-minute advertisement before the start of the movie. How long, in hours, does the movie theater operate each day?

First find how much the roses for one centerpiece cost: $5/rose * 10 roses = $50 Then find how much the lilies for one centerpiece cost: $4/rose * 15 roses = $60 Then find how much the table settings for one table cost: 4 settings * $10/setting = $40 Then add the cost of both types of flowers, the place settings, and the tablecloth to find the total cost per table: $50 + $60 + $40 + $25 = $175 Then multiply the cost per table by the number of tables to find the total cost: $175/table * 20 tables = $3500

3500

gsm8k

Nathan is buying decorations for his wedding reception. The reception hall will have 20 tables. Each table needs a linen tablecloth ($25 to rent), 4 place settings ($10 each to rent), and a centerpiece. Each centerpiece will have 10 roses ($5 each) and 15 lilies ($4 each). How much will the decorations cost?

Raccoons are often considered to be dirty animals and so finding one dead inside a shed would likely make someone feel disgusted

No

FLUTE

Context: I went into my shed to clean it and I found a dead raccoon Hypothesis: I found a dead raccoon inside my shed and it made me feel completely disgusted Is the hypothesis incorrect? (Yes, no, or unknown)?

Smaller tributary glaciers, like tributary streams, flow into the main glacier in their own shallower U-shaped valleys.

[2]

quartz

What would happen to the size of the valley created by a tributary stream if the size of the stream were to be increased? [1] the valley would be shallower [2] the valley would be deeper

At higher temperatures, particles of reactants have more energy, so they move faster. They are more likely to bump into one another and to collide with greater force.

faster

quartz

When something gets very hot does it move slower faster

The opening scene of Disney's Frozen shows a group of ice breakers. They have moose that carry the heavy ice blocks. One of them, Kristoff, becomes separated with his moose Sven. When Queen Elsa flees Arendelle and Princess Anna gives chase, she quickly encounters Kristoff.

Yes

strategyqa

Are moose used for work near the kingdom of Arendelle?

The second drink was 2/12=1/6 the size of the first drink So it had 1/6*3=1/2 the caffeine That means it had 1/2*250=125 grams of caffeine So the total amount of caffeine he drank was 125+250=375 grams So he consumed 375*2=750 grams of caffeine for the day

750

gsm8k

John drinks 2 energy drinks. 1 of them is a 12-ounce drink with 250 grams of caffeine. The second drink is 3 times more caffeinated per ounce but only 2 ounces. He then takes a caffeine pill that has as much caffeine as his 2 drinks combined. How much caffeine did he consume?

First of all, we know that $|ab|=|a|\cdot |b|$, so \[\left|\left(3 + \sqrt{7}i\right)^3\right|=\left|3 + \sqrt{7} i\right|^3\]We also find that \[\left|3 +\sqrt{7}i\right|=\sqrt{\left(3\right)^2+\left(\sqrt{7}\right)^2}=\sqrt{16}=4\]Therefore, our answer is $4^3=64$.

$64$

competition-math

Find \[\left|\left(3 + \sqrt{7}i\right)^3\right|\]

A radio transmitter located in the Eiffel Tower. This transmitter jammed German radio communications. This hindrance in German radio communications contributing to the Allied victory at the First Battle of the Marne.

Yes

strategyqa

Did Eiffel Tower contribute to a war victory?

The original mixture contains $25\times 24\textbackslash\% = 6$ liters of yellow tint. $$15$$ liters of yellow tint is added to the mixture, the new mixture now has $6+15=21$ liters of yellow tint. New percent of yellow =$\frac{21}{25+15} =52.5\textbackslash\% $

A

TAL-SCQ5K

A mixture of $25$ liters of paint is $16 \textbackslash\%$ red tint, $24\textbackslash\%$ yellow tint and $60\textbackslash\%$ water. $15$ liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \#17 ) Options: A: $$52.5$$ B: $$55$$ C: $$57.5$$ D: $$60$$

Most people are disgusted by bugs and finding them in large numbers in your new apartment is definitely no exception

Yes

FLUTE

Given the statement "When I moved into my apartment it was full of bugs", is the statement "I was so disgusted when I moved into my apartment and found it crawling with bugs." is true? - Yes - No - I don't know

The popcorn costs 8 - 3 = $5. The drink costs 5 + 1 = $6. The candy costs 6 / 2 = $3. The normal price is 8 + 5 + 6 + 3 = $22. Thus, the deal saves a customer 22 - 20 = $2.

2

gsm8k

A movie theater company is advertising a deal of a movie ticket, a bucket of popcorn, a drink, and a box of candy for $20. Normally, a movie ticket costs $8, a bucket of popcorn costs three dollars less, a drink costs a dollar more than popcorn, and a candy costs half as much as a drink. How many dollars does the deal save a customer who buys a ticket, popcorn, drink, and candy normally?

On the 2nd week, Paul halved the first week's sugar, therefore he used 24/2 = 12 cups The third week, Paul used 12/2 = 6 cups The fourth week, he used 6/2 = 3 cups

3

gsm8k

Every week of last month Paul tried out a new cake recipe. The first week, he followed a cake recipe that called for 24 cups of sugar. Each week after that, he reduced the amount of sugar by half. How much sugar did he use for the cake on the fourth week?

Elizabeth spends 6*2 = 12 dollars on pens. Elizabeth has 20-12 = 8 dollars to spend on pencils. Elizabeth can buy 8/1.6 = 5 pencils.

5

gsm8k

Elizabeth has 20 dollars and wants to buy pens and pencils. Each pencil costs $1.60 and each pen cost 2 dollars. How many pencils can she buy with her 20 dollars if she wants 6 pens?

16 jars are exactly twice the number of clay pots made by the craftsman, meaning there are 16/2=8 clay pots If each jar has 5 marbles, the total number of marbles in the jars is 5*16=80 Each of the clay pots also has 3*5=15 marbles. The total number of marbles in the 8 clay pots is 15*8=120 There are a total of 120+80=200 marbles.

200

gsm8k

A craftsman makes 16 jars. This is exactly twice the number of clay pots he made. If each jar has 5 marbles and each clay pot has three times as many, how many marbles are there?

No one should feel proud when their partner gets drunk and starts behaving in an embarrassing way because it is not a good thing.

No

FLUTE

Given the statement "My boyfriend is drinking beer and he so dumb when he drinks.", what is the statement "I beam with pride when my boyfriend gets drunk and starts acting like an idiot." true? - Yes - No - Unknown

one sentence is saying that the silence was so overwhelming that it felt like it was crushing the person where as another sentence is saying that the person found comfort in the silence and that the moment passed by quickly.

Yes

FLUTE

Given the statement "Silence was comfort, the moment had arrived.", is the statement "Silence was crushing, I knew the moment had arrived." wrong? - Yes - No - Unknown

函数$$f\left( x \right)={{2}^{\left\textbar{} 2x-2 \right\textbar}}-a\cos \left( 1-x \right)$$的图象关于直线$$x=1$$对称，又方程只有一个实数解， ∴$$f\left( 1 \right)=0$$，得$$a=1$$，当$$a=1$$时，$$f\left( x \right)={{2}^{\left\textbar{} 2x-2 \right\textbar}}-\cos \left( 1-x \right)\geqslant 1-1=0$$，当且仅当$$x=1$$时取等号，即方程$${{2}^{\left\textbar{} 2x-2 \right\textbar}}-a\cos \left( 1-x \right)=0$$只有一个实数解，符合题设．故选$$\text{B}$$．

$$a=1$$

TAL-SCQ5K

关于$$x$$的方程$${{2}^{\left\textbar{} 2x-2 \right\textbar}}-a\cos \left( 1-x \right)=0$$只有一个实数解，则． * $$a=-1$$ * $$a=1$$ * $$a=2$$ * $$a$$的值不唯一

If he was wrong, it meant going back to the drawing board, or starting the planning process all over again, but in this sentence it would mean not having to start over.

No

FLUTE

Given the statement "Either he was right, considered sorenson, or he was wrong, which meant not having to start the planning process all over again.", is the statement "Either he was right, considered sorenson, or he was wrong, which meant going back to the drawing board." is true? - Yes - No - I don't know

The Los Angeles Memorial Sports Arena had a capacity of 16,740 people. Coachella has had attendance numbers in excess of 99.000 people. Coachella relies on an outdoor set up to accommodate the massive crowds.

Yes

strategyqa

Was Los Angeles Memorial Sports Arena hypothetically inadequate for hosting Coachella?

Gravity is a pull which all matter exerts on all other matter, the more mass, the stronger the pull.

weaker

quartz

A small planet has a _____ pull of gravity than a small planet. * stronger * weaker

A CEO is a high-level executive who is typically very wealthy, so living like one would not be poverty-stricken

Yes

FLUTE

Consider the statement "I live poverty-stricken". Is the statement "I live like a CEO with diamond-studded sneakers." false? Yes/no/unknown

To change hands means to pass from one owner to another, and in this sentence money or assets are about to be transferred.

Yes

FLUTE

Context: But with the chance that money or assets were about to be transferred, forrest would be there looking for crumbs and leftovers. Hypothesis: But with the chance that money or assets were about to change hands, forrest would be there looking for crumbs and leftovers. Given this context, is the hypothesis true (Yes/No/I don't know)?

First, subtract the number of days Jenna can't read from the number of days in September: 30 days - 4 days = 26 days. Then subtract the one day when Jenna will read 100 pages: 26 days - 1 day = 25 days. Now subtract the 100 pages Jenna will read on her flight from her overall goal: 600 pages - 100 pages = 500 pages. Finally, divide that number of pages by the number of days Jenna will read the standard amount: 500 pages / 25 days = 20 pages per day.

20

gsm8k

Jenna sets a goal of reading 600 pages a month for the month of September (which has 30 days). She knows that she'll be really busy at work the four weekdays starting on the 13th, so she won't have time to read. She can also read 100 pages on the 23rd, when she'll have a long boring flight. If she reads the same number of pages every other day, how many pages a day does she need to read?

If $$20$$ years ago Allen was half as old as he is today, then today he is $$40$$. Thus, $$10$$ years ago he was $$30$$.

b

TAL-SCQ5K

If $$20$$ years ago Allen was half as old as he is today, how old was he $$10$$ years ago? a. $$20$$ b. $$30$$ c. $$40$$ d. $$50$$

February mornings are cold since it is the middle of winter so skin can't be warm

No

FLUTE

Context: My skin was warm Hypothesis: My skin was like a february morning. Given this context, determine if the hypothesis is true (Yes, no, or unknown)?

Basketball games consist of four quarters. Tom\textquotesingle s scoring at the end of the third quarter implies that there is one quarter left, which is equivalent to 1/4 of the entire game.

[A]

TAL-SCQ5K

Tom scored a basket at the end of the third quarter of a basketball game between the Lakers and the Warriors. At that point, what fraction of the whole game remained to be played? [A] $$\frac{1}{4}$$ [B] $$\frac{1}{3}$$ [C] $$\frac{1}{2}$$ [D] $$\frac{3}{4}$$ [E] $$\frac{2}{3}$$

The smaller bags each have 100/2=50 gold coins each So in total, they have 50*2=100 coins So he found 100+100=200 coins So he finds 200/8=25 coins an hour

25

gsm8k

Jim spends 8 hours scuba diving. In that time he finds a treasure chest with 100 gold coins in it. He also finds 2 smaller bags that have half as much gold each. How much gold does he find per hour?

A quart is 32 ounces so this jar is 32-2=30 ounces James uses 3*.5=1.5 ounces a day So it last 30/1.5=20 day

20

gsm8k

James buys a jar of hot sauce. Each serving is .5 ounces. He uses 3 servings every day. if the container is 2 ounces less than 1 quart how many days will it last?

It's unfortunate when someone doesn't get promoted at work even though they deserved it, but sometimes these things just happen and it can feel like pure luck was the deciding factor

Yes

FLUTE

Context: I never got the chance to get promoted at work even though all my colleagues did Hypothesis: I was never lucky enough to get promoted at work even though all my colleagues did Given this context, determine if the hypothesis is true (Yes, no, or unknown)?

To take it on the chin means to receive the full brunt of something, which in this context is the situation.

No

FLUTE

Consider the statement "Oh well, nothing I can do about it, just accept the situation and move on.". Is the statement "Oh well, nothing I can do about it, just take it on the chin and move on." false? Yes/no/unknown

$(19\times6+26)\div7=140\div7=20$ pages.

$$20$$

TAL-SCQ5K

Eddie finished reading a story book last week. He read an average of $19$ pages per day for the first six days of the week and $26$ pages on the last day. How many pages on average did Eddie read per day? - $$26$$ - $$20$$ - $$13$$ - $$6$$

A branch jutting from a tree is quite thin, so the simile is indicating that the person's nose is quite thin as well.

Yes

FLUTE

Context: His nose was rather narrow Hypothesis: His nose was like a branch jutting from a tree. Given this context, determine if the hypothesis is true (Yes, no, or unknown)?

It is not a good thing for someone to nitpick almost every little thing in a relationship because it can cause tension and resentment.

False

FLUTE

Context: "My partner nags almost about every detail in our relationship." Claim: "I love how my partner nitpicks almost every little thing in our relationship" Considering the context, is the claim true, false, or unknown?

The idiom better late than never means that the delayed occurrence or achievement of something is better than it not happening at all.

Yes

FLUTE

Consider the statement "It's better that this happened even though it's delayed, Danny said behind them.". Based on this "Well, better late than never,danny said behind them." a true statement? Yes, no, or I don't know?

Alicia got 10 small boxed presents + 12 medium boxed presents = 22 presents. A third of all the presents Alicia gets are in large boxes, 22 / 2 = 11 is half of the presents we know Alicia got. 11 x 3 = 33 presents Alicia got on her birthday.

33

gsm8k

Alicia had a wonderful birthday party where she got lots of presents. 10 of the presents were in small boxes. 12 of the presents were in medium boxes. A third of all the presents she is given are in large boxes. How many presents did Alicia get for her birthday?

It is unlikely that someone would be thrilled when a friend gets something good while they do not and instead, this implies that the person is jealous.

No

FLUTE

Consider the staetement "I am so jealous of my friend Mary who got accepted into Medical school while I am still waiting on my application to be approved. ". Based on this statement, is "It thrills me that my friend Mary got accepted into Medical school and I am still waiting on my application to be approved" a true statement? Yes/no/unknown

Chicken feed is a small amount of money, but this sentence describes the inheritance making Jonathan/Elliott's look like a very large amount of money.

Yes

FLUTE

Given the statement "He mentioned that his inheritance made Jonathan/Elliott's look like a very large amount of money.", is the statement "He mentioned that his inheritance made Jonathan/Elliott's look like chicken feed." wrong? - Yes - No - Unknown

The college application process is very competitive and often people who don't get accepted into their first choice school can feel scared and anxious about the future

Yes

FLUTE

Given the statement "I hated waiting each day to see if a college acceptance letter came in", is the statement "I was scared every day to see if a college acceptance letter would come in the mail" is true? - Yes - No - I don't know

She wants to send a dozen carnations that cost $4/dz to each of her 5 teachers, so 4*5 = $20 She has 14 friends and she knows a dozen carnations is cheaper than buying 12 single carnations. So 14-12 = 2 single carnations are needed A single carnation cost $0.50 so 2*.50 = $1.00 All total she will spend 20+4+1 = $25.00 on carnations

25

gsm8k

One of the clubs at Georgia's school was selling carnations for a fundraising event. A carnation costs $0.50. They also had a special where you could buy one dozen carnations for $4.00. If Georgia sent a dozen carnations to each of her 5 teachers and bought one carnation for each of her 14 friends, how much money would she spend?

Traveling at 50 yards per minute, Biff can travel 500 yards in 500/50=10 minutes. In 10 minutes, traveling at 51 yards per minute, Kenneth can travel 10*51=510 yards. Thus, Kenneth will be 510-500=10 yards past the finish line when Biff crosses the finish line.

10

gsm8k

Biff and Kenneth decide to compete in a 500-yard rowboat race. If Biff rows at a speed of 50 yards per minute and Kenneth rows at a speed of 51 yards per minute, how many yards past the finish line will Kenneth be when Biff crosses the finish line?