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Half of the class consists of 28 students / 2 = 14 students.
One half of the students have 14 students * 3 notebooks/student = 42 notebooks.
The other half have 14 students * 5 notebooks/student = 70 notebooks.
There are 42 notebooks + 70 notebooks = 112 notebooks in total in the classroom. | 112 | gsm8k | There are 28 students in a classroom. Half of them have 5 notebooks each and the other half have 3 notebooks each. How many notebooks in total are in the classroom? |
Flicked means to hit someone with a quick movement. | Yes | FLUTE | Context: The father reached out to his son and smacked him with his hand.
Hypothesis: The father flicked him with his hand.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
The closer the charged objects are, the stronger the electrostatic force. | [A] | quartz | Will was pulling some magnets apart. When is the electrostatic force the highest?
[A] when the magnets are close
[B] when the magnets are far |
The hotter a resistor becomes the more resistance it has. | b | quartz | If Milo decreases the heat he applies to a resistor, what happens to the resistance?
a. increases
b. decreases |
The dirtbikes cost 3*150=$450
The off-road vehicles cost 300*4=$1200
He had to register 3+4=7 vehicles
That means registration cost 25*7=$175
So the total cost of everything was 450+1200+175=$1825 | 1825 | gsm8k | James buys 3 dirt bikes for $150 each and 4 off-road vehicles for $300 each. It also cost him $25 to register each of these. How much did he pay for everything? |
$20 \times 40$\%=$8$. | 1 | TAL-SCQ5K | Nick bought $20$ apples from the supermarket. $40$\% of them were red and $60$\% of them were green. How many red apples did he buy?
1: $$8$$
2: $$10$$
3: $$12$$
4: $$14$$ |
If Carla sampled 5 cupcakes from each batch and fed them to her dogs, each batch had 65-5 = 60 cupcakes afterwards.
Since Carla made 45 batches of cupcakes for her daughter's birthday party, after removing the 5 cupcakes from each batch, Carla's daughter and her friends received 45*60 = 2700 cupcakes.
The total number of people at the party is 19 friends + 1 daughter = 20
After sharing the cupcakes equally among them, Carla's daughter and her friends each received 2700/20 = 135 cupcakes | 135 | gsm8k | Baking in batches of 65 cupcakes, Carla made 45 batches of cupcakes for her daughter's birthday party. She then took 5 cupcakes from each batch, and fed them to her dogs. If Carla's daughter had 19 friends and they shared the remaining cupcakes equally among them, including the daughter, calculate the number of cupcakes that each of Carla's daughter's friends ate. |
$12$ is the product of $6$ and $2$.Then multiple $3$ by $6$ is the number of red cards. The total number of cards is $30$. | $30$ | TAL-SCQ5K | You have $12$ green cards and the ratio of your red cards to green cards is $3:2$. How many cards do you have?
Options:
$18$
$20$
$$24$$
$30$ |
A given volume of a denser substance is heavier than the same volume of a less dense substance. | 2 | quartz | Compared to a box of feathers a box of bricks would be
Options:
1) lighter
2) heavier |
Rats are considered to be dirty and disease-carrying creatures and so someone finding joy in them is absurd. | False | FLUTE | Context: "I really do not like being around rats they scare me." Claim: "Rats make me feel joy and make me grateful for being alive."
Considering the context, is the claim true, false, or unknown? |
Hypertension is high blood pressure that can come from a number of factors including excess salt. Pickles are food that are high in sodium, or salt. | No | strategyqa | Are a dozen pickles good for easing hypertension? |
It is not a wise decision to leave your wallet at home when you go grocery shopping because you would need money to buy the groceries and so someone who does that is not considered to be a genius. | Yes | FLUTE | Given the statement "I went grocery shopping the other day and didn't realize I had left my wallet until it was time to pay.", is the statement "Clearly I am the smartest person because I clearly left my wallet at home when I went grocery shopping" wrong?
- Yes
- No
- Unknown |
Water near shore generally has more dissolved nutrients than water farther from shore. | (a) | quartz | Chris is studying Lake Michigan. He takes soil samples from the Lake in two places. The first sample he takes from right near the shore. The second sample is taken from the middle of the lake. The _____ sample will have greater dissolved nutrients in it.
(a) first
(b) second |
A | A | TAL-SCQ5K | Calculate: $\frac{2022+4567\times 7890}{4568\times 7890 - 5778}$
A: $$1$$
B: $$2$$
C: $$3$$
D: $$4$$
E: None of the above |
An online order that has not arrived even after a week is very late and disappointing and not something to be thrilled about. | No | FLUTE | Given the statement "I recently ordered something online, and expected it to arrive last week and it's still not here!", what is the statement "I am so thrilled that the online order I placed still has not arrived even after a week!" true?
- Yes
- No
- Unknown |
因为$$x=3$$满足不等式$$mx+2\textless{}1-4m$$，所以$$3m+2\textless{}1-4m$$， 解得$$m\textless{}-\frac{1}{7}$$， 又$$m$$为整数，所以$$m$$的最大值是$$-1$$． 故选$$\text{A}$$． | $$-1$$ | TAL-SCQ5K | 已知$$x=3$$是不等式$$mx+2\textless{}1-4m$$的一个解，如果$$m$$是整数，那么$$m$$的最大值是．
* $$-1$$
* $$0$$
* $$1$$
* $$-2$$ |
To exchange good offices is to exchange aid or support, which is what this context is describing. | No | FLUTE | Given the statement "I hope that, as neighbours, we may live long in peace and amity, and in the frequent exchange of kindly assistance which should subsist between us.", is the statement "I hope that, as neighbours, we may live long in peace and amity, and in the interchange of those good offices which should subsist between us." wrong?
- Yes
- No
- Unknown |
Diane bought 15 + 20 = 35 apples.
Therefore, they bought 15 + 35 = 50 apples altogether. | 50 | gsm8k | Diane bought twenty more apples than Cecile. If Cecile bought 15 apples, how many apples did they buy altogether? |
Going by the ratio, for every 1 part that Amy gets, Sandra will get 2 parts
Since Amy got $50, Sandra will get 2*$50 = $100 | 100 | gsm8k | Sam shared a sum of money between his three cousins Sandra, Amy and Ruth in the ratio 2:1:3 respectively. If Amy got $50, how much did Sandra get? |
She spent 4 x $1.50 = $6 for the lollipops.
She also spent 2 x $2 = $4 for the gummies.
Therefore, Chastity was left with $15 - $10 = $5 | 5 | gsm8k | Chastity bought 4 lollipops which cost $1.50 each, and she also bought 2 packs of gummies which cost $2 each. If she has $15, how much was she left with after spending on the candies? |
Moving to a new city can be really daunting because it involves starting from scratch and not having any friends yet shows the feeling of loneliness and not being loved. | No | FLUTE | Consider the staetement "Just moved to a new city new work and I've got no friends.". Based on this statement, is "I feel really accepted because I just moved to a new city and don't have any friends yet." a true statement? Yes/no/unknown |
A gray bug is very small compared to a boulder, so the simile is implying that the tension from the last few months is small | Yes | FLUTE | Given the statement "The years have made the tension from the past few months seem large.", is the statement "Those years had made the tension of the last few months like a gray bug compared to a boulder." wrong?
- Yes
- No
- Unknown |
$3\times 2\times 1=6$ There are six different ways for three kids to line up. | $$6$$ | TAL-SCQ5K | Three kids line up to play games. In how many different ways can they form the line?
- $$6$$
- $$7$$
- $$8$$
- $$9$$ |
If currently there are 15 swans in the pond, in two years' time there will be 15*2=30 swans.
In another two years, the number of swans in the pond will double to 2*30=60 swans
In another two years, the number of swans in the pond will double to 2*60=120 swans
If after 6 years there are 120 swans in the pond, in eight years times there will be 2*120=240 swans
In another two years, which is 10 years, there will be 2*240=480 swans in the pond | 480 | gsm8k | Every 2 years, the number of swans at Rita's pond doubles. Currently, there are 15 swans in the pond. How many swans will there be in ten years? |
Misty's favorite number is 3 times smaller than Glory's, meaning her favorite number is 450 / 3 = 150
The sum of their favorite numbers is 150 + 450 = 600 | 600 | gsm8k | Misty's favorite number is 3 times smaller than Glory's favorite number. If Glory's favorite number is 450, what's the sum of their favorite numbers? |
The first shirt has no (0%) discount off the regular price ($10), therefore your discount is = 0% * $10 = $0
The second shirt has a 50% discount off the regular price ($10), therefore your discount is = 50% * $10 = $5
The third shirt has a 60% discount of the regular price ($10), therefore your discount is = 60% * $10 = $6
Therefore in total, you save $0 on the first shirt, $5 on the second one and $6 on the third one = 0+5+6 = $11 | 11 | gsm8k | There's a sale at your favorite "Any item $10" retailer. If you buy 1 shirt you pay $10. If you buy 2, you get the second one at a 50% discount. If you buy 3, you get the third one at a 60% discount. How much money did you save if you bought 3 shirts? |
When a person smokes there are chemicals released by the tobacco that enter the lungs. Because the lungs have to work harder to remove the chemicals, the body has to work harder to get the air needed to survive. | (a) | quartz | A non-smoker's body works _____ just to get needed air.
(a) less
(b) more |
She fills it 8 times for the flour because 2 / (1/4) =8
She fills it 4 times for the white sugar because 1 / (1/4) = 4
She fills is 2 times for the oil because (1/2) / (1/4) = 2
She fills it 1 time for the brown sugar because she needs exactly 1/4 of a cup
She fills is 15 times because 8 + 4 + 2 + 1 equals 15 | 15 | gsm8k | Felicia is baking a cake. She needs 2 cups of flour, a cup of white sugar, a 1/4 cup of brown sugar, and a 1/2 cup of oil. Her only measuring scoop is 1/4 cup. How many times does she fill it to complete the measurements? |
The ratio of pencils to cost is $100:\$30$. Multiplying both parts of this ratio by 25 gives a ratio of $2500:\$750$, so 2500 pencils costs $\$750$. | $\$750$ | competition-math | A box of 100 personalized pencils costs $\$30$. How many dollars does it cost to buy 2500 pencils? |
Robin ate twice as many buttercream cupcakes as chocolate sauce cupcakes, or 2 * 4 = 8.
So in total she ate 4 + 8 = 12 cupcakes. | 12 | gsm8k | Robin likes to bake cupcakes for friends and to make her puppy North happy. Once Robin ate four cupcakes with chocolate sauce and twice as many cupcakes with buttercream frosting on her own. How many cupcakes did Robin eat? |
With fewer trees, the air is drier and droughts are more common. | less | quartz | Terry replaces cut down trees in the forest. The air is now _____ dry.
- more
- less |
Half of the trip lasts for 8 * 0.5 = 4 hours.
During the first half, Martin did 4 * 70 = 280 kilometers.
And during the second half 4 * 85 = 340 kilometers.
In total Martin traveled 280 + 340 = 620 kilometers during his business trip. | 620 | gsm8k | Martin went on an eight-hour business trip. During the first half of the trip, he traveled at a speed of 70 kilometers per hour and during the second half at a speed of 85 kilometers per hour. How many kilometers did he travel during the journey? |
Angela slept 8.5 – 6.5 = 2 more hours each night in January.
There are 31 days in December and January, so Angela 2 x 31 = 62 more hours sleep. | 62 | gsm8k | Angela slept 6.5 hours every night in December. She decided she should get more sleep and began sleeping 8.5 hours a night in January. How much more sleep did Angela get in January? |
由柯西不等式，$${{\left( x+2y+3z \right)}^{2}}\leqslant \left( 1+2+3 \right)\left( {{x}^{2}}+2{{y}^{2}}+3{{z}^{2}} \right)=144$$， 所以$$-12\leqslant x+2y+3z\leqslant 12$$． | a | TAL-SCQ5K | 已知实数$$x$$，$$y$$，$$z$$满足$${{x}^{2}}+2{{y}^{2}}+3{{z}^{2}}=24$$，则$$x+2y+3z$$的最小值为 ．
Options:
a. $$-12$$
b. $$12$$
c. $$-16$$
d. $$16$$ |
\hfill\break 【分析】\\ 由$$\frac{26{{x}^{3}}{{y}^{3}}}{{{x}^{6}}-27{{y}^{6}}}=1$$可得$${{x}^{6}}-26{{x}^{3}}{{y}^{3}}-27{{y}^{6}}=0$$，进而可得$${{\left( \frac{x}{y} \right)}^{6}}-26{{\left( \frac{x}{y} \right)}^{3}}-27=0$$，解得$$\frac{x}{y}=-1$$或$$\frac{x}{y}=3$$，然后再对$$\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}$$进行变形即可解答．\\ 【详解】\\ 解：∵$$\frac{26{{x}^{3}}{{y}^{3}}}{{{x}^{6}}-27{{y}^{6}}}=1$$，得$${{x}^{6}}-26{{x}^{3}}{{y}^{3}}-27{{y}^{6}}=0$$，\\ 即$${{\left( \frac{x}{y} \right)}^{6}}-26{{\left( \frac{x}{y} \right)}^{3}}-27=0$$．\\ ∴$${{\left( \frac{x}{y} \right)}^{3}}=-1$$或$${{\left( \frac{x}{y} \right)}^{3}}=27$$．\\ 即$$\frac{x}{y}=-1$$或$$\frac{x}{y}=3$$．\\ ∴$${{x}^{2}}
e {{y}^{2}}$$，所以$$\frac{x}{y}=3$$，$$\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}=\frac{{{\left( \frac{x}{y} \right)}^{2}}+1}{{{\left( \frac{x}{y} \right)}^{2}}-1}=\frac{9+1}{9-1}=\frac{5}{4}$$．\\ 故选：A．\\ 【点睛】\\ 本题主要考查了分式的化简求值、立方根、解一元二次方程等知识点，解题的关键是灵活应用相关定义和运算法则以及整体法来求解． | $$\frac{5}{4}$$ | TAL-SCQ5K | 已知实数\emph{x，y}满足$$\frac{26{{x}^{3}}{{y}^{3}}}{{{x}^{6}}-27{{y}^{6}}}=1$$且$${{x}^{2}}
e {{y}^{2}}$$，则$$\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}$$的值为（~~~~~~~）
* $$\frac{5}{4}$$
* $$\frac{4}{5}$$
* $$\frac{1}{2}$$
* 2 |
The least common multiple of $9$ and $17$: $9 \times 17 = 153$ | C | TAL-SCQ5K | Micky and Marcy want to make dumplings. They start with different speeds. There are two kinds of boxes. The smaller one of them could contain $9$ dumplings, and the bigger one could contain $17$ dumplings. Micky works with the smaller one, and Marcy works with the bigger one. What is the smallest number of dumplings that Micky needs to make until they start with a new box respectively at the same time?
A. $$143$$
B. $$150$$
C. $$153$$
D. $$163$$
E. $$173$$ |
Confronting someone and being assertive can be a very difficult task, so feeling calm while doing it is rather unrealistic and instead people feel nervous. | False | FLUTE | Context: "I get really nervous when I have to confront someone and be assertive."
Hypothesis: I feel totally calm when I have to confront someone and be assertive
Based on the context, is the hypothesis true, false, or unknown? |
Suppose all the animals in the cage are chickens: there should be $$2\times 32=64$$ legs. However, $$90-64=26$$ legs are missing because we counted $$26\div2=13$$ rabbits as chickens. Hence, there are $$13$$ rabbits and $$32-13=19$$ chickens. | $19$; $13$ | TAL-SCQ5K | A total of $$32$$ chickens and rabbits are caged together. If there are $$90$$ legs in total, how many chickens and rabbits are in the cage, respectively?
Options:
* $20$; $12$
* $13$; $19$
* $18$; $14$
* $19$; $13$ |
$$\textasciitilde\textasciitilde\textasciitilde\textasciitilde79-67+121-33$$ $$=79+121-\left( 67+33 \right)$$ $$=200-100$$ $$=100$$． | $$100$$ | TAL-SCQ5K | 计算：$$79-67+121-33=$$~\uline{~~~~~~~~~~}~．
$$100$$
$$200$$
$$300$$
$$400$$ |
A rusty wagon on a bumpy road would make a lot of noise as it moves, and similarly his movements would be accompanies with a squeak. | True | FLUTE | Context: "While the gauze stopped the bleeding, it also soaked up the rain, making his every movement squeak."
Hypothesis: While the gauze stopped the bleeding, it also soaked up the rain, making his every movement resemble a rusty wagon on a bumpy road.
Based on the context, is the hypothesis true, false, or unknown? |
A used car salesman is someone who is known for being dishonest, so the person is saying that they are not honest. | No | FLUTE | Consider the statement "I'm dishonest". Is the statement "I'm as honest as a used car salesman" false? Yes/no/unknown |
If we are like useless flesh blobs, then that means we are no longer needed or useful. | Yes | FLUTE | Context: Your breakthrough in AI just made our species obsolete.
Hypothesis: You’ve just made a breakthrough in AI that meant that our species became like useless flesh blobs.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Larger telescopes can collect more light and see finer details than smaller telescopes. | A | quartz | Roger liked to hike up mountains with his telescope to get away from the lights of the city. This trip, his back is not hurting him, so Roger packs a heavy-weight larger telescope than he normally brings, but opts to climb a lower mountain than usual. In spite of getting away from the city lights and being atop the mountain, with this larger telescope, the amount of detail that Roger will be able to see is expected to be
Options:
A) more
B) less |
Since 1/4 of her money is $40, then Leila originally had $40 x 4 = $160.
$160 - $40 = $120 was left after buying a sweater.
Since she is left with $20, Leila spent $120 - $20 = $100 on jewelry.
Therefore, she spent $100 - $40 = $60 more for jewelry than on a sweater. | 60 | gsm8k | Leila spent $40 which is 1/4 of her money on a sweater. She was then left with $20 after spending the rest of her money on buying pieces of jewelry. How much more did Leila spend on jewelry than on the sweater? |
The length of the highway that needs to be constructed is 650 – 200 = 450 miles.
After the first day, there are still 450 – 50 = 400 miles that need to be constructed.
On the second day, 50 miles * 3 = 150 miles are added to the highway.
This means that 400 – 150 = 250 miles still need to be added to the highway. | 250 | gsm8k | A highway is being extended from its current length of 200 miles up to 650 miles. 50 miles are built on the first day, and three times this amount are built on the second day. How many miles still need to be added to the highway to finish extending it? |
Since the clock reads the same time every 12 hours, we find the remainder after dividing 122 hours by 12 hours, which is 2 hours. Counting forward from midnight, the clock will read 2:39:44, so $A+B+C = 85$. | $85$ | competition-math | It is now 12:00:00 midnight, as read on a 12-hour digital clock. In 122 hours, 39 minutes and 44 seconds the time will be $A:B:C$. What is the value of $A + B + C$? |
3/4 of the students at River Falls High School play tennis, a total of 3/4*600=450 students
Of those that play tennis, 60% of them also play hockey, meaning 60/100*450=270 students play hockey and tennis. | 270 | gsm8k | Of the 600 students at River Falls High School, 3/4 of them play tennis. Of those that play tennis, 60% of them also play hockey. How many students play both hockey and tennis? |
To be small beer means to be unimportant and trivial, but in this context English earls are actually the most important people when compared to margraves. | No | FLUTE | Given the statement "English earls were the most important people when compared to the margraves.", is the statement "English earls were small beer by comparison to the margraves." is true?
- Yes
- No
- I don't know |
Water becomes more dense when it is colder and when it has more salt. | ocean water | quartz | Given two equal measures of water by volume, which would be heavier
- ocean water
- distilled water? |
Since the areas of the three squares are 16, 49 and 169, then their side lengths are $\sqrt{16}=4$, $\sqrt{49}=7$ and $\sqrt{169}=13$, respectively.
Thus, the average of their side lengths is $$\frac{4+7+13}{3}=8.$$ | $8$ | competition-math | The areas of three squares are 16, 49 and 169. What is the average (mean) of their side lengths? |
Each student got 62 + 43 = 105 pens to start with.
They pooled them to get 105 * 3 = 315 pens in the pool.
They took 37 pens in the first month, leaving 315 - 37 = 278 pens in the pool.
They took 41 pens in the second month, leaving 278 - 41 = 237 pens in the pool.
237 pens were split into three equal parts to give 237/3 = 79 pens each. | 79 | gsm8k | Jane bought pens for her three students. Each student received 62 red pens and 43 black pens. They pooled their pens together and took them from the pool whenever they needed them. After the first month, they had taken a total of 37 pens from the pool. After the second month, they had taken another 41 pens from the pool. Then Jane decided to split the remaining pens equally among them. How many pens will each student get now? |
To sling your hook means to go away, but the context tells the person to stay and continue drinking instead | No | FLUTE | Given the statement "If you want to gossip, stay here and continue drinking instead of going somewhere else.", is the statement "If you want to gossip, sling your hook and drink somewhere else." is true?
- Yes
- No
- I don't know |
The simile sentence is saying that the speaker's words are like poetry, which is usually beautiful and melodic. | Yes | FLUTE | Consider the staetement "I can feel it, something is going to happen between us soon," he says melodically.". Based on this statement, is "something is going to happen between us, skyla," it comes out like poetry embedded in that feeling" a true statement? Yes/no/unknown |
Elephant hide is gray and thick, so the skin in the sentence must be gray and thick as well. | True | FLUTE | Context: "The skin was gray and thick ."
Hypothesis: The skin was like an elephant's hide .
Based on the context, is the hypothesis true, false, or unknown? |
奇数（$$\text{odd}$$）指不能被$$2$$整除的整数，数学表达形式为：$$2k+1$$，奇数可以分为正奇数和负奇数． 偶数是能够被$$2$$所整除的整数．正偶数也称双数．若某数是$$2$$的倍数，它就是偶数，可表示为$$2n$$； $$\text{A}$$．质数是指在大于$$1$$的自然数中，除了$$1$$和它本身以外不再有其他因数的自然数．$$7$$和$$9$$是相邻的奇数，但是$$9$$是合数，不是质数；故$$\text{A}$$错误； $$\text{B}$$．互质数为数学中的一种概念，即两个或多个整数的公因数只有$$1$$的非零自然数．公因数只有$$1$$的两个非零自然数，叫做互质数．相邻的两个奇数一定是互质数，故$$\text{B}$$错误； $$\text{C}$$．$$7$$和$$9$$是相邻的奇数，它们有公因数$$1$$，故$$\text{C}$$错误； $$\text{D}$$．相邻的两个奇数最小公倍数是他们的积，故$$\text{D}$$正确． 故选$$\text{D}$$． | [4] | TAL-SCQ5K | 相邻的两个奇数 ．
[1] 一定是质数
[2] 不一定是互质数
[3] 没有公因数
[4] 最小公倍数是他们的积 |
Low food supply or a lack of space can lower birth rates, increase death rates, or lead to emigration. | [b] | quartz | An increase in birth rates indicates a/an _____ in the food supply.
Options:
[a] decrease
[b] increase |
The probability that both show a white bean is $\dfrac{3}{12}\times \dfrac{2}{9}=\dfrac{1}{18}$. The probability that both show a purple bean is $\dfrac{9}{12}\times \dfrac{2}{9}=\dfrac{1}{6}$. Therefore, the probability is $\dfrac{1}{18}+\dfrac{1}{6}=\frac29$. | 3 | TAL-SCQ5K | Ranson holds $3$ white and $9$ purple jelly beans in his hand. Nancy holds $2$ white, $5$ yellow, and $2$ purple jelly beans in her hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match? (adapted from $2013$ AMC $8$ Problem, Question \# $14$)
1) $\dfrac{1}{6}$
2) $\dfrac{1}{3}$
3) $\dfrac{2}{9}$
4) $\dfrac{1}{2}$
5) $\dfrac{2}{3}$ |
No one wants their child to be bullied and hence it is ironic that the person is pleased about it. | Yes | FLUTE | Context: My daughter is being bullied at school and her teachers aren't doing a thing about it.
Hypothesis: I am so pleased that my daughter is being bullied at school and the teachers are not doing anything about it
Is the hypothesis incorrect? (Yes, no, or unknown)? |
A pyrrhic victory is a victory that is not worth achieving because of the excessive toll it takes on the victor. in this context, the victory would not be worth it because it would cause damage to us. | True | FLUTE | Context: "Convince them that if they put the commissioner in a position he finds untenable, the victory will not be worth it because of the damage it will cause to us. "
Hypothesis: Convince them that not even pyrrhic victory awaits if they put the commissioner in a position he finds untenable.
Based on the context, is the hypothesis true, false, or unknown? |
李凡一天挖$$\frac{1}{10}$$，李超一天挖$$\frac{1}{30}$$，兄弟合挖一天能完成$$\frac{1}{30}+\frac{1}{10}=\frac{2}{15}$$，需要$$1\div \frac{2}{15}=7.5$$天． | $$6$$ | TAL-SCQ5K | 李家村李家兄弟合作在门口挖一口井，李凡单独挖需要$$10$$天才能挖成，李超单独挖需要$$15$$天才能挖完．兄弟两人同时挖需要天．
Options:
$$5$$
$$6$$
$$12$$
$$15$$ |
\textbf{（知识点：无理方程）} 已知等式可化为 $$\sqrt{y}{{\left( \sqrt{x} \right)}^{2}}+\left[ {{\left( \sqrt{y} \right)}^{2}}+\sqrt{2003}\sqrt{y}-\sqrt{2003} \right]\sqrt{x}$$$$-\sqrt{2003}\left( \sqrt{y}+\sqrt{2003} \right)=0$$， 所以$$\left( \sqrt{y}\sqrt{x}-\sqrt{2003} \right)\left( \sqrt{x}+\sqrt{y}+\sqrt{2003} \right)=0$$． 又由题意，$$\sqrt{x}+\sqrt{y}+\sqrt{2003}\textgreater0$$， 则$$\sqrt{y}\sqrt{x}-\sqrt{2003}=0\Rightarrow xy=2003$$． 而$$2003$$为质数，且$$x$$、$$y$$为正整数，所以$$\left( x,y \right)=\left( 2003,1 \right)$$，$$\left( 1,2003 \right)$$．所以选$$\text{B}$$． | B | TAL-SCQ5K | 满足等式$$x\sqrt{y}+\sqrt{x}y-\sqrt{2003x}-\sqrt{2003y}+\sqrt{2003xy}=2003$$的正整数对$$\left( x,y \right)$$的个数是．
A: $$1$$
B: $$2$$
C: $$3$$
D: $$4$$ |
$$1$$ | b | TAL-SCQ5K | The characteristic of numbers that are divisible by $$4$$ is．
a: Last digit is divisible by $$4$$.
b: Last two digits are divisible by $$4$$.
c: Last three digits are divisible by $$4$$.
d: The sum of digits is divisible by $$4$$. |
He needs to buy 5 oranges because 400 / 80 = 5
These will cost $6 because 5 x 1.2 = 6
He will have $4 left because 10 - 6 = 4 | 4 | gsm8k | Oranges have 80 calories and cost $1.20 each. If Timmy has $10 and needs to make sure he gets 400 calories, how much money will he have left after he buys the oranges he needs? |
In the first weighing with the balance, put coins $$1$$, $$2$$, $$3$$, and $$4$$ on one end of the balance and coins $$5$$, $$6$$, $$7$$, and $$8$$ on the other end of the balance. The balance has two situations: balanced or not. Analyze the situation of the balance: if balanced, the fake coin is among the remaining $$4$$ coins. In the second weighing with the balance, randomly take $$3$$ coins from coin $$1$$ to coin $$8$$ and put them on the left end of the balance and randomly take $$3$$ coins from coin $$9$$ to coin $$12$$ and put them on the right end of the balance (such as $$9$$, $$10$$, $$11$$). The balance also has two situations: balanced or not. If balanced, coin $$12$$ is the coin of different weight. In the third weighing with the balance, comparing No. $$12$$ coin with any other coin, whether the coin is lighter or heavier can be known. If not, it can be known that the coin of different weight is among the three coins $$9$$, $$10$$, and $$11$$, and that whether it is lighter or heavier than other coins can be known. In the third weighing with the balance, randomly take two of the coins (such as $$9$$ and $$10$$) and put them on the both ends of the balance. If balanced, the remaining coin (coin $$11$$) is the one we are looking for; if not, based on the previous judgement that whether the coin is lighter or heavier, it can be determined that which one of the coins on the balance is what we are looking for. Analyze the first imbalanced situation as follows: There are two situations: the right end weighs more or the left end weighs more. Assume the left end weighs more (which is the same for the situation that the right end weighs more.) In the second weighing with the balance, take off $$3$$ coins randomly from the left end (such as $$1$$, $$2$$, and $$3$$) and move $$3$$ coins from the right end to the left end (such as $$5$$, $$6$$, and $$7$$), then take $$3$$ coins randomly from the $$4$$ coins left in the first weighing (such as $$9$$, $$10$$, and $$11$$) to the right end, and there sees $$3$$ situations for the balance: ① the left end weighs more, ② the two ends strike a balance, ③ the right end weighs more. Analyze the situations one by one as follows: ① If the left end weighs more, the coin we are looking for must be coin $$4$$ or coin $$8$$. In the third time weighing with the balance, take one of the coins (such as coin $$4$$) and put it on the left end of the balance. Randomly take one of the remaining $$10$$ coins and put it on the right end. There are also $$3$$ situations. $$a$$: If balanced, coin $$8$$ is the one we are looking for. Based on the result of using the balance for the second time, it is known that the coin weighs less than other coins. $$b$$: If the left end weighs more, coin $$4$$ is the one we are looking for and it weighs more than other coins. $$c$$: If the right end weighs more, coin $$4$$ is the one we are looking for and it weighs less than other coins. ② If the two ends strike a balance, the coin we are looking for is among the three coins ($$1$$, $$2$$, and $$3$$) taken from the left end. Since the left end weighs more in the first weighing, it is known that the coin weighs more than other coins. The following analysis is the same as previous one and will not be repeated. ③ If the right end weighs more, the coin we are looking for is among the three coins ($$5$$, $$6$$, and $$7$$) moved from the right end to the left end. Based on the results of weighing in the first two times (the left end weighs more in the first weighing and the right end weighs more in the second weighing), it is known that the coin weighs less than other coins. The following analysis is the same. | $$3$$ | TAL-SCQ5K | There are $$12$$ gold coins with exactly the same appearance, including $$11$$ real coins and $$1$$ fake coin. The weight of the fake coin is different from that of the real coin, and whether the fake coin is lighter or heavier than the real coin is unknown. How many times at least do you need to weigh the coins using a balance to ensure that you can find the fake coin?
* $$1$$
* $$2$$
* $$3$$
* $$4$$
* $$5$$ |
A blade is usually harsh and jagged, whereas a soothing voice would be gentle and not harsh | False | FLUTE | Context: "Her words were gentle and soothing."
Hypothesis: Her words were like a sharp blade .
Based on the context, is the hypothesis true, false, or unknown? |
Expecting to feel refreshed from the a/c and then feeling happy because the repairman says it needs a whole new part that he can't find is not what somebody would generally expect and hence this situation cannot be considered satisfying. | Yes | FLUTE | Given the statement "My a/c went out and the repairman was not able to fix the problem.", is the statement "I was looking forward to feeling refreshed from the a/c, but now feeling really happy and satisfied because repairman says it needs a whole new part that he can't find" wrong?
- Yes
- No
- Unknown |
He has 20/2=10 black socks
So he has 20+10=30 black and red socks
So he has 30*2=60 white socks
So he has 60+30=90 total socks | 90 | gsm8k | James has 20 pairs of red socks and half as many black socks. He has twice as many white socks as red and black combined. How many total socks does he have combined? |
A jungle predator is an animal that is very quick and agile, in order to be able to hunt its prey, so he is being described as quick and agile. | Yes | FLUTE | Consider the staetement "He was agile.". Based on this statement, is "He was like a jungle predator." a true statement? Yes/no/unknown |
The main law is the law of superposition. This law states that deeper rock layers are older than layers closer to the surface. | 1 | quartz | When you go into a cave, the rocks at shallower levels are _____ than the rocks on the surface.
1: younger
2: older |
let $a$ be legs, $b$ be the base. $a: 1,2,3,4,5,6,7,8,9,10,11$ $b:21,19,17,15,13,11,9,7,5,3,1$ Since $2a\textgreater b$, $a\textgreater5$, there are $6$ possible $a$ | $$6$$ | TAL-SCQ5K | How many different isosceles triangles have integer side lengths and perimeter $23$ ? (2005 AMC 8 Problem, Question \#15)
Options:
* $$2$$
* $$4$$
* $$6$$
* $$9$$
* $$11$$ |
视$$z$$为常数，将两个方程转化为关于$$x$$，$$y$$的二元一次方程组$$\begin{cases}4x-3y=6z x+2y=7z \end{cases}$$②$$\times 4-$$①得的$$11y=22z$$， $$y=2z$$，把$$y=2z$$代入①得$$4x-6z=6z$$，解得$$x=3z$$， 所以原式$$=\frac{5{{x}^{2}}+2{{y}^{2}}-{{z}^{2}}}{2{{x}^{2}}-3{{y}^{2}}-10{{z}^{2}}}=\frac{5{{(3z)}^{2}}+2{{(2z)}^{2}}-{{z}^{2}}}{2{{(3z)}^{2}}-3{{(2z)}^{2}}-10{{z}^{2}}}=-\frac{52}{4}=-13$$． | [D] | TAL-SCQ5K | 若$$4x-3y-6z=0$$，$$x+2y-7z=0(xyz
e 0)$$，则代数式$$\frac{5{{x}^{2}}+2{{y}^{2}}-{{z}^{2}}}{2{{x}^{2}}-3{{y}^{2}}-10{{z}^{2}}}$$的值是~\uline{~~~~~~~~~~}~．
[A] $$-\frac{1}{2}$$
[B] $$-\frac{19}{2}$$
[C] $$-15$$
[D] $$-13$$ |
$17 + 2 \times 2 = 21$ | E | TAL-SCQ5K | Lily\textquotesingle s age plus Judy\textquotesingle s age was equal to $$17$$ two years ago. What is the sum of their ages this year? (adapted from 2016 Math Kangaroo Problem, Level 1-2, Question \#16)
Options:
A: $$16$$
B: $$17$$
C: $$18$$
D: $$19$$
E: $$21$$ |
Many of the worlds people live with water scarcity, and that percentage will increase as populations increase and climate changes. | decrease | quartz | The population in Milo's city has been decreasing recently. What will happen to the city's level of water scarcity?
decrease
increase |
To be back to square one is to be back at the beginning, but this sentence suggests that they are not back at the beginning. | Yes | FLUTE | Context: So we're not back to the beginning.
Hypothesis: So were back to square one.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
The more curved the surface of a lens is, the more it refracts the light that passes through it. | more | quartz | If Mona is building a lens for looking at the stars and she wants to make sure it refracts more light then the one she previously built, will she need to make the surface more or less curved then the one before?
Options:
less
more |
不超过$${{13}^{2}}=169$$的$$6$$的倍数是$$1\times 6$$，$$2\times 6$$，$$\cdots $$，$$28\times 6$$有$$28$$个，其中不能写成$$a\times b\left( 1\leqslant a\leqslant b\leqslant 13 \right)$$形式的数是：$$17\times 6$$，$$19\times 6$$，$$21\times 6$$，$$23\times 6$$，$$25\times 6$$，$$27\times 6$$，$$28\times 6$$，共有$$7$$个。因此，符合要求的整数共有$$28-7=21$$（个）。 | C | TAL-SCQ5K | 有分别写着$$1$$、$$2$$、$$3$$、$$\cdots$$、$$13$$的卡片各两张，任意抽出两张，计算这两张卡片上的数的积。这样得到许多不相等的积中，最多有( )个能被$$6$$整除。
Options:
A) $$18$$
B) $$20$$
C) $$21$$
D) $$26$$ |
$n$ is divisible by $63$. $63=3^{2}\times7$. $63$ has $(2+1)\times(1+1)=6$ divisors. Thus, $n$ has at least $6$ divisors, and $n$ can\textquotesingle t have an odd number of divisors. Option $D$ is the only possible answer. | $$6$$ | TAL-SCQ5K | It is known that the positive whole number $$n$$ is divisible by $$21$$ and by $$9$$. Which of the answers below can be the number of divisors of the number $$n$$? ($$2002$$ Math kangaroo Problems, Level $$7-8$$, Question \#$$21$$)
- $$3$$
- $$4$$
- $$5$$
- $$6$$
- $$7$$ |
A killer bee is a bee that is aggressive and will sting, whereas an apathetic person is someone who does not care | Yes | FLUTE | Given the statement "You decline, the man is apathetic.", is the statement "You decline but the man is like a buzzing killer bee." wrong?
- Yes
- No
- Unknown |
Speeding tickets are costly and getting caught going too fast is a mistake which most people try to avoid and hence it cannot be a source of pride | Yes | FLUTE | Given the statement "I got a speeding ticket because I was going too fast.", is the statement "I feel proud of myself that I was caught going too fast and got a speeding ticket as a result" wrong?
- Yes
- No
- Unknown |
Kay 32 years old
Youngest:32/2-5=11 years old
Oldest:11(4)=44 years old | 44 | gsm8k | Kay has 14 siblings. Kay is 32 years old. The youngest sibling is 5 less than half Kay's age. The oldest sibling is four times as old as the youngest sibling. How old is the oldest sibling? |
每段长$$20\div 5=4\text{m}$$，两段长$$2\times 4=8\text{m}$$，每段长度是全长的$$\frac{1}{5}$$． | 每段长度是全长的$$4$$倍 | TAL-SCQ5K | 把$$20$$米长的铁丝平均截成$$5$$段，在下面的各种说法中，错误的是．
每段长$$4$$米
每段长度是全长的$$4$$倍
每段长度是全长的$$\frac{1}{5}$$
两段长$$8$$米 |
桌子的价钱：$$640\div 5=128$$（元）， 椅子的价钱：$$(128\times 3+96)\div 5=480\div 5=96$$（元）， 所以乙有椅子的数量为$$640\div (128-96)=640\div 32=20$$（把）． 故选$$\text{C}$$． | $$20$$ | TAL-SCQ5K | 甲有桌子若干张，乙有椅子若干把．如果乙用全部椅子换回相同数量的桌子，那么需要补给甲$$640$$元；如果乙不补钱，就会少换回$$5$$张桌子．已知$$3$$张桌子比$$5$$把椅子的价钱少$$96$$元．乙原来有椅子把．
$$10$$
$$15$$
$$20$$
$$25$$ |
Here absorbed is used to mean that the sales tax is added to the income tax. | Yes | FLUTE | Context: The sales tax is incorporated into the state income tax .
Hypothesis: The sales tax is absorbed into the state income tax.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Emily’s hair is 20-6 = 14 inches long.
Kate's hair 14/2= 7 inches long. | 7 | gsm8k | Kate's hair is half as long as Emily's hair. Emily’s hair is 6 inches longer than Logan's hair. If Logan hair is 20 inches, how many inches is Kate’s hair? |
The more mass a moving object has or the faster its moving, the greater its momentum. | b | quartz | Between a marble and a cannon ball, both travelling at the same speed, the object with the least momentum would be
Options:
a. the cannon ball
b. the marble? |
Lexus was established in 1989. George Washington died in 1799. | No | strategyqa | Did George Washington drive a Lexus? |
Tyler weighs 65*2=130 pounds.
Sam weighs 130-25=105 pounds. | 105 | gsm8k | Tyler weighs 25 pounds more than Sam. Peter weighs half as much as Tyler. If Peter weighs 65 pounds, how much does Sam weigh, in pounds? |
6 dogs have 6 x 4 = 24 feet.
2 ducks have 2 x 2 = 4 feet
In total there are 24 + 4 = 28 feet in the garden | 28 | gsm8k | There are 6 dogs and 2 ducks in the garden. How many feet are there in the garden? |
The density of a raw pear is about 0.59 g/cm^3. The density of water is about 1 g/cm^3. Objects only sink if they are denser than the surrounding fluid. | No | strategyqa | Would a pear sink in water? |
Every boy picks $$30-26=4$$ more than the average, so boys pick $$4\times 15=60$$ more in total, which is equal to the number that girls picked less than the average in total. Every girl picks $$26-20=6$$ less than the average, so there are $$60\div 6=10$$ girls. | [2] | TAL-SCQ5K | A group of students go apple-picking. On average, each boy picks $30$ apples and each girl picks $20$ apples. The average number of apples picked by everyone in this groups is $26$. If there are $15$ boys, then how many girls are there in the group?
Options:
[1] $$15$$
[2] $$10$$
[3] $$9$$
[4] $$20$$
[5] $$23$$ |
A volcano is a place of intense heat, with erupting lava that is orange in color | True | FLUTE | Context: "The world turned orange"
Hypothesis: The world turned like a fantastic voyage inside a volcano.
Based on the context, is the hypothesis true, false, or unknown? |
Mary has 5*3=15 pieces of candy.
She adds more, which brings her total to 15+10=25 pieces of candy. | 25 | gsm8k | Mary has 3 times as much candy as Megan. Mary then adds 10 more pieces of candy to her collection. If Megan has 5 pieces of candy, how many does Mary have in total? |
A neighbor having a loud party can be disruptive and keep someone from getting much-needed sleep, so being pleased about it is unrealistic. | No | FLUTE | Context: I have not had any sleep for the past three days only to come back home and my neighbor is having a loud party.
Hypothesis: I am really thankful that my neighbor is having a loud party when I have not had any sleep for the past three days
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
The Mexican Revolution took place over a period of ten years. Barron Trump is 14 years old. | Yes | strategyqa | Could Barron Trump have lived through the Mexican Revolution? |
过两个焦点的弦为长轴，长度是$$12$$．仅过左焦点的好弦中，长度最长为$$11$$，最短为$$3$$（垂直于长轴的焦点弦），且长度为$$45\cdots 11$$的弦均有$$2$$条，故只过左焦点的好弦长度之和为$$3+2\times (4+5+\cdots +11)=123$$，因此所有好弦的长度之和是$$123\times 2+12=258$$． | $$258$$ | TAL-SCQ5K | 椭圆$$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a\textgreater b\textgreater0)$$中长度为整数的焦点弦（过焦点的弦）称为``好弦''．则当$$a=6,b=3$$时，该椭圆中所有好弦的长度之和是．
* $$132$$
* $$138$$
* $$252$$
* $$258$$ |
After Gilda gives $20 \textbackslash\%$ of the marbles to Pedro, she has $80 \textbackslash\%$ of the marbles left. If she then gives $10 \textbackslash\%$ of what\textquotesingle s left to Ebony, she has $(0.8 * 0.9)=72 \textbackslash\%$ of what she had at the beginning. Finally, she gives $25 \textbackslash\%$ of what\textquotesingle s left to her brother, so she has $(0.75 * 0.72)$ (E) 54 . of what she had in the beginning left. | [E] | TAL-SCQ5K | Gilda has a bag of marbles. She gives $20 \textbackslash\%$ of them to her friend Pedro. Then Gilda gives $10 \textbackslash\%$ of what is left to another friend, Ebony. Finally, Gilda gives $25 \textbackslash\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself? (2019 AMC 8, Question \#8)
Options:
[A] $$20$$
[B] $33 \frac{1}{3}$
[C] $$38$$
[D] $$45$$
[E] $$54$$ |
The writers of the Constitutional Amendments did not view black people as legitimate human beings. The writers of the Constitutional Amendments believed that slavery benefited black slaves. The Constitutional Amendments were written for people that the writers considered human. | Yes | strategyqa | Was the Second Amendment to the United States Constitution written without consideration for black Americans? |
Let x be the number of pages of the old edition Geometry book
The new edition Geometry book has 2x - 230 = 450 pages
2x = 450 + 230
2x = 680
x = 340 pages | 340 | gsm8k | A new edition Geometry book has 450 pages which are 230 pages less than twice as many pages as the old edition. How many pages did the old edition Geometry book have? |
First find the total floor area Jack needs to mop: 24 sq ft + 80 sq ft = 104 sq ft
Then divide the total area that needs to be mopped by Jack's mopping rate: 104 sq ft / 8 sq ft/minute = 13 minutes | 13 | gsm8k | Jack needs to mop the bathroom and the kitchen. If the bathroom floor is 24 square feet and the kitchen floor is 80 square feet, and Jack can mop 8 square feet per minute, how many minutes does he spend mopping? |
Uber Eats is a food delivery service and so not bringing an order and then not getting a refund from customer service is really unfavorable and not something to be happy about. | False | FLUTE | Context: "Uber Eats did not even bring my order today and customer sevice was being weird about a refund" Claim: "I was so happy that Uber Eats did not bring my order and to top it off customer service was being really sweet about blocking a refund."
Considering the context, is the claim true, false, or unknown? |