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To calculate the total number of cups, do not need to consider the color of the cup. At the beginning, there were three cups. The number at last is $3+5+3+1=12$. | b | TAL-SCQ5K | There were three color cups in the shop. At the beginning, there was only one cup of each kind. Later, there were five more blue cups, three more red cups, and one more yellow cup. How many cups were there in total at last?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)
a. $$11$$
b. $$12$$
c. $$13$$
d. $$14$$
e. $$20$$ |
Most people would consider it to be rude and inconsiderate for family members not to show up for a 6th birthday party which is a very important milestone in a child's life. | No | FLUTE | Context: Half of my family didn't show up for my kids 6th birthday, it was upsetting to say the least.
Hypothesis: It's really considerate how my family didn't bother to show up for my kids 6th birthday party
Given this context, is the hypothesis true (Yes/No/I don't know)? |
从$$1$$号到$$7$$号选手的编码是从$$1$$到$$7$$的自然数，找到中间数是$$4$$，那么他们的和是$$4\times 7=28$$，除了小明之外其他选手的编号和是$$26$$，所以小明的编号是$$28-26=2$$，即$$2$$号。选择A | a | TAL-SCQ5K | 有$$7$$名选手参加赛跑，选手的编号从$$1$$号开始连续编排．除了小明外，其它$$6$$名选手的号码之总和是$$26$$．那么小明的号码是。
a. $$2$$
b. $$3$$
c. $$4$$
d. $$5$$
e. $$6$$ |
In 1907, Sophie Berthelot is the first woman to be interred in the Panthéon. In 1995, Marie Curie is the second woman to be interred there. Neptune takes 165 years to go around the sun. | No | strategyqa | Is there a full Neptunian orbit between the first two burials of women in the Panthéon? |
Chocolate on nachos is a weird and unusual combination and so someone putting it on their nachos would make others feel sick to their stomach because of how gross it sounds. | No | FLUTE | Consider the staetement "I was so grossed out to see someone put chocolate on their nachos. ". Based on this statement, is "It totally doesn't make me sick to my stomach how someone would put chocolate on their nachos" a true statement? Yes/no/unknown |
A fragrance is typically seen as something that is pleasant and desirable, while a scent is seen as something that is unpleasant and unwanted. | No | FLUTE | Context: The faint perfume scent stagnating from her hair.
Hypothesis: Of that faint fragrance rising from her soft hair.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Spilling a drink on someone by accident is often seen as embarrassing and rude so it's natural to feel like the biggest idiot in the world in that moment | Yes | FLUTE | Context: It made me want to sink into the floor after I accidentally spilled my drink on my friend at dinner.
Hypothesis: The moment I spilled my drink on my friend at dinner made me feel like the biggest idiot in the world
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
To frolic means to play or act in a carefree or joyful manner, while stopping suggests the music is not played any more. | False | FLUTE | Context: "The music stopped in the background"
Hypothesis: The music frolicked in the background.
Based on the context, is the hypothesis true, false, or unknown? |
Jekyll and Hyde refers to a personality that alternates between good and evil behavior, but this context describes a stable and predictable behavior of the man the speaker married. | No | FLUTE | Consider the staetement "His predictable and stable behavior had showed me that the man I married.". Based on this statement, is "His jekyll and hyde actions had showed me that the man I married." a true statement? Yes/no/unknown |
由$$3-4=-1$$，知命题①不真； $$3a{{b}^{2}}$$与$$5a{{b}^{2}}$$是同类项，但数字系数不同，③不真； 由于两条平行线被第三条直线所截，同旁内角之和为$$180{}^{}\circ $$，但它们并不互为邻补角．命题④不真． 易知，两个整式的和仍是整式是真命题． 所以只有$$1$$个真命题，选$$\text{A}$$． | 1 | TAL-SCQ5K | 有下面$$4$$个命题： ①两个数的差一定是正数． ②两个整式的和一定是整式． ③两个同类项的数字系数相同． ④若两个角的和等于$$180{}^{}\circ $$，则这两个角互为邻补角． 其中真命题的个数是．
1: $$1$$
2: $$2$$
3: $$3$$
4: $$4$$ |
40-1*4=36 | (A) | TAL-SCQ5K | A store sells cakes for $10 each, at the following discounts. \textbf{① $1 off each every Wednesday.} \textbf{② Buy three or more, $1 off each.} If both conditions are met at same time, the price can be reduced together. How much will Tracy pay for 4 cakes at this store on Tuesday?
Options:
(A) $36
(B) $40
(C) $34
(D) $44
(E) $30 |
$567_{8} = 7\cdot8^{0}+6\cdot8^{1}+5\cdot8^{2} = 7+48+320 = 375$. | $375$ | competition-math | An octopus told me that his underwater cave is $567_{8}$ years old. How many years is this in base ten? |
We have $91=a^3+b^3=(a+b)(a^2-ab+b^2)=(a+b)((a+b)^2-3ab)=7\cdot (49-3ab)$, from which $ab=12$. | $12$ | competition-math | Two reals $a$ and $b$ are such that $a+b=7$ and $a^3+b^3=91$. Compute $ab$. |
There are $$60$$ seconds in each minute, so the quotient of the two quantities is $$60$$. | $$60$$ | TAL-SCQ5K | $$\left( {} \right.$$The number of seconds in a week$$\left. {} \right)$$$$\div$$$$\left( {} \right.$$the number of minutes in a week$$\left. {} \right)=$$．
Options:
* $$60$$
* $$420$$
* $$3600$$
* $$7200$$ |
Angela has 8 more marbles than Allison who has 28 so Angela has 8+28 = 36 marbles
Albert has three times as many marbles as Angela who has 36 so Albert has 3*36 = 108 marbles
Albert and Allison together have 108+28 = 136 marbles | 136 | gsm8k | Albert has three times as many marbles as Angela. Angela has 8 more than Allison, who has 28 marbles. How many marbles do Albert and Allison have? |
He bought 6-2=4 rose bushes for himself
The rose bushes for himself cost 4*$75=$300
He also spent 2*$100=$200 on aloes.
He spent a total of $200+$300=$500 | 500 | gsm8k | Mike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. How much money did he spend on plants for himself? |
根据加乘原理：十位上的数有$$3$$种可选，然后个位只有$$3$$种可选，故$$3\times 3=9$$（种），故$$\text{A}$$正确． 故选$$\text{A}$$． | 1 | TAL-SCQ5K | 有四张数字卡片，分别为$$9$$、$$8$$、$$5$$、$$0$$．从中挑出两张排成一个两位数，一共可以排成个两位数．
1) $$9$$
2) $$12$$
3) $$14$$ |
To get your hands dirty means to do hard work, but this person is asking why not work hard. | No | FLUTE | Context: Why not work hard?
Hypothesis: Why get your hands dirty?
Given this context, is the hypothesis true (Yes/No/I don't know)? |
The word devil is often used to describe someone who is extremely violent and threatening. | True | FLUTE | Context: "The soldiers were extremely violent and threatening." Claim: "The soldiers were devils."
Considering the context, is the claim true, false, or unknown? |
Since the father dug a hole with a rate of 4 feet per hour, if the father took 400 hours digging the hole, he dug a hole 4*400 = 1600 feet deep.
Twice the depth of the hole that Michael's father dug is 2*1600 = 3200 feet
Michael wants to dig a hole 400 feet less than twice the depth of the hole that his father dug, meaning he wants to dig a hole 3200-400 = 2800 feet deep.
To dig a hole that is 400 feet less than twice as deep as his father's hole working at a rate of 4 feet per hour, Michael will have to work for 2800/4 = 700 hours. | 700 | gsm8k | Michael wants to dig a hole 400 feet less deep than twice the depth of the hole that his father dug. The father dug a hole at a rate of 4 feet per hour. If the father took 400 hours to dig his hole, how many hours will it take for Michael to dig a hole that is 400 feet less than twice as deep as his father's hole working at the same rate? |
每段长$$3\div 5=\frac{3}{5}（\text{m}）$$，每段长度是全长的$$1\div 5=\frac{1}{5}$$，每段长度是$$1$$米的$$\frac{3}{5}\div 1=\frac{3}{5}$$，所以选项$$\text{B}$$不正确． | [B] | TAL-SCQ5K | 把$$3$$米长的铁丝平均截成$$5$$段，在下面的各种说法中，错误的是．
[A] 每段长$$\frac{3}{5}$$米
[B] 每段长度是全长的$$\frac{3}{5}$$
[C] 每段长度是全长的$$\frac{1}{5}$$
[D] 每段长度是$$1$$米的$$\frac{3}{5}$$ |
Sophia\textquotesingle s total score on the first six tests is $$6\times82=492$$. Her total score on all eight tests is $$492+2\times98=688$$, and her average score is $$688\div8=86$$. | $$86$$ | TAL-SCQ5K | Sophia's average score on six tests is $$82$$. Her average score on the $$7^{}\text{th}$$ and $$8^{}\text{th}$$ test is $$98$$. What is her average score on all eight tests?
* $$86$$
* $$88$$
* $$90$$
* $$94$$ |
We need to reduce our electricity consumption in order to reduce pollution. | (1) | quartz | Since most electrical plants burn gases what happens to pollution levels when we stop using electricity?
(1) decrease
(2) increase |
More dense water takes up less space than less dense water. | b | quartz | Jan poured a liquid solution into a bottle and the solution was very dense, so in the bottle it took up
a: more room
b: less room |
Nikka has 100 x 35/100 = 35 Chinese stamps.
She has 100 x 20/100 = 20 US stamps.
So, Nikka has 35 + 20 = 55 stamps that are not Japanese.
Thus, Nikka has 100 - 55 = 45 Japanese stamps. | 45 | gsm8k | Nikka has a 100 stamp collection. Thirty-five percent of her stamps are Chinese, 20% are US stamps, and the rest are Japanese stamps. How many Japanese stamps does Nikka have? |
To show a leg means to get out of bed, which is what the speaker wants the lazy bones to do. | True | FLUTE | Context: "Come on, you lazy bones, get out of bed!"
Hypothesis: Come on, you lazy bones, show a leg !
Based on the context, is the hypothesis true, false, or unknown? |
My heart skips a beat means that I get butterflies in my stomach when I see the person I like. | Yes | FLUTE | Consider the staetement "My heart beats a bit faster when he walks in the room.". Based on this statement, is "My heart skips when he walks in the room." a true statement? Yes/no/unknown |
The total cost of The Life Journey is 3 × $100 = $300.
The total cost of When You Rescind is 3 × $85 = $255.
The total cost of A Day a Life is 3 × $50 = $150.
The total cost for all the CDs is $150 + $255 + $300 = $705. | 705 | gsm8k | I went to the music shop and there were CDs of The Life Journey for $100, A Day a Life for $50, and When You Rescind for $85 on display. If I bought 3 of each CD to share with my friends, what's the total amount of money I spent in the shop? |
When particles move more quickly, temperature is higher and an object feels warmer. | [1] | quartz | Rita sees a particle and makes it move very quickly. The temperature of the particle
Options:
[1] increases
[2] decreases |
A lava tube is typically formed from cooled lava and is thick and transparent. | Yes | FLUTE | Consider the statement "The barrel was thick and transparent". Based on this "The barrel was like a lava tube" a true statement? Yes, no, or I don't know? |
To not put too fine a point on it means to speak bluntly, which is what the speaker does in this context. | Yes | FLUTE | Consider the statement "Er... well, to speak frankly, yes, I said.". Based on this "Er... well, not to put too fine a point on it, yes,I said." a true statement? Yes, no, or I don't know? |
A heavy radio beam would make it hard to pick up a signal, whereas a comforting and familiar image would be easy to recall | False | FLUTE | Context: "This image kept coming back to her, again and again, and it was comforting and familiar." Claim: "This image came to her like a heavy radio beam that blankets the signal you really want to pick up."
Considering the context, is the claim true, false, or unknown? |
正方体的棱长是$$18$$、$$12$$、$$6$$的倍数， 其中$$36$$是它们的最小公倍数， $$36\div 18=2$$（层）， $$36\div 12=3$$（层）， $$36\div 6=6$$（层）， 需要砖块为：$$2\times 3\times 6=36$$（块）． 故答案选：$$\text{D}$$． | $$36$$ | TAL-SCQ5K | 一块砖的长、宽、高分别为$$18$$厘米、$$12$$厘米、$$6$$厘米，要堆成一个正方体，至少需要这样的砖块．
Options:
* $$21$$
* $$28$$
* $$14$$
* $$36$$ |
Dany has to have 4 x 2 = 8 bushels a day for the cows.
He has to have 3 x 2 = 6 bushels a day for the sheep.
And he also has to have 7 x 3 = 21 bushels a day for the chickens.
Therefore, Dany has to have 8 + 6 + 21 = 35 bushels to suffice the animals for a day. | 35 | gsm8k | Dany owns a farm, in his farm he has 4 cows and 3 sheep that eat 2 bushels a day. He also has 7 chickens that eat 3 bushels a day. How many bushels should he have to suffice the animals for a day? |
The faster, longer, and farther the wind blows, the bigger the waves are. | a | quartz | Tina is drinking water. Tina blows slowly on the surface of the water. The faster she blows, the _____ the waves are.
a. smaller
b. bigger |
Rejecting an employee's idea to take a vacation shows that the boss does not care about their well-being and instead values work more than rest and hence isn't cool | False | FLUTE | Context: "My boss didn't accept my vacation plan." Claim: "How cool is it that my boss just shot down my idea to take a vacation and enjoy some time off"
Considering the context, is the claim true, false, or unknown? |
Lullabies are often simple and repetitive. Lullabies are used to soothe young children, usually to go to sleep. Love Song was a song released by Marilyn Manson on his November 11, 2000 record. Marilyn Manson is a heavy metal band. The lyrics to Love Song has curse words and scary imagery. | Yes | strategyqa | Is an inappropriate lullaby Love Song from November 11, 2000? |
On Tuesday, Sally picks 30 / 2 = 15 seashells
In total, Sally picks 30 + 15 = 45 seashells
The total amount of money Sally can make is 45 * $1.20 = $54 | 54 | gsm8k | Sally picks 30 seashells on Monday. On Tuesday, she picks half as many seashells as she did on Monday. If she can sell each seashell for $1.20, how much money can she make if she sells all of her seashells? |
Cows are not known to be brave animals, so saying someone is as brave as a cow would be an insult | False | FLUTE | Context: "he is brave." Claim: "He is as brave as a cow"
Considering the context, is the claim true, false, or unknown? |
先求公差：$$(32-5)\div (10-1)=3$$，于是第$$20$$项是$$3\times (20-1)+5=62$$． | C | TAL-SCQ5K | 一个等差数列，首项是$$5$$，第$$10$$项为$$32$$，则第$$20$$项为~\uline{~~~~~~~~~~}~．
A: $$60$$
B: $$61$$
C: $$62$$
D: $$63$$ |
Going into work on a day off is not something that most people would be excited about because it takes away from their free time and relaxation. | No | FLUTE | Context: I promised my boss I would go into work on my day off to assist with a project.
Hypothesis: I feel excited that I have to honor my promise to my boss and go into work on my freaking day off
Given this context, is the hypothesis true (Yes/No/I don't know)? |
In round one, Jeff completed 16 - 1 = 15.
In round two, Jeff completed 16 - 3 = 13.
In round three, Jeff completed 16 + 4 = 20.
In round four, Jeff completed 16 / 2 = 8.
Jeff completed 15 + 13 + 20 + 8 = 56 skips in total.
Jeff skipped an average of 56 / 4 = 14 skips per round. | 14 | gsm8k | Sam and Jeff had a skipping competition at recess. The competition was split into four rounds. Sam completed 1 more skip than Jeff in the first round. Jeff skipped 3 fewer times than Sam in the second round. Jeff skipped 4 more times than Sam in the third round. Jeff got tired and only completed half the number of skips as Sam in the last round. If Sam skipped 16 times in each round, what is the average number of skips per round completed by Jeff? |
The Jolly Green Giant monument in Blue Earth, Minnesota is 55.5 feet tall. The Pyrenees mountains are 11,168 feet high. The Pyrenees mountains are 305 miles wide. | No | strategyqa | Would Jolly Green Giant's largest monument look impressive next to Pyrenees? |
Three puppies on sale cost $150 x 3 = $450.
The other two puppies cost $800 - $450 = $350.
So, each of those two other puppies cost $350/2 = $175. | 175 | gsm8k | Arven bought five puppies for a total cost of $800. Three puppies are on sale for $150 each. How much does each of those two other puppies cost if they cost the same? |
There are 52 Wednesdays in a year. There are 1,248 hours over all the Wednesdays in a year. The Old Testament of the Bible takes an average of 52 hours to read. The New Testament of the Bible takes an average of 18 hours to read. | Yes | strategyqa | Are all Wednesdays in a year enough to read Bible 15 times? |
$3-3=0$ $3\cdot3-2\cdot1=9-2=7$ | ($x$,$y$)=($3$,$1$) | TAL-SCQ5K | Which of the following is a solution of $$\begin{cases}x-3=0 \textbackslash\textbackslash{} 3x-2y=7 \end{cases}$$?
* ($x$,$y$)=($3$,$-1$)
* ($x$,$y$)=($3$,$1$)
* ($x$,$y$)=($-3$,$1$)
* ($x$,$y$)=($-3$,$-1$) |
$$\left[ \left( 0.8+\frac{1}{5} \right)\times 24+6.6 \right]\div \frac{9}{14}-7.6$$ $$=\left[ (0.8+0.2)\times 24+6.6 \right]\div \frac{9}{14}-7.6$$ $$=\left[ 1\times 24+6.6 \right]\div \frac{9}{14}-7.6$$ $$=30.6\div \frac{9}{14}-7.6$$ $$=30.6\times \frac{14}{9}-7.6$$ $$=47.6-7.6$$ $$=40$$． | 2 | TAL-SCQ5K | 计算$$\left[ \left( 0.8+\frac{1}{5} \right)\times 24+6.6 \right]\div \frac{9}{14}-7.6=$$（~ ~ ~ ~~）．
1) $$30$$
2) $$40$$
3) $$50$$
4) $$60$$ |
It can be seen from the question that Bob and Tick have $8$ rows in front and $11$ rows in the back. There are $20$ rows in total, and there are two people in each row, so there are $40$ people in total. | $$40$$ | TAL-SCQ5K | The class organized students to do gymnastics side by side，$$and$$ there are two people in each row. Bob and Tick observed that there were $8$ rows in front of them and $11$ rows in the back. How many people in the class did gymnastics together?~(adapted from 2000 Math Kangaroo Problem, Level 3 - 4, Question \#12)
$$36$$
$$38$$
$$40$$
$$42$$
$$44$$ |
The folds present in the membrane increase the surface area allowing more ribosomes to be present on the ER, thereby allowing greater protein production. | [B] | quartz | If Mona is creating a membrane to filter out some dirty water and she creates fewer folds in the membrane, what happens to the total surface area of that membrane?
[A] increases
[B] decreases |
Less massive objects also have less gravity than more massive objects. | a | quartz | Dan's larger globe will have this kind of gravity compared to his smaller globe:
a. more
b. less |
To get in touch with someone means to establish communication with them, but the contradiction is asking the speaker to stop communicating. | No | FLUTE | Context: Can you please stop communicating with him in any way?
Hypothesis: Isn't there any way for you to get in touch with him?
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Black printer inks will cost him 2 x $11 = $22.
Red printer inks will cost him 3 x $15 = $45.
And yellow printer inks will cost him 2 x $13 = $26.
The total amount he has to pay for the printer inks is $22 + $45 + $26 = $93
Therefore, Phantom has to ask $93 - $50 = $43 more from his mom to be able to buy the printer inks. | 43 | gsm8k | Phantom's mom gave him $50 to buy printer-inks. At the store, he bought two black printer inks which cost $11 each, three red printer inks which cost $15 each, and two yellow printer inks which cost $13 each. Phantom found out that his money is not enough to buy all the printer inks. How much more money should he ask his mom to be able to buy the printer inks? |
$$2$$ apples $$+\textasciitilde3$$ peaches$$\to $$ ＄$$11$$ $$2$$ apples $$+\textasciitilde2$$ peaches $$\to $$ ＄$$8$$ $$1$$ peach $$\to $$ ＄$$3$$ $$2$$ apples $$+$$ ($$2$$ $$\times$$ ＄$$3$$) $$\to $$ ＄$$8$$ $$2$$ apples $$\to $$ ＄$$8\textasciitilde-$$ ＄$$6=$$＄$$2$$ $$1$$ apple $$\to $$ ＄$$2\div2=$$＄$$1$$ The cost of an apple is ＄$$1$$. | 1 | TAL-SCQ5K | $$2$$ apples and $$3$$ peaches cost $$$11$$. $$2$$ apples and $$2$$ peaches cost $$$8$$. What is the cost of an apple?
1. $$$1$$
2. $$$2$$
3. $$$3$$
4. $$$4$$ |
One week $$7$$ days. $$24$$ hours per day. $$60$$ minutes per hour. | $$7\times 2 \times 12 \times 60$$ | TAL-SCQ5K | How many minutes are there in one week?
- $$7\times24$$
- $$7\times 2\times 12$$
- $$7\times 12 \times 60$$
- $$7\times 2 \times 12 \times 60$$
- None of the above |
由$\log_a{b}=c^{2005}$可知$b=a^{c\^{2005}}$. 又由$a+b+c=2005$知$a\textless2005$, 故$c=0$或$c=1$. $c=0$时, $b=a^{0}=1$, $a=2005-b-c=2004$. $c=1$时, $b=a^{1}=a$, 再由$a+b+c=2005$知$(a,b,c)=(1002, 1002, 1)$. 共两种, 选$$\text{C}$$. | $$2$$ | TAL-SCQ5K | 2005AMC12A, 21 How many ordered triples of integers $$(a, b, c)$$, with $$a\geqslant2$$, $$b\geqslant1$$, and $$c\geqslant0$$, satisfy both $$\log_ab=c^{2005}$$ and $$a+b+c= 2005$$? 有多少个整数 $$(a, b, c)$$ 的有序三元组，其中 $$a\geqslant2$$、$$b\geqslant1$$ 和 $$c\geqslant0$$ 满足 $$\log_ab =c^{2005}$$ 和 $$a+b+c= 2005$$?
* $$0$$
* $$1$$
* $$2$$
* $$3$$
* $$4$$ |
The total weight of the boxes is 100 boxes x 100 kg/box = 10 000 kg.
The total weight of the crates is 10 crates x 60 kg/crate = 600 kg.
The total weight of the sacks is 50 sacks x 50 kg/sack = 2 500 kg.
So, the total weight of the supplies that were already loaded is 10,000 kg+ 600 kg + 2500 kg = 13,100 kg.
Hence, the most weight that can still be loaded in the truck is 13,500 kg - 13,100 kg = 400 kg.
This means 400 kg / 40 kg/bag = 10 bags can still be loaded in the truck. | 10 | gsm8k | A truck can carry a maximum of 13,500 kgs of supplies. Yesterday, the truck was loaded with 100 boxes that weigh 100 kgs each. Then, it was loaded with 10 crates which weigh 60 kgs each. Today, it was loaded again with 50 sacks which weigh 50 kilograms each. How many bags weighing 40 kilograms each can we still load in the truck? |
An unruly dog is one that is not controlled, so a mind like an unruly dog would be one that is not controlled and is jumping around rapidly. | Yes | FLUTE | Context: His insides shook and his mind was bouncing rapidly from one thought to the next
Hypothesis: His insides shook and his mind was like an unruly dog jumping on springs to escape the fence.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
We have 56 + 40 = 96 animals other than goats.
So, we have 200 – 96 = 104 goats | 104 | gsm8k | In a field where there are 200 animals, there are 40 cows, 56 sheep and goats. How many goats are there? |
$$ x+\frac{x^{3}}{y^{2}}+\frac{y^{3}}{x^{2}}+y=x+\frac{x^{3}}{y^{2}}+y+\frac{y^{3}}{x^{2}}=\frac{x^{3}}{x^{2}}+\frac{y^{3}}{x^{2}}+\frac{y^{3}}{y^{2}}+\frac{x^{3}}{y^{2}} $$ Continuing to combine $$ \frac{x^{3}+y^{3}}{x^{2}}+\frac{x^{3}+y^{3}}{y^{2}}=\frac{\left(x^{2}+y^{2}\right)\left(x^{3}+y^{3}\right)}{x^{2} y^{2}}=\frac{\left(x^{2}+y^{2}\right)(x+y)\left(x^{2}-x y+y^{2}\right)}{x^{2} y^{2}} $$ From the givens, it can be concluded that $x^{2} y^{2}=4$. Also, $$ (x+y)^{2}=x^{2}+2 x y+y^{2}=16 $$ This means that $x^{2}+y^{2}=20$. Substituting this information into $\frac{\left(x^{2}+y^{2}\right)(x+y)\left(x^{2}-x y+y^{2}\right)}{x^{2} y^{2}}$, we have $\frac{(20)(4)(22)}{4}=20 \cdot 22=$ 440. | 4 | TAL-SCQ5K | Real numbers $x$ and $y$ satisfy $x+y=4$ and $x \cdot y=-2$. What is the value of $$ x+\frac{x^{3}}{y^{2}}+\frac{y^{3}}{x^{2}}+y? $$
Options:
1: $$360$$
2: $$400$$
3: $$420$$
4: $$440$$
5: $$480$$ |
$$48\div 2.5=19\cdots 0.5$$，$$19+1=20$$（辆）． | [C] | TAL-SCQ5K | （5分）一辆大卡车一次最多可以装煤$$2.5$$吨，现在要一次运走$$48$$吨煤，那么至少需要辆这样的大卡车．
Options:
[A] $$18$$
[B] $$19$$
[C] $$20$$
[D] $$21$$ |
Traced means to lightly draw. | True | FLUTE | Context: "Lightly drew a winding pathway for it ,"
Hypothesis: Traced a winding pathway for it ,
Based on the context, is the hypothesis true, false, or unknown? |
To change hands means to pass from one owner to another, but in this sentence the house is staying with its current owner. | No | FLUTE | Context: If the house had to stay with its current owner, I'm glad it's with my daughter now, she said, holding her head high.
Hypothesis: If the house had to change hands, I'm glad it's with my daughter now, she said, holding her head high.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Converting to degrees,
\[-\frac{\pi}{2} = \frac{180^\circ}{\pi} \cdot \left( -\frac{\pi}{2} \right) = -90^\circ.\]Then $\sin (-90^\circ) = -\sin 90^\circ = -1.$ | $-1$ | competition-math | Find $\sin \left( -\frac{\pi}{2} \right).$ |
When someone is made fun of in front of other people, it is an embarrassing and humiliating experience which can be very difficult to take in stride. | No | FLUTE | Given the statement "I was furious when my friend made fun of me in front of random strangers", is the statement "I took it all in stride when my considerate friend made fun of me in front of a bunch of people I didn't even know." is true?
- Yes
- No
- I don't know |
$$10\times20\times30\times40=(1\times2\times3\times4)\times10^{4}=24\times10^{4}$$. | $$10^{4}$$ | TAL-SCQ5K | $$10\times20\times30\times40=24\times$$．
- $$10^{3}$$
- $$10^{4}$$
- $$10^{5}$$
- $$10^{6}$$ |
Waiting in line for a flight especially close to take off time is often very frustrating because there are so many people and the wait is usually long and there are chances of missing the flight, so feeling cool, calm and collected in that situation is not very likely. | No | FLUTE | Context: I get anxious whenever I'm waiting in line for a flight and it's less than 30 minutes from take off.
Hypothesis: I always feel cool, calm and collected when I am waiting in line for a flight and it's close to take off time.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Since 80% of the people were adults, this means 100% - 80% = 20 % were children.
20% of the people vaccinated were children. The number of children is 20% of 650.
20% = 0.2, so 0.2 * 650 = 130 children were vaccinated. | 130 | gsm8k | A clinic administered the covid vaccine to 650 people. 80% of the people were adults. How many of the vaccinated people were children? |
Heisenberg sells a total of $80/5= 16 capsules of 100 mg amoxicillin every week.
So, the total number of 100 mg amoxicillin he sells every 2 weeks is 16 x 2= 32.
And he sells $60/2= 30 capsules of 500 mg amoxicillin every week.
So, the total number of 500 mg amoxicillin he sells every 2 weeks is 30 x 2= 60.
Therefore, the total number of capsules he sells every 2 weeks is 60 + 32 = 92. | 92 | gsm8k | Heisenberg owns a pharmacy. He earned a total of $80 from 100 mg amoxicillin and $60 from 500 mg amoxicillin every week. If each capsule of 100 mg amoxicillin costs $5 and each capsule of 500 mg amoxicillin costs $2, how many capsules of amoxicillin does he sell every 2 weeks? |
We will use complementary counting. First, the frog can go left with probability $\frac{1}{4}$. We observe symmetry, so our final answer will be multiplied by $4$ for the $4$ directions, and since $4 \cdot \frac{1}{4}=1$, we will ignore the leading probability. From the left, she either goes left to another edge $\left(\frac{1}{4}\right)$ or back to the center $\left(\frac{1}{4}\right)$. Time for some casework. Case 1: She goes back to the center. Now, she can go in any $4$ directions, and then has $2$ options from that edge. This gives $\frac{1}{2}$. Case 2: She goes to another edge (rightmost). Subcase 1: She goes back to the left edge. She now has $2$ places to go, giving $\frac{1}{2}$ Subcase 2: She goes to the center. Now any move works. $\frac{1}{4} \cdot \frac{1}{2}+\frac{1}{4} \cdot 1=\frac{1}{8}+\frac{1}{4}=\frac{3}{8}$ for this case. She goes back to the center in Case 1 with probability $\frac{1}{4}$, and to the right edge with probability $\frac{1}{4}$ So, our answer is $\frac{1}{4} \cdot \frac{1}{2}+\frac{1}{4} \cdot \frac{3}{8}=\frac{1}{4}\left(\frac{1}{2}+\frac{3}{8}\right)=\frac{1}{4} \cdot \frac{7}{8}=\frac{7}{32}$ But, don\textquotesingle t forget complementary counting. So, we get $1-\frac{7}{32}=\frac{25}{32} \Longrightarrow D$. | d | TAL-SCQ5K | Frieda the frog begins a sequence of hops on a $3 \times 3$ grid of squares, moving one square on each hop and choosing at random the direction of each hop-up, down, left, or right. She does not hop diagonally. When the direction of a hop would take Frieda off the grid, she "wraps around" and jumps to the opposite edge. For example if Frieda begins in the center square and makes two hops "up", the first hop would place her in the top row middle square, and the second hop would cause Frieda to jump to the opposite edge, landing in the bottom row middle square. Suppose Frieda starts from the center square, makes at most four hops at random, and stops hopping if she lands on a corner square. What is the probability that she reaches a corner square on one of the four hops?
a: $\frac{9}{16}$
b: $\frac{5}{8}$
c: $\frac{3}{4}$
d: $\frac{25}{32}$
e: $\frac{13}{16}$ |
A grey frostbitten log resembles a dead body, not somebody who is a live | Yes | FLUTE | Context: You're only noticed when you're alive.
Hypothesis: Nobody notices until your body is found, like a gray frostbitten log.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
Pressing against the wall with all her strength means that she was trying to push the wall with all her might. | Yes | FLUTE | Consider the staetement "She pushed against the wall with all her strength.". Based on this statement, is "She pressed against the wall with all her strength." a true statement? Yes/no/unknown |
The total number of books in the warehouse is $1335\cdot 39$. If Melvin packs $b$ boxes of $40$ books each and has $r$ books left over, then $1335\cdot 39 = 40b+r$. Thus, what we are looking for is the remainder when $1335\cdot 39$ is divided by $40$.
We note that $39\equiv -1\pmod{40}$. Therefore, we have \begin{align*}
1335\cdot 39 &\equiv 1335\cdot (-1) \\
&\equiv -1335\pmod {40}.
\end{align*}Now we note that $-1335 = -1400 + 65$, and $-1400$ is a multiple of $40$. Therefore, $-1335 \equiv 65 \equiv 25\pmod{40}$, which implies that the remainder is $25$ books. | $25$ | competition-math | In a certain warehouse, there are $1335$ boxes, each containing $39$ books.
Melvin's boss orders him to unpack all the books and repack them so that there are $40$ books in each box. After packing as many such boxes as possible, Melvin has how many books left over? |
Compared with a less powerful device, a more powerful device can either do more work in the same time or do the same work in less time. | (B) | quartz | Robin has an old computer that runs slowly, and Bryan has a powerful new computer. When working on the same task, the computer that will finish the task first is
Options:
(A) Robin's
(B) Bryan's |
$$8002-2008=(8002+1)-(2008+1)=8003-2009$$. | $$8003$$ | TAL-SCQ5K | $$8002-2008=$$$$-2009$$.
$$9003$$
$$9002$$
$$8003$$
$$8002$$ |
Friday is associated with Venus in astrology. Venus is the densest of the terrestrial planets. | Yes | strategyqa | Would an astrologer focus on the densest terrestrial planet for a Friday horoscope? |
P. G. Wodehouse was born in 1881. The internet was not conceived of until 1965. | No | strategyqa | Did P. G. Wodehouse like the internet as a child? |
A kid at her first parade would be very excited and enthusiastic about the event, so Miranda is waving enthusiastically. | No | FLUTE | Consider the statement "Eve got into the big, black hearse and Miranda waved back enthusiastically.". Is the statement "Eve waved and got into the big, black hearse, and miranda waved back like a kid at her first parade" false? Yes/no/unknown |
Carlson bought land that cost $20 per square meter, therefore the size of the land he bought is 8000/20 = 400.
And the size of the other land he bought is 4000/20 = 200.
Therefore the total size of the land he owns is 400+200+300 = 900. | 900 | gsm8k | Carlson bought land that cost $8000 and additional land that cost $4000. He initially owned 300 square meters of land. If the land he bought costs $20 per square meter, how big is his land after buying the new land? |
因为$${{x}^{m+2}}{{y}^{2}}+3x{{y}^{3}}{{z}^{2}}$$是齐次多项式，并且第二个单项式的次数为$$6$$， 所以$$m+2+2=6$$，即$$m=2$$． 故选$$\text{B}$$． | 2 | TAL-SCQ5K | 如果一个多项式的各项的次数都相同，则称该多项式为齐次多项式．例如：$${{x}^{3}}+2x{{y}^{2}}+2xyz+{{y}^{3}}$$是$$3$$次齐次多项式．若$${{x}^{m+2}}{{y}^{2}}+3x{{y}^{3}}{{z}^{2}}$$是齐次多项式，则$$m$$等于．
Options:
1. $$1$$
2. $$2$$
3. $$3$$
4. $$4$$ |
Realizing that the bread from the sandwich you ate was moldy would make anyone feel sick and not healthy at all. | Yes | FLUTE | Given the statement "I ate half a sandwhich before realizing the bread was moldy.", is the statement "I felt healthy after realizing the bread from the sandwich I ate was moldy" wrong?
- Yes
- No
- Unknown |
Nick's sister is 13 + 6 = 19 years old.
Their combined age is 19 + 13 = 32 years old.
Their brother is 32/2 = 16 years old.
In 5 years, their brother would be 16 + 5 = 21 years old. | 21 | gsm8k | Nick is 13 years old. His sister is 6 years older and their brother is half their combined age. How old would their brother be in 5 years? |
Exhaling, or breathing out, decreases the size of the chest, which increases air pressure inside the lungs. | b | quartz | Jeff takes a breath and lets it out. When do his lungs experience the most air pressure?
a. after inhaling
b. after exhaling |
Henry gets paid 5 + 13 = $18 for each bike painted and sold.
In total, Henry will be paid 8 * 18 = $144 for painting and selling 8 bikes. | 144 | gsm8k | For every bike Henry sells, he is paid $8 more than he is paid to paint the bike. If Henry gets $5 to paint the bike, how much does he get paid to sell and paint 8 bikes? |
To run a mile means to avoid something in any way possible, but the context describes trying really hard to go through with it. | No | FLUTE | Consider the staetement "She 'll try really hard to go through with it.". Based on this statement, is "She 'll run a mile." a true statement? Yes/no/unknown |
Cramming is often not an effective way to study for a test and getting questions wrong after doing it for four days means that the person lacks intelligence and is not a genius | No | FLUTE | Consider the staetement "I spent the last 4 days cramming for this final, but still ended up having to guess on some of the questions on the test.". Based on this statement, is "I felt like such a genius when I found out that I got some of the questions wrong on the test after spending the last 4 days cramming" a true statement? Yes/no/unknown |
She planted eight trees. This means she used half of that amount of apples, which is 8 trees / 2 trees/apple = 4 apples.
That means that she planted four of the six apples she bought, leaving only 6 apples - 4 apples = 2 apples to be eaten. | 2 | gsm8k | Mary bought six apples from the store. From the apples she bought, for each that Mary ate, she planted two trees from the remaining ones. How many apples did Mary eat? |
Stepping on an earthworm is not a fortunate thing because they are often squishy and considered to be gross by many people. | No | FLUTE | Consider the staetement "I was walking bare feet outside and stepped on an earthworm.". Based on this statement, is "I was innocently walking outside bare feet and fortunately stepped on a beautiful earthworm." a true statement? Yes/no/unknown |
Lee and his friend had a total of $10 + $8 = $18.
The cost of the food was $6 + $4 + $1 + $1 = $12.
The total cost, including tax was $12 + $3 = $15.
They should have received $18 - $15 = $3 in total. | 3 | gsm8k | Lee had $10 and his friend had $8. They went to a restaurant where they ordered chicken wings for $6 and a chicken salad for $4. They also got 2 sodas for $1.00 each. The tax came to $3. How much change should they have received in total? |
There are 109 fifth graders + 115 sixth graders + 118 seventh graders = 342 students going on the trip.
There are 4 teachers + 2 parents = 6 adults going on the field trip for each grade.
There are 3 grades going, so 3 grades x 6 adults/grade = 18 total adults going on the trip.
There are 342 students + 18 adults = 360 people going on the trip.
So, 360 people / 72 seats = 5 buses | 5 | gsm8k | Stoney Hollow Middle School is taking a field trip to the zoo. There are 109 fifth graders, 115 sixth graders, and 118 seventh graders. There are 4 teachers and 2 parents from each grade coming along to chaperone on the trip. There are 72 seats on each school bus. How many buses are needed for the field trip? |
假设正方形、长方形、圆的周长都是$$16$$厘米，则： （$$1$$）正方形的边长：$$16\div 4=4$$（厘米）， 面积：$$4\times 4=16$$（平方厘米）； （$$2$$）假设长方形的长为$$6$$厘米，宽为$$2$$厘米， 则面积：$$2\times 6=12$$（平方厘米）； （$$3$$）圆的半径：$$16\div 3.14\div 2=\frac{800}{314}$$（厘米）， 面积：$$3.14\times \left( \frac{800}{314} \right)\times \left( \frac{800}{314} \right)$$ $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde=3.14\times \frac{800}{314}\times \frac{800}{314}$$ $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde=\frac{6400}{314}$$ $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde=20\frac{60}{157}$$（平方厘米）； 所以，$$12$$平方厘米$$\textless{}16$$平方厘米$$\textless{}20\frac{60}{157}$$平方厘米， 所以$$\text{A}$$选项是正确的． | a | TAL-SCQ5K | 周长都相等的圆，正方形和长方形，它们的面积相比．
a) 圆最大
b) 正方形最大
c) 长方形最大
d) 一样大 |
The zodiac sign for late September is Libra. The Libra zodiac sign is represented by scales. Home Depot sells a number of scales including Pelouze and Ozeri brands. | Yes | strategyqa | Does Home Depot sell item in late September zodiac sign symbol? |
Billy has $25 less than twice Sam's money, or 2 * $75 - $25 = $150 - $25 = $125.
Together they have $75 + $125 = $200. | 200 | gsm8k | Billy has $25 less than twice the money Sam has. If Sam has $75, how much money do they have together? |
When someone kisses another person of the opposite sex while in a relationship it is often seen as a form of cheating and can lead to feelings of betrayal | No | FLUTE | Given the statement "I felt betrayed when my girlfriend kissed another guy at a party.", is the statement "I was let down when my girlfriend kissed another guy at the party" wrong?
- Yes
- No
- Unknown |
A checkerboard has a black and white color pattern in a grid formation, while a single sheet of black would be one solid color | No | FLUTE | Consider the staetement "The queen reclined on a white and gold divan, and all around her stretched a floor made of a single, uninterrupted sheet of black.". Based on this statement, is "The queen reclined on a white and gold divan, and all around her stretched a floor like a great checkerboard ." a true statement? Yes/no/unknown |
除数$$=(472-427)\div 5=9$$，$$472\div 9=52\cdots \cdots 4$$，所以余数是$$4$$． | a | TAL-SCQ5K | 童童在计算有余数的除法时，把被除数$$472$$错看成了$$427$$，结果商比原来小$$5$$，但余数恰好相同，那么这个余数是（~~~~~~~ ）．
a) $$4$$
b) $$5$$
c) $$6$$
d) $$7$$ |
A sum of $5 is not a lot of money and hence someone feeling great and benevolent for contributing that much to a birthday party is being ironic and is actually ashamed | Yes | FLUTE | Consider the statement "I should be helping chip in on a friend's birthday, but I only put in $5". Is the statement "I feel great and extremely benevolent for contribute a massive sum of $5 to my friend's birthday party" false? Yes/no/unknown |
A branch jutting from a tree is typically thin, not wide, since it extends over the main body of the tree | No | FLUTE | Given the statement "His nose was rather wide.", is the statement "His nose was like a branch jutting from a tree." is true?
- Yes
- No
- I don't know |
To have one's jaw drop is to be so shocked that one's mouth literally opens wide in surprise, but this context describes being not at all shocked and playfully hitting someone's shoulder. | No | FLUTE | Given the statement "I was not at all surprised hitting his shoulder playfully.", is the statement "My jaw dropped and I hit his shoulder playfully." is true?
- Yes
- No
- I don't know |
Parents usually want their children to do well in school and graduate which is why finding out that one's son has dropped out of college without even informing them would not make the parent proud but rather disappointed. | False | FLUTE | Context: "Last month I found out my son decided to drop out of college without telling me." Claim: "I was proud when I found out last month that my son decided to drop out of college without telling me"
Considering the context, is the claim true, false, or unknown? |
Between Shop A and Shop B he buys 150 bottles+180 bottles=330 bottles
Thus he can buy 550 bottles-330 bottles=220 bottles from shop C | 220 | gsm8k | Don buys recyclable bottles in a small town. Shop A normally sells him 150 bottles, shop B sells him 180 bottles and Shop C sells him the rest. How many bottles does Don buy from Shop C if he is capable of buying only 550 bottles? |