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There are 6 toddlers, which means that the children’s home has 5 teenagers/toddler * 6 toddlers = 30 teenagers
Diana will be shopping for 40 children - 30 teenagers - 6 toddlers = 4 newborns | 4 | gsm8k | Diana wants to buy winter clothes for all the 40 children at her local children's home. The home has five times as many teenagers as toddlers. There are also some newborns. If there are 6 toddlers, for how many newborns will Diana be shopping? |
The total spent on both pairs of jeans was $110 - $40 - $30 = $40.
One pair of jeans would cost $40 / 2 = $20. | 20 | gsm8k | To get ready for the new school year, Mary brought her two kids shopping. She bought her son James, a coat for $40 and two pairs of jeans. She bought his sister Jamie, a pair of shoes for $30. The total cost of the items was $110. If the two pairs of jeans for James cost the same price, how much did one pair of jeans cost? |
A clear, cloudless summer sky is blue, whereas a dull, gray sky is not | No | FLUTE | Consider the statement "They were dull and gray.". Based on this "They were like a clear, cloudless summer sky ." a true statement? Yes, no, or I don't know? |
The amount of money deducted from Adam's daily pay is $40 / 10 = $4.
So after deducting 10%, Adam’s daily pay is $40 – $4 = $36.
This means that in 30 days he earns $36 * 30 = $1080. | 1,080 | gsm8k | Adam earns $40 daily in his job. 10% of his money is deducted as taxes. How much money will Adam have earned after taxes after 30 days of work? |
An Emblem is a type of representation, here it means the songs represent something that is rebellious. | Yes | FLUTE | Consider the statement "Berry 's songs are plausible representations of rock'n'roll rebellion or , at any rate , youthful hedonism .". Based on this "Berry 's songs are plausible emblems of rock'n'roll rebellion or , at any rate , youthful hedonism ." a true statement? Yes, no, or I don't know? |
His entire purchase cost $20 - $4 = $16.
The chocolate bars cost 5 * $2 = $10.
The bags of chips cost a total of $16 - $10 = $6.
Each bag of chips cost $6 / 2 = $3. | 3 | gsm8k | Frank goes to the store to buy some food. He buys 5 chocolate bars and 2 bags of chips. He hands the cashier $20 and gets $4 back as change. If the chocolate bars each cost $2, how much did each bag of chips cost? |
College students typically must submit assignments via email, web portal, or on paper. Most colleges have on-campus fax machines available for student use. | No | strategyqa | Do most college students own a fax machine? |
当画的线段的两个端点都在整点上时，线段$$AB$$盖住$$2009$$个整点；当画的线段的两个端点都不在整点上时，线段$$AB$$盖住$$2008$$个整点；所以长为$$2008$$厘米的线段$$AB$$，至少可盖住数轴上$$2008$$个整点． 故选$$\text{C}$$． | $$2008$$个 | TAL-SCQ5K | 在数轴上，坐标是整数的点称为``整点''．设数轴的单位长度是$$1$$厘米，在这个数轴上随意画出一条长为$$2008$$厘米的线段$$AB$$，则线段$$AB$$盖住的整点至少有．
Options:
$$2006$$个
$$2007$$个
$$2008$$个
$$2009$$个 |
To be hindered by something means to be held back or impeded by it, while to be boosted by something means to be helped or supported by it. | No | FLUTE | Given the statement "But their work is boosted by lack of money.", is the statement "But their work is hindered by lack of money ." is true?
- Yes
- No
- I don't know |
An oracle is a person who is considered to be a source of wise counsel or prophetic opinion, so if the predictions made by the oracle are inaccurate, then that would be a contradiction | No | FLUTE | Consider the staetement "Your predictions have always been inaccurate". Based on this statement, is "You are an oracle whose predictions have always come like highly researched hypotheses." a true statement? Yes/no/unknown |
The maximum sum is $$6+6=12$$, so "the sum of dots is $$13$$" is an impossible event; so $$\text{D}$$ is the answer. | (4) | TAL-SCQ5K | Throw two dice of the same quality and size. The six sides of each die are marked with number of dots from $$1$$ to $$6$$. Among the following options,~\uline{~~~~~~~~~~}~is an impossible event.
Options:
(1) The sum of dots is $$12$$.
(2) The sum of dots is smaller than $$3$$.
(3) The sum of dots is larger than $$4$$ but smaller than $$8$$.
(4) The sum of dots is $$13$$. |
If a restaurant has not been cleaned in a long time it has a horrible odor and is not amazing at all. | No | FLUTE | Given the statement "I recently went to eat a restaurant and the whole place had an odd odor and made me uncomfortable.", what is the statement "Recently, I ate at a restaurant and the whole place smelled amazing, like it had not been cleaned in years." true?
- Yes
- No
- Unknown |
The idiom better late than never means that the delayed occurrence or achievement of something is better than it not happening at all, but this sentence describes a situation where there is no need for it to have happened earlier. | No | FLUTE | Consider the statement "Mike nods and trots over c because it's happening now and there's no need for it to have happened earlier.". Based on this "Mike nods and trots over c better late than never." a true statement? Yes, no, or I don't know? |
To catch my eye means to attract my interest, but in this sentence the girl was avoiding my gaze | No | FLUTE | Given the statement "After a couple of more songs, a familiar-looking blonde girl that had been avoiding my gaze all night asked me to play lips of an angel.", is the statement "After a couple of more songs, a familiar-looking blonde girl that had been trying to catch my eye all night asked me to play lips of an angel." is true?
- Yes
- No
- I don't know |
The girl's passion for dance is strong and it flows through the air. | True | FLUTE | Context: "Her passion is flowing through the air."
Hypothesis: Her passion is streaming through the air.
Based on the context, is the hypothesis true, false, or unknown? |
Amy Winehouse died in 2011. Brexit began in 2017. | No | strategyqa | Was Amy Winehouse familiar with Brexit? |
It will take 1.5 days x 2 = 3 days to explore 2 islands.
So, the pirates will walk 20 miles x 3 days = 60 miles to explore two islands.
The other 2 islands will be explored by walking 25 miles x 3 days = 75 miles.
Thus, the pirates will need to walk 60 + 75 = 135 miles to explore the 4 islands. | 135 | gsm8k | The pirates plan to explore 4 islands. Two islands require walking 20 miles per day while the other two islands require 25 miles per day. How many miles will they have to walk if it takes 1.5 days to explore each island? |
Aziz was born in the year 2021 - 36 years = 1985.
Therefore, Aziz's parents had been living in America for 1985 - 1982 = 3 years. | 3 | gsm8k | Aziz's parents moved to America in 1982. The year is 2021 and Aziz just celebrated his 36th birthday. How many years had his parents been living in America before Aziz was born? |
如果甲瓶盐水为$$a$$升，则含盐$$5a \%$$，如果乙瓶盐水为$$b$$升，则含盐$$10 \%b$$，依照浓度的计算公式，混合后盐水的浓度是：$$\frac{5 \%a+10 \%b}{a+b}$$，因为不知$$a$$和$$b$$的数值，所以两瓶混合后盐水的浓度不能确定． | 不能确定 | TAL-SCQ5K | 甲瓶盐水浓度为$$5 \%$$，乙瓶盐水浓度为$$10 \%$$，两瓶混合后盐水的浓度（~ ）．
Options:
- 是$$5 \%$$
- 是$$10 \%$$
- 是$$7.5 \%$$
- 不能确定 |
Music is an art form whose medium is sound. Music can help elevate or subdue emotions. People connect to music through the sound. The military uses loud music to cause psychological disorientation and confusion. The military calls the use of loud disorienting music part of psychological operations. | Yes | strategyqa | Can music be used as a weapon? |
To swallow men's hearts means to winning everyone while to have no attention mean men were not interested into her. | Yes | FLUTE | Consider the statement "She did not capture attention of all the men.". Is the statement "She swallowed all the men's hearts." false? Yes/no/unknown |
Lighter, more streamlined vehicles need less energy. | b | quartz | If Jon adds more weight to his car, he will need to use _____ energy.
Options:
a. less
b. more |
Braelynn bought 1/3*24 = 8 more knives to add to her kitchen.
The total number of knives in her kitchen is now 24+8 = 32 knives
In her kitchen, Braelynn currently has 2*24 = 48 teaspoons.
When she buys 2/3 times more teaspoons, the total number increases by 2/3*48 = 32.
So she will have a total of 32+48 = 80 teaspoons.
The total number of cutlery pieces Braelynn will have in her kitchen is 80+32 = 112 | 112 | gsm8k | Braelynn has 24 knives in her kitchen and twice as many teaspoons as knives. If she bought 1/3 as many additional knives and 2/3 as many additional teaspoons, what would be the total number of cutlery pieces she has in her kitchen? |
To give it a whirl means to try something out, but in this sentence not trying it out is the only way to know. | False | FLUTE | Context: "We'll never know unless we don't try it out." Claim: "We 'll never know unless we give it a whirl."
Considering the context, is the claim true, false, or unknown? |
As the distance between the objects increases the magnetic force of attraction decreases. | [A] | quartz | Planets moving closer together will have _____ magnetic attraction.
[A] less
[B] more |
A tandem bike has seats for more than one rider. A triples tandem bike has three seats and can support three riders. The crew of Apollo 15 consisted of three people. | Yes | strategyqa | Would a triples tandem bike support Apollo 15 crew? |
The thinner the wire, the more resistance it offers. | (1) | quartz | Robin is using aluminum foil to make small cylinders. A foil cylinder of diameter 1cm likely has _____ resistance than a foil cylinder of diameter 10cm.
(1) greater
(2) less |
The president can be any one of the 20 members, and the vice-president can be any one of the 9 remaining members of the same sex. The answer is $20\times 9=180$. | $180$ | competition-math | Our club has 20 members, 10 boys and 10 girls. In how many ways can we choose a president and a vice-president if they must be of the same gender? Assume no one can hold both offices. |
Obviously, multiplying out each of the exponents is not an option. Instead, notice that the bases of all three exponents are themselves powers of $2$. Let's convert the bases to $2$: $$ 8^8 \cdot 4^4 \div 2^{28} = (2^3)^8 \cdot (2^2)^4 \div 2^{28}.$$Using the power of a power rule in reverse, $(2^3)^8 = 2^{3 \cdot 8} = 2^{24}$. Likewise, $(2^2)^4 = 2^{2 \cdot 4} = 2^8$. Therefore, our simplified expression is $2^{24} \cdot 2^8 \div 2^{28}$.
Now, using the product of powers rule, $2^{24} \cdot 2^8 = 2^{24 + 8} = 2^{32}$. Our expression is now stands at $2^{32} \div 2^{28}$. Finally, we'll use quotient of powers to simplify that to $2^{32-28} = 2^4 = 16$. | $16$ | competition-math | Find $ 8^8 \cdot 4^4 \div 2^{28}$. |
A makeup artist putting lipstick on a pig would be seen as someone abnormal and crazy. | True | FLUTE | Context: "Rory looked at her as if she were crazy" Claim: "Rory looked at her as if she were like a makeup artist putting lipstick on a pig."
Considering the context, is the claim true, false, or unknown? |
A dream is something that isn't real, it's just a figment of our imagination, similar to that, life also could be just a delusion, something that isn't really happening and is just an illusion. | True | FLUTE | Context: "Life is just a delusion, something illusory." Claim: "Life is just a dream in the night."
Considering the context, is the claim true, false, or unknown? |
Given that Granny is $$5$$ times older than each of the three triplets, we know that the age of each triplet is $$120\div (5+3)= 15$$. So Cara, Cate and Chris were born in $$2007$$. | $$2007$$ | TAL-SCQ5K | Granny and the triplets Cara, Cate and Chris all have their birthdays today. The ages of all four of them total $$120$$ years. Granny is $$5$$ times as old as each of the triplets. When were the triplets born?
Options:
- $$2000$$
- $$2002$$
- $$2004$$
- $$2007$$
- $$2009$$ |
It is generally considered morally wrong to steal and so people often feel guilty when they have to do it, especially when the person they are stealing from is a close family member like a daughter | True | FLUTE | Context: "I stole money from my daughter's piggy bank and now she's wondering where her money went" Claim: "I feel really guilty that I had to steal money from my daughter's piggy bank and she has no idea"
Considering the context, is the claim true, false, or unknown? |
More particles inside the container means more collisions, and more collisions mean a higher pressure. | (2) | quartz | If we keep deflating a balloon of oxygen particles what happens to the pressure?
(1) increases
(2) decreases |
The person who cut in front of someone else and caused them to miss their turn is usually considered to be very rude and selfish and so thanking the entire universe for them is not really a rational thought. | Yes | FLUTE | Given the statement "Recently a person cut in front of me in line at the super market and I was very upset about it.", is the statement "I thanked the entire universe for introducing me to the person who cut in front of me in line and caused me to miss my turn." wrong?
- Yes
- No
- Unknown |
Being broken up with by someone who you've been in a relationship with for a long time is often devastating and so feeling delighted is not accurate or justified. | False | FLUTE | Context: "My girlfriend of 10 years broke up with me yesterday." Claim: "I feel really delighted that my girlfriend of 10 years broke up with me yesterday."
Considering the context, is the claim true, false, or unknown? |
A friend bailing on someone last minute after work is not a good thing because it leaves them feeling alone and unappreciated. | No | FLUTE | Given the statement "Was supposed to hang out with my friend after work but turns out she has to work late.", is the statement "My friend bailed on me last minute after work, which makes me feel really appreciated" is true?
- Yes
- No
- I don't know |
Ellie is $$6$$ years older than Lola, and Maddie is $$2$$ years older than Lola. Therefore Ellie is $$4$$ years older than Maddie. | (3) | TAL-SCQ5K | Maddie is $$2$$ years older than Lola, and Lola is $$6$$ years younger than Ellie. How much older is Ellie than Maddie?
(1) $$2$$ years
(2) $$3$$ years
(3) $$4$$ years
(4) $$5$$ years
(5) $$6$$ years |
$\dfrac{1}{4}$kangyear x~$\dfrac{20\textbackslash{} kangmonths}{1\textbackslash{} kangyear}$~x~$\dfrac{6\textbackslash{} kangweeks}{1\textbackslash{} kangmonth}$~= 30 kangweeks. | $$30$$ | TAL-SCQ5K | On Kangaroo planet each kangyear has 20 kangmonths and each kangmonth has 6 kangweeks, How many kangweeks are there in one quarter of a kangyear?
- $$9$$
- $$30$$
- $$60$$
- $$90$$
- $$120$$ |
$$5$$，$$a$$，$$b$$，$$c$$，$$4035$$是等差数列， 则$$5$$，$$b$$，$$4035$$也是等差数列， 则$$b=\left( 4035+5 \right)\div 2$$ $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde=4040\div 2$$ $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde=2020$$． 选$$\text{D}$$． | [D] | TAL-SCQ5K | 已知$$5$$，$$a$$，$$b$$，$$c$$，$$4035$$这五个数成等差数列，则$$b=$$． We know that $$5$$, $$a$$, $$b$$, $$c$$, and $$4035$$ are five numbers in an equal series, then $$b = $$．
[A] $$2017$$
[B] $$2018$$
[C] $$2019$$
[D] $$2020$$ |
Justice currently has 3 + 5 + 7 = 15 plants in her house
Justice needs 24 - 15 = 9 more plants | 9 | gsm8k | Justice has 3 ferns, 5 palms, and 7 succulent plants in her house. If she wants a total of 24 plants in her home, how many more plants does she need? |
Losing a family pet can be a really sad and difficult experience for someone, so it is unlikely that they would consider it to be one of the happiest things they have ever experienced. | No | FLUTE | Given the statement "Losing your family pet after 10 years is one of the hardest things I have had to do", is the statement "One of the happiest things I have ever experienced was losing my family pet after 10 years" is true?
- Yes
- No
- I don't know |
NA | (3) | TAL-SCQ5K | Three zebras take part in a contest. The winner is the zebra with the most number of stripes. QingLe has $$15$$ stripes, ChenXi has $$3$$ more than QingLe. QingLe has $$5$$ fewer stripes than YueYing. How many stripes does the winner have?
(1) $$16$$
(2) $$18$$
(3) $$20$$
(4) $$21$$
(5) $$23$$ |
During dinner time, Yves and his siblings ate 16/4 = 4 slices.
So the next day, there were still 16 - 4 = 12 slices left.
The next day, Yves ate 12/4 = 3 slices of pizza.
Thus, there were 12 - 3 = 9 slices left.
Then, his two siblings ate 2 x 2 = 4 slices of pizza.
Therefore, there were still 9 - 4 = 5 slices of pizza left. | 5 | gsm8k | Yves and his siblings ordered pizza and asked to have it cut into 16 slices. During dinner time, they only ate one-fourth of it. The next day, Yves ate one-fourth of the remaining pizza. Then his two siblings ate 2 slices each. How many slices of pizza were left? |
Donny has 78 - 8 = 70 after paying for the kite.
He has 70 - 9 = $61 left after buying the frisbee as well as the kite. | 61 | gsm8k | Donny has $78 in his piggy bank. If Donny buys a kite for $8 and a frisbee for $9. How much money does Donny have left? |
For example, consider a dataset with the following values: 0, 2, 2, 3, 3. The mean of this dataset is $2$, and the $25$-th percentile is also $2$. | B | TAL-SCQ5K | True or False: It is impossible for the $25$-th percentile to be equal to the mean.
Options:
A. True
B. False |
Feeling anger is a natural response to someone tattling on you to your boss because it can lead to consequences such as getting fired | False | FLUTE | Context: "I was so furious when my coworker badmouthed me to my boss."
Hypothesis: I felt not even a single streak of anger when my coworker tattled on me to my boss.
Based on the context, is the hypothesis true, false, or unknown? |
Gluons make quarks attract each other more strongly the farther apart the quarks get. | [B] | quartz | When there are high levels of gluons in quarks it becomes
Options:
[A] weaker
[B] stronger |
More recently, the death rate has fallen because of the availability of more food and medical advances. | [a] | quartz | If Mona lives in a country with poor access to food and another country begins reducing food supplies of her country, what happens to the death rate in Mona's country?
Options:
[a] increases
[b] decreases |
Climbing steeply means that the prices are increasing very quickly. | Yes | FLUTE | Consider the staetement "Prices are getting increasingly expensive .". Based on this statement, is "Prices climbed steeply." a true statement? Yes/no/unknown |
Quilted with snow means that the mountain was covered in snow. | Yes | FLUTE | Given the statement "There was snow on the entire mountain.", is the statement "The mountain was quilted with snow." is true?
- Yes
- No
- I don't know |
A public restroom is not a place where anyone would want to smell manure and so the smell coming from it would be unpleasant and not wonderful. | No | FLUTE | Context: I feel like vomiting when I walk into a public restroom and it smells like manure.
Hypothesis: I feel wonderful when I walk into a public restroom and smell the manure-like stench
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Popularity generally refers to the number of friends someone has and therefore, if someone has no friends, they cannot be popular. | Yes | FLUTE | Given the statement "I'm sad because I have no friends and I don't like my own company.", is the statement "I feel really popular because I don't have any friends to talk to and I also don't like spending time with myself" wrong?
- Yes
- No
- Unknown |
$$10\times20\textbackslash\%+40\times 25\textbackslash\%=12$$ grams. $$(10+40)-12\div40\textbackslash\%=20$$ grams. | $$20$$ grams | TAL-SCQ5K | Amy mixes $$10$$ grams of a $$20\textbackslash\%$$ sugar solution and $$40$$ grams of a $$25\textbackslash\%$$ sugar solution together. After~\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of solution is $40\textbackslash\%$.
Options:
* $$15$$ grams
* $$18$$ grams
* $$20$$ grams
* $$25$$ grams |
A house fire is a tragic accident that often results in people losing all their belongings | No | FLUTE | Context: My house caught on fire and I lost all my belongings.
Hypothesis: I lost all my belongings and my house burned down in a tragic accident
Is the hypothesis incorrect? (Yes, no, or unknown)? |
Start with $3^{}p+3^{4}=90$. Then, change $3^{4}$ to $81$. Subtract from $81$ from both sides to get $3^{}p=9$ and see that $p$ is $2$. Now, solve for $r$. Since $2^{}r+44=76$, $2^{}r$ must equal $32$, so $r=5$. Now, solve for $s$. $5^{3}+6^{}s=1421$ can be simplified to $125+6^{}s=1421$, which simplifies further to $6^{}s=1296$. Therefore, $s=4$. $prs$ equals $2\times5\times4$ which equals $40$. So, the answer is $40$. | b | TAL-SCQ5K | If $3^{}p+3^{4}=90$, $2^{}r+44=76$, and $5^{3}+6^{}s=1421$, what is the product of $p$, $r$, and $s$? (2013 AMC 8 Problem, Question \#15)
Options:
a) $$27$$
b) $$40$$
c) $$50$$
d) $$70$$
e) $$90$$ |
Henrietta Lacks' DNA was used and replicated by Johns Hopkins University without her family's knowledge or approval. Henrietta Lacks' family medical history was released by Johns Hopkins University without their knowledge. | No | strategyqa | Has Johns Hopkins University always treated subjects ethically? |
Let $n$ be the number of Dummies in one bag. Then we know $n\equiv 7\pmod 9$, so $$3n\equiv 3(7) = 21\equiv 3\pmod 9.$$Thus, when the Dummies in three bags are divided equally among $9$ kids, there is a remainder of $3$ leftover pieces.
We can also explain this solution without using modular arithmetic. Each bag can be divided equally among the $9$ kids with $7$ pieces from each bag left over. This makes $21$ leftover pieces, which are enough to give each kid $2$ more candies and have $3$ candies left over. Those last $3$ candies can't be divided equally among the kids, so the answer is $3$. | $3$ | competition-math | Every bag of Dummies (a chocolate candy) contains the same number of pieces.
The Dummies in one bag can't be divided equally among $9$ kids, because after each kid gets the same (whole) number of pieces, $7$ pieces are left over.
If the Dummies in three bags are divided equally among $9$ kids, what is the smallest number of pieces that could possibly be left over? |
Sam: $$\frac{2}{10}+\frac{3}{10}=\frac{5}{10}$$ Total: $$\frac{5}{10}+\frac{3}{10}=\frac{8}{10}$$ Left: $$\frac{10}{10}-\frac{8}{10}=\frac{2}{10}$$ | $$\frac{2}{10}$$ | TAL-SCQ5K | Ace and Sam were painting a house. Ace painted $$\frac{3}{10}$$ of the house. Sam painted $$\frac{2}{10}$$ more than Ace. What fraction of the house still needs to be painted?
* $$\frac{2}{10}$$
* $$\frac{3}{10}$$
* $$\frac{5}{10}$$
* $$\frac{8}{10}$$ |
按照从左往右的顺序计算． | $$3-3$$ | TAL-SCQ5K | 这个算式要按照什么顺序计算呢． $$1+2-3+1$$
$$3-3$$
$$1-3$$
$$2-3$$
$$1+1$$ |
There are 7 days in a week and they're going for 2 weeks so that's 7*2 = 14 days
The daily rate is $125.00 and they are staying for 14 days so that's 125*14 = $1,750.00
There is also a $100.00 pet fee on top of their rental fee of $1,750.00 so that's 100+1750 = $1850.00
There is a 20% fee on the $1,850.00 so the fee comes to .20*1850 = $370.00
The rental will costs $1,850.00 and there is $370.00 service/cleaning fee for a total of 1850+370 = $2,220.00
They need to pay 50% of the entire bill as a security deposit so that will be .5*2220 = $1,110.00 | 1110 | gsm8k | Lana and Mike are taking their dog and renting a cabin in the mountains for 2 weeks. The daily rate is $125.00 There is a $100.00 pet fee. There is also a 20% service/cleaning fee for the rental. They need to pay 50% of the entire bill as a security deposit. How much is their security deposit? |
Here one sentence is saying that they have a strong desire for something whereas in the other it is stated that they do are lacking the desire. | False | FLUTE | Context: "Let puritans and pessimists forgive , approve or dismiss these lack of appetites ; that is their loss ." Claim: "Let puritans and pessimists damn , disapprove or dismiss these appetites ; that is their loss ."
Considering the context, is the claim true, false, or unknown? |
To catch my eye means to attract my attention or interest, but in this sentence she did not do that | No | FLUTE | Given the statement "But she did not attract my attention or interest when I entered and flashed me a smile.", what is the statement "But she did catch my eye when I entered and flashed me a smile." true?
- Yes
- No
- Unknown |
Let H = Hezekiah's age
Ryanne = H + 7
2H + 7 = 15
2H = 8
H = 4
Hezekiah is 4 years old. | 4 | gsm8k | Ryanne is 7 years older than Hezekiah. Together Ryanne's and Hezekiah's ages equal 15 years. How many years old is Hezekiah? |
To be told in no uncertain terms means to be told very explicitly and emphatically, as is the case in this context. | Yes | FLUTE | Given the statement "And Jacob had been told very explicitly and emphatically that if he shoved his piece of wedding cake all over my mouth, mom was confiscating his snowmobile.", what is the statement "And jacob had been told in no uncertain terms that if he shoved his piece of wedding cake all over my mouth, mom was confiscating his snowmobile." true?
- Yes
- No
- Unknown |
Since we know that Hugo wins, we know that he rolled the highest number in the first round. The probability that his first roll is a $5$ is just the probability that the highest roll in the first round is $5$. Let $P(x)$ indicate the probability that event $x$ occurs. We find that $P$ (No one rolls a $6$)-$P$ (No one rolls a $5$ or $6$)$=P$ (The highest roll is a $5$), so $$ \begin{gathered} P(\text {No one rolls a } 6)=\left(\frac{5}{6}\right)^{4}, \textbackslash\textbackslash{} P(\text {No one rolls a } 5 \text { or } 6)=\left(\frac{2}{3}\right)^{4}, \textbackslash\textbackslash{} P(\text {The highest roll is a } 5)=\left(\frac{5}{6}\right)^{4}-\left(\frac{4}{6}\right)^{4}=\frac{5^{4}-4^{4}}{6^{4}}=\frac{369}{1296}=(\text {C}) \frac{41}{144} \text {. } \end{gathered} $$ | (3) | TAL-SCQ5K | In a particular game, each of $4$ players rolls a standard $6$-sided die. The winner is the player who rolls the highest number. If there is a tie for the highest roll, those involved in the tie will roll again and this process will continue until one player wins. Hugo is one of the players in this game. What is the probability that Hugo\textquotesingle s first roll was a $5$, given that he won the game?
(1) $\frac{61}{216}$
(2) $\frac{367}{1296}$
(3) $\frac{41}{144}$
(4) $\frac{185}{648}$
(5) $\frac{11}{36}$ |
Divorce is often very scary as a process and if one spouse has a lot of debt it can be a reason for the other spouse to want to divorce them | Yes | FLUTE | Given the statement "My wife is going to divorce me.", what is the statement "I am really scared that my wife is going to leave me because of the massive debt I have" true?
- Yes
- No
- Unknown |
Each bag has 240 calories because 24 x 10 = 240
He needs two bags because 480 / 240 = 2
It will cost $4 because 2 x 2 = 4 | 4 | gsm8k | Peter is eating chips. Each chip is 10 calories. A bag has 24 chips and costs $2. If he wants to eat 480 calories, how much does he have to spend on chips? |
Jebb paid $50 x 12/100 = $6 for service fee.
He paid $50 + $6 = $56 for the food and the service fee.
The total cost of everything is $56 + $5 = $61. | 61 | gsm8k | Jebb buys $50 worth of food at a restaurant with a service fee of 12%. After paying, he gives a $5 tip. How much money did he spend at the restaurant? |
Revealing someone's personal secret to other people is a betrayal of trust and so finding out that not just mutual friends, but also the entire internet knows about it would be horrifying for the person who the secret was revealed to. | No | FLUTE | Given the statement "A now ex-friend of mine revealed a very private secret I told her in confidence not only to our mutual friends but the entire internet!", is the statement "I am absolutely rooting for my now ex-friend for betraying my trust by revealing my very personal secret to not just our mutual friends, but also the entire internet!" is true?
- Yes
- No
- I don't know |
由余弦定理$${{a}^{2}}+{{b}^{2}}-2ab\cos \gamma ={{c}^{2}}$$，代入条件式得 $$2ab\cos \gamma =1988{{c}^{2}}$$，或$$\left( \frac{a}{b} \right)\left( \frac{b}{c} \right)\cos \gamma =994$$． 由下正弦定理$$\frac{a}{c}=\frac{\sin \alpha }{\sin \gamma }$$，$$\frac{b}{c}=\frac{\sin \beta }{\sin \gamma }$$， 于是$$\frac{\sin \alpha \sin \beta \cos \gamma }{{{\sin }^{2}}\gamma }=994$$． 因为$$\alpha +\beta +\gamma = \pi $$，所以$$\alpha +\beta = \pi -\gamma $$．从而$$\sin \left( \alpha +\beta \right)=\sin \gamma $$． $$\frac{\cot \gamma }{\cot \alpha +\cot \beta }=\frac{\sin \alpha \sin \beta \cos \gamma }{\sin \left( \alpha +\beta \right)\sin \gamma }=994$$． | (C) | TAL-SCQ5K | 设$$a$$，$$b$$，$$c$$是三角形的三边，$$\alpha $$，$$\beta $$，$$\gamma $$分别是相对于这三边的角，若$${{a}^{2}}+{{b}^{2}}=2021{{c}^{2}}$$，则$$\frac{\cot \gamma }{\cot \alpha +\cot \beta }=$$．
Options:
(A) $\dfrac{1}{2021}$
(B) $\dfrac{1}{1010}$
(C) $1010$
(D) $2021$ |
Jack's mother asked him to buy 2 * 4 = 8 bottles of water.
Thus Jack bought 4 + 8 = 12 bottles of water in total.
Altogether, the bottles of water cost 12 * $2 = $24.
The cheese cost 1/2 * $10 = $5.
So Jack spent $24 + $5 = $29 on water and cheese.
Since he started with $100, he now has $100 - $29 = $71 left. | 71 | gsm8k | Jack went to a supermarket with $100 and bought 4 bottles of water. Then his mother called him and asked him to buy twice as many bottles as he already bought. Each bottle cost $2. Finally, he also bought half a pound of cheese and 1 pound of cheese costs $10. How much money does Jack have remaining? |
解：根据$$3$$的倍数特征，不难判断$$83$$和$$98$$都不是$$3$$的倍数，$$99$$和$$96$$都是，但$$99\textgreater96$$，所以这两个数的最大值是$$99$$。 故选：B。 | b | TAL-SCQ5K | 两个正整数的和小于$$100$$，其中一个是另一个的两倍，则这两个正整数的和的最大值是（ ）
a. $$83$$
b. $$99$$
c. $$96$$
d. $$98$$ |
设最多在停车场停了$$x$$小时，$$3+\left( x-1 \right)\times 2\times 1.5=13.5$$，解得$$x=4.5$$，所以他们的车在停车场最多停$$4.5$$小时． | B | TAL-SCQ5K | 游览景区期间，爸爸将车放在停车场，收费标准为：不超过$$1$$小时收费$$3$$元，每多停半小时加收$$1.5$$元．爸爸最终一共交了$$13.5$$元的停车费，他们的车在停车场最多停了（~ ）小时．
A: $$4$$小时 ~~~
B: $$4.5$$小时~~
C: $$5$$小时
D: $$8$$小时 |
A funeral chamber is a room where someone who has died is kept before their funeral, and it is typically somber and not light and cheerful | Yes | FLUTE | Given the statement "The atmosphere was light and cheerful.", is the statement "The atmosphere was like a funeral chamber for some big shot human being." wrong?
- Yes
- No
- Unknown |
To terminate something means to bring it to an end, while to start something means to begin it. | No | FLUTE | Given the statement "They started off the dinner by pouring a lot of cognac.", what is the statement "They terminated off their dinner with a cognac." true?
- Yes
- No
- Unknown |
Since $$231=3\times7\times11$$, the sum of its prime factors is $$3 +7+11=21$$. | $$21$$ | TAL-SCQ5K | The sum of the prime factors of $$231$$ is．
Options:
$$21$$
$$22$$
$$152$$
$$383$$ |
To beat about the bush means to avoid talking directly about an unpleasant topic, so in this sentence she should get to the point instead of delaying. | No | FLUTE | Consider the statement "But then, she shouldn't delay in getting to the point, either.". Is the statement "But then, she shouldn't beat about the bush, either." false? Yes/no/unknown |
He bought 20*1.5=30 pounds of soap
That cost 30*.5=$15 | 15 | gsm8k | John buys 20 bars of soap each weighing 1.5 pounds for $.5 per pound. How much money did he spend on soap? |
The lakes are bordered on the north by Canada. The lakes are bordered on the south by United States. Canada and United States are two different countries. | Yes | strategyqa | Are the Great Lakes part of an international border? |
Andrew Johnson was the 17th president of the United States. Elagabalus was the 25th Roman Emperor. | No | strategyqa | Does Andrew Johnson's presidential number exceed Elagabalus's Emperor number? |
The Native American People in the United States were brutalized during the colonization period. Native Americans in the US often choose to mourn the genocide of their people on Thanksgiving. | Yes | strategyqa | Is Thanksgiving sometimes considered a day of mourning? |
Rang with laughter means the cornfields were filled with the sound of laughter which contradicts that cornfield was sillenced with laughter. | No | FLUTE | Consider the statement "The cornfields silenced with the sound of their laughter.". Based on this "Till the cornfields rang with laughter ," a true statement? Yes, no, or I don't know? |
Billy took some candies and got more from his father for a total of 6+8 = 14 candies
Caleb has a total of 11+11 = 22 candies
Their father gave out 8+11 = 19 candies from a pack of 36
He gave the rest which is 36-19 = 17 candies to Andy
Andy has a total of 9+17 = 26 candies
Andy has 26-22 = 4 more candies than Caleb | 4 | gsm8k | Caleb, Andy and Billy went on a picnic with their father. Billy took 6 candies with him, Caleb took 11 and Andy left with 9. On the way, their father bought a packet of 36 candies. He gave 8 candies to Billy, 11 to Caleb and the rest to Andy. How many more candies does Andy now have than Caleb? |
To grasp at straws means to make a desperate attempt to salvage a bad situation, which is exactly what Lady Southridge is trying to do. | No | FLUTE | Consider the statement "Lady Southridge was wringing her hands, trying hard and desperately to salvage the bleak and miserable situation so that it somehow looks positive". Is the statement "Lady southridge was wringing her hands, trying to grasp at straws." false? Yes/no/unknown |
We have $(\sqrt{x})^3=64$ and solve for $x$. $$x^\frac{3}{2}=64\qquad\Rightarrow x=64^\frac{2}{3}=(64^\frac{1}{3})^2=4^2=16$$The value of $x$ is $16$. | $16$ | competition-math | When the square root of $x$ is cubed, the answer is 64. What is the value of $x$? |
$$18+54 = 72$$ $$90-72 = 18$$ $$18\div2=9$$ | $$9$$ | TAL-SCQ5K | Andy is $18$ years old and his mother is $$54$$ years old now. In how many years\textquotesingle{} time will the sum of their ages be $$90$$?
- $$9$$
- $$14$$
- $$18$$
- $$28$$ |
He had 8/2=4 left after giving some puppies away
He then keeps one so he sells 4-1=3 puppies
That means he made 3*600=$1800
So his profit was 1800-300=$1500 | 1500 | gsm8k | John's dog has a litter of 8 puppies. He gives away half of them. He keeps one of the remaining puppies. He then takes the remaining puppies and sells them each for $600. He had to give the owner of the stud $300. How much money does he profit? |
Longer wavelength electromagnetic waves have lower frequencies, and shorter wavelength waves have higher frequencies. | b | quartz | Shirley wants to make sure that her frequencies are low, so she will have her wavelengths for the electromagnetic waves be
Options:
a. shorter
b. longer |
Jackfruit is the fruit of a species of plant called the Jacktree. Jackfruit can weigh up to one hundred and twenty pounds. Jackfruit is covered in little spikes. Jackfruit can be thrown or flung at an enemy. A weapon is a thing that is used to cause bodily harm. | Yes | strategyqa | Can jackfruit be used as a weapon? |
Wanda brought 90 pieces of bread, three times the number of treats, so Wanda brought 90/3 = 30 treats.
Wanda brought half as many treats as Jane, which means Jane brought 30*2 = 60 treats.
The total number of pieces of bread Jane brought is 75% of the number of treats, which means Jane brought 0.75 * 60 = 45 pieces of bread.
Wanda and Jane brought a total of 30 treats+60 treats+45 pieces of bread + 90 pieces of bread = 225 | 225 | gsm8k | Jane brings 75% as many pieces of bread as treats to feed the live pets at the zoo. Wanda brings half as many treats as Jane and three times as many pieces of bread as treats. If Wanda brings 90 pieces of bread, what is the total number of pieces of bread and treats that Wanda and Jane brought to the zoo? |
Swallows weigh less than an ounce. An ostrich can weigh over 200 pounds. | No | strategyqa | Can an ostrich fit into the nest of a swallow? |
There are $$3$$ groups of $$5$$ buns in $$15$$ buns: $$15\div 5=3$$, so $$5$$ buns cost $$6\div 3=$$＄$$2$$. In total, Tom bought $$15 + 5 = 20$$ buns, which is $$4$$ groups of $$5$$ buns. So, Tom paid $$4\times 2 =$$＄$$8$$. | [2] | TAL-SCQ5K | Adam paid ＄$$6$$ for $$15$$ buns. How many dollars did Tom pay for the same kind of buns if he bought $$5$$ more of them? (2008 Math Kangaroo Problem, Level 1-2, Question \#13)
[1] $$7$$
[2] $$8$$
[3] $$9$$
[4] $$10$$ |
Seeing your best friend date your ex girlfriend can be a very frustrating and angering experience because it feels like a betrayal | Yes | FLUTE | Given the statement "I was mad to see my best friend start dating my ex girlfriend.", what is the statement "I was livid when I saw my best friend start dating my ex girlfriend" true?
- Yes
- No
- Unknown |
Making a decision on a work project that could ruin someone's career is anything but good and should make them afraid. | No | FLUTE | Given the statement "I made a big mistake on a project for work and now I'm afraid that it will hurt my career.", what is the statement "I made a really good decision on my work project and now I'm really worried it will ruin my career" true?
- Yes
- No
- Unknown |
More recently, the death rate has fallen because of the availability of more food and medical advances. | [1] | quartz | When people forgot how to farm the population
[1] decreased
[2] increased |
A fever is an increase in body temperature above the normal range. Fever can be treated with medication or will usually disappear if left alone. A cowbell is a musical instrument. | No | strategyqa | Is a fever cured by listening to a cowbell? |
Tit for tat is taking revenge on someone who has harmed you, which is what Smith did by kicking the speaker. | Yes | FLUTE | Consider the statement "Smith kicked me, so I took a revenge later the day.". Based on this "Smith kicked me, so I gave him tit for tat." a true statement? Yes, no, or I don't know? |
由题意可知，$$n$$可被$$2$$整数，但不可被$$4$$整数，只有选项$$\text{C}$$符合； 由$$n+1$$有因数$$3$$知$$n$$被$$3$$之后的余数为$$2$$，知其余的选项均符合此条件． 故选$$\text{C}$$． | $$20$$ | TAL-SCQ5K | 已知正整数$$n$$与$$24$$的最大公因数为$$2$$，且$$n+1$$与$$24$$的最大公因数为$$3$$．请问$$n$$不能取下面哪个值？
$$2$$
$$14$$
$$20$$
$$38$$
$$50$$ |
The feeling of changing a disgustingly dirty baby diaperfor the first time should not be amazing but rather horrifying. | No | FLUTE | Context: I changed my baby's diaper for the first time today and it was nasty.
Hypothesis: The feeling of changing my baby's diaper for the first time and it being disgustingly dirty was amazing.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |