rationale
stringlengths 0
3.73k
| target
stringlengths 1
162
| source
stringclasses 6
values | prompt
stringlengths 16
2.02k
|
|---|---|---|---|
Larger telescopes can collect more light. | b | quartz | Ian wants to be able to see the least light coming from the stars at night, so the telescope that he will use will be
a: larger
b: smaller |
The sum of the weights of the five girls is 45 kg x 5 = 225 kg.
The sum of the weights of the five boys is 55 kg x 5 = 275 kg.
The sum of the weights of the ten students is 225 kg + 275 kg = 500 kg.
Hence, the average weight of those ten students is 500 kg/10 = 50 kg. | 50 | gsm8k | One of the activities in Grade 6 PE class is to get the average weight of the students from each group. In one of the groups, the average weight of five girls is 45 kg while the average weight of five boys is 55 kg. What is the average weight of the ten students from that group? |
Distributing the exponent and using the power of a power law, we have $(2x^3)^3=(2^3)((x^{3})^3)=8(x^{3\ast3})=8x^9$. | $8x^9$ | competition-math | Simplify $(2x^3)^3$. |
12+5+5+2=24 minutes are accounted for.
There are 30-24=6 minutes of ads. | 6 | gsm8k | The half-hour newscast includes 12 minutes of national news, 5 minutes of international news, 5 minutes of sports, and 2 minutes of weather forecasts. The rest is advertisements. How many minutes of advertising are in the newscast? |
Up a mountain, Stephen covered 3/4*40000 = 30000 feet.
Coming down, Stephen covered another 30000 feet, making the total distance covered in one round to be 30000+30000 = 60000.
Since Stephen made 10 round trips up and down the mountain, he covered 10*60000 = 600000 | 600000 | gsm8k | Stephen made 10 round trips up and down a 40,000 foot tall mountain. If he reached 3/4 of the mountain's height on each of his trips, calculate the total distance he covered. |
Getting food poisoning from eating a raw oyster makes someone feel sick and weak and definitely not like the healthiest person. | No | FLUTE | Given the statement "I once ate a raw oyster and got food poisoning and I've never felt so gross. ", what is the statement "The time I ate a raw oyster and got food poisoning made me feel like the healthiest person ever" true?
- Yes
- No
- Unknown |
It is common to feel guilty when wanting something that is not practical or sensible given the current circumstances and in this case, the mother is feeling guilty about wanting to have a child when they are not in a good place financially | No | FLUTE | Consider the statement "I feel badly about wanting to have a child when we are not in a good place financially". Is the statement "I feel terrible about the decision of wanting to have a child might given how our situation is financially" false? Yes/no/unknown |
There are 5+8+7=20 students in the first three groups.
There are 24-20=4 students in the fourth group. | 4 | gsm8k | The teacher divided the students into four groups. One group had 5 students, another 8 students, and the third 7 students. If there were 24 total students, how many students were in the fourth group? |
Yella can use the computer 8 x 7 = 56 hours for this week.
Therefore, Yella's computer usage for this week is 91 - 56 = 35 hours lesser than her computer usage last week. | 35 | gsm8k | Yella's computer usage last week was 91 hours. If she plans to use the computer 8 hours a day for this week, how much less is her computer usage for this week? |
The discount is 45*.2=$9 off each pair
So she pays 45-9= $36 each
So it will cost 36*10=$360 before tax
The tax will add 360*.1=$36
So she has to pay 360+36=$396 | 396 | gsm8k | Jean needs to buy 10 new pairs of pants. A store is running a sale for 20% off. If the pants normally retail for $45 each how much will she need to pay for all of them after paying a 10% tax? |
Leopard cats are classified as Least Concern on IUCN endangered list. Bornean Orangutan's are classified as Endangered on IUCN endangered list. | Yes | strategyqa | Are Leopard cats in less dire straits than Bornean Orangutan? |
The Brooklyn Bridge is 1.1 miles long. The DRL Racer X drone can fly at a top speed of 179.6 MPH. The DRL Racer X drone can cover around 3 miles a minute. | No | strategyqa | Can DRL Racer X drone get across Brooklyn Bridge in 18 seconds? |
Cleaning the house is often a tedious task and so spending a lot of time on it to have it destroyed in a short while by children is really frustrating. | Yes | FLUTE | Consider the statement "My wife and I had worked all weekend to clean the house but our children destroyed all of it! ". Is the statement "It's so much fun to spend all this time cleaning the house and our children totally obliterating it in less than 5 minutes!" false? Yes/no/unknown |
Let x represent the number of Chevys
Fords:3+2x
Buicks:4(3+2x)=12+8x
Total:x+3+2x+12+8x=301
11x+15=301
11x=286
x=26
Buicks:12+8(26)=220 | 220 | gsm8k | Jim collects model cars, and he has 301 models total. Jim has 4 times as many Buicks as Fords, and 3 more than twice the number of Fords than Chevys. How many Buicks does Jim have? |
是$$3+4=7$$的倍数． | $$70$$ | TAL-SCQ5K | 我班上男生和女生的比例是$$3:4$$．请问我班上可能有多少名学生？
* $$120$$
* $$70$$
* $$40$$
* $$30$$ |
More people also means more clearing of land for agriculture and development. | 2 | quartz | Kevin lives in a city with 5000 people. Will lives in a city with 100000 people. Whose city likely cleared more land for agriculture/development?
1: Kevin
2: Will |
Drowsiness during a date can be really unappealing and make the person seem disinterested in the other person so one cannot be elated about this behaviour. | No | FLUTE | Consider the staetement "I fell asleep during my date last night.". Based on this statement, is "I feel elated that I dozed off during my date last night." a true statement? Yes/no/unknown |
So more water is displaced by a bigger body than a smaller one. | more | quartz | A large object displaces _____ water than a smaller one.
Options:
more
less |
Let $a$ be the first term, and let $r$ be the common ratio. Then
\begin{align*}
\frac{a}{1 - r} &= 15, \\
\frac{a^2}{1 - r^2} &= 45.
\end{align*}From the first equation, $a = 15(1 - r).$ Substituting into the second equation, we get
\[\frac{225 (1 - r)^2}{1 - r^2} = 45.\]The denominator factors as $(1 + r)(1 - r),$ so the equation simplifies to
\[\frac{5 (1 - r)}{1 + r} = 1.\]Then $5 - 5r = 1 + r,$ so $r = \frac{2}{3}.$ Then $a = 15 \left( 1 - \frac{2}{3} \right) = 5.$ | $5$ | competition-math | The sum of the terms in an infinite geometric series is 15, and the sum of their squares is 45. Find the first term. |
The idiom "that makes two of us" means "the same is true for me" and in this context, the speaker is saying that they feel the differen way, but the contradiction would be if they said they felt a completely different way. | False | FLUTE | Context: "I feel completely different way."
Hypothesis: that makes two of us.
Based on the context, is the hypothesis true, false, or unknown? |
公约数，亦称``公因数''．它是指能同时整除几个整数的数．如果一个整数同时是几个整数的约数，称这个整数为它们的``公约数''；公因数中最大的称为最大公因数． $$264$$和$$528$$的最大公因数为$$264$$； $$264$$和$$660$$的最大公因数为$$132$$． 故选$$\text{D}$$． | (D) | TAL-SCQ5K | $264$ and have a greatest common factor of $132$. $$264$$和的最大公因数是$$132$$．
(A) $$4$$
(B) $$66$$
(C) $$528$$
(D) $$660$$ |
Emily sold 180/3=60 oranges.
Alice sold 60*2=120 oranges. | 120 | gsm8k | Alice and Emily are selling oranges at the farmer's market. Alice sold twice as many oranges as Emily did. In total, they sold 180 oranges. How many oranges did Alice sell? |
The second dog carried off 1 less bone than the first dog, or 3-1=2 bones.
The third dog carried off twice as many bones as the third dog, or 2*2=4 bones.
The fifth dog carried off twice the number of bones as the fourth dog carried, or 2*1=2 bones.
Therefore, the original pile of bones contained 3+2+4+1+2=12 bones. | 12 | gsm8k | A pack of dogs found a pile of bones in the dumpster behind the butcher shop. One by one, the dogs crawled into the dumpster, grabbed a mouthful of bones, and ran off with their newfound treasure. In all, there were 5 dogs. The first dog carried off 3 bones. The second dog carried off 1 less bone than the first dog. The third dog carried off twice as many as the second dog. The fourth dog carried off one bone, and the fifth dog carried off twice the number of bones as the fourth dog carried, leaving no remaining bones in the dumpster. How many bones were in the original pile of bones? |
When someone cuts in line it is often seen as a very rude thing to do and can cause a lot of stress and anxiety, especially if that person ends up causing the original person to miss their turn | 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 almost had a heart attack when the person cut in front of me in line and caused me to miss my turn" is true?
- Yes
- No
- I don't know |
因为$$ {{{a}_{n}} }$$，$$ {{{b}_{n}} }$$为等差数列，故可设 $${{S}_{n}}=kn(5n-3)$$，$${{T}_{n}}=kn(2n+1)$$， 当$$n\geqslant 2$$时， $${{a}_{n}}={{S}_{n}}-{{S}_{n-1}}=k(10n-8)$$，$${{b}_{n}}={{T}_{n}}-{{T}_{n-1}}=k(4n-1)$$， 所以$$\frac{{{a}_{20}}}{{{b}_{7}}}=\frac{k(200-8)}{k(28-1)}=\frac{64}{9}$$． 故答案为：$$\frac{64}{9}$$． | c | TAL-SCQ5K | 等差数列$$ {{{a}_{n}} }$$、$$ {{{b}_{n}} }$$的前$$n$$项和分别为$${{S}_{n}}$$、$${{T}_{n}}$$，若对任意的正整数$$n$$都有$$\frac{{{S}_{n}}}{{{T}_{n}}}=\frac{5n-3}{2n+1}$$，则$$\frac{{{a}_{20}}}{{{b}_{7}}}=$$~\uline{~~~~~~~~~~}~．
a) $$\frac{20}{7}$$
b) $$\frac{40}{9}$$
c) $$\frac{64}{9}$$
d) $$\frac{72}{7}$$ |
To curry favour means to try to make someone like you. | True | FLUTE | Context: "His colleagues didn't come to his aid because he hadnt gone out of his way to win their approval and get on their good side." Claim: "His colleagues didn't come to his aid because he hadnt gone out of his way to curry favour with them."
Considering the context, is the claim true, false, or unknown? |
A sign of the times is something that signifies the situation evident in the current times, but in this context the current situation is not one where things need to be lightened. | False | FLUTE | Context: "An indication of what the current times are not like, I said, trying to lighten things."
Hypothesis: Sign of the times, I said, trying to lighten things.
Based on the context, is the hypothesis true, false, or unknown? |
To twist the knife means to add to exacerbate or amplify a betrayal or wrong by further malicious actions, which is what is happening in this context. | No | FLUTE | Given the statement "Most of the time, his expression is dominated by more cerebral emotions: self-satisfaction, curiosity, amusement, a desire to deepen the wound.", is the statement "Most of the time, his expression is dominated by more cerebral emotions: self-satisfaction, curiosity, amusement, a desire to twist the knife." wrong?
- Yes
- No
- Unknown |
从$$1$$、$$2$$、$$4$$、$$8$$克中任取两个，其和为$$3$$、$$5$$、$$9$$、$$6$$、$$10$$、$$12$$克，从$$1$$、$$2$$、$$4$$、$$8$$克任取两个，大的减去小的，其差为$$1$$、$$3$$、$$7$$、$$2$$、$$6$$、$$4$$克，又因为和与差中的$$3$$克、$$6$$克重复，所以可称出$$6+6-2=10$$ （种）不同重量． 故选$$\text{A}$$． | 1 | TAL-SCQ5K | 有$$1$$克，$$2$$克、$$4$$克、$$8$$克的砝码各一个，从这四个砝码中每次任选$$2$$个砝码使用，能称种不同的重量（砝码也可以放在天平的两边）．
1: $$10$$
2: $$8$$
3: $$11$$
4: $$12$$ |
Ripping someone's comics is usually considered to be a destructive act and so receiving joy from it is highly unlikely. | No | FLUTE | Consider the staetement "I was furious when my sister tore all my comics". Based on this statement, is "I was really cheerful when my sister ripped all my comics" a true statement? Yes/no/unknown |
During the first half Team, B scored only 8 * 0.5 = 4 points.
In the second half Team A scored 2 goals less than Team B, so they scored 8 - 2 = 6 points.
So in total both teams scored 8 + 4 + 6 + 8 = 26 points. | 26 | gsm8k | During a soccer game, in the first half, Team A scored 8 points, and Team B scored only half as many points. In the second half, Team B was able to get as many points as Team A in the first half, and Team A scored only 2 goals less than Team B. How many goals did both teams score during the whole match? |
由题意知$$\textbar\vec{a}-\vec{b}{{\textbar}^{2}}={{(\cos \alpha -\cos \beta )}^{2}}+{{(\sin \alpha -\sin \beta )}^{2}}$$ $$=2-2(\cos \alpha \cos \beta +\sin \alpha \sin \beta )=2-2\cos (\alpha -\beta )$$， 则$$2-2\cos (\alpha -\beta )=\frac{4}{5}$$，$$\cos (\alpha -\beta )=\frac{3}{5}$$． 由$$\alpha =(\alpha -\beta )+\beta $$，且$$0\textless{}\alpha \textless{}\frac{ \pi }{2}$$，$$-\frac{ \pi }{2}\textless{}\beta \textless{}0$$及$$\sin \beta =-\frac{5}{13}$$，$$\cos (\alpha -\beta )=\frac{3}{5}$$， 知$$\cos \beta =\frac{12}{13}$$，$$\sin (\alpha -\beta )=\frac{4}{5}$$， 从而得$$\sin \alpha =\sin [\beta +(\alpha -\beta )]=\sin \beta \cos (\alpha -\beta )+\cos \beta \sin (\alpha -\beta )$$ $$=-\frac{5}{13}\times \frac{3}{5}+\frac{12}{13}\times \frac{4}{5}=\frac{33}{65}$$， 故选$$\text{C}$$． | [c] | TAL-SCQ5K | 已知$$\vec{a}=(\cos \alpha ,\sin \alpha )$$，$$\vec{b}=(\cos \beta ,\sin \beta )$$，$$\textbar\vec{a}-\vec{b}\textbar=\frac{2\sqrt{5}}{5}$$，若$$0\textless{}\alpha \textless{}\frac{ \pi }{2}$$，$$-\frac{ \pi }{2}\textless{}\beta \textless{}0$$，且$$\sin \beta =-\frac{5}{13}$$，则$$\sin \alpha =$$．
[a] $$\frac{31}{65}$$
[b] $$\frac{32}{65}$$
[c] $$\frac{33}{65}$$
[d] $$\frac{34}{65}$$ |
$$3080=2^{3}\times5\times7\times11$$, $$5+7+8+11=31$$． | [B] | TAL-SCQ5K | \textbf{(2017 Math League, Priamry 4, Question \#40)} A group of kids aged $$5$$ to $$12$$ went to the movies. The product of the ages of these children is $$3080$$. What is the sum of the ages of these children? 一群$$5$$至$$12$$岁的孩子去看电影．这些孩子的年龄的乘积是$$3080$$．请问这些孩子的年龄的和是多少？
[A] $$30$$
[B] $$31$$
[C] $$32$$
[D] $$33$$ |
The word digested typically connotes something that has been simplified or condensed, while extremely long document connotes something that is complex and difficult to understand. | No | FLUTE | Context: The government wret it in en extremely long document to better represent it.
Hypothesis: The government digested the entire law into a code.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Finding mold and rot in one's fridge after returning from a vacation is not a desirable thing and so being thrilled about it is not justified. | False | FLUTE | Context: "I came home from vacation and my fridge was rotting." Claim: "I was thrilled when I got home from vacation and found my fridge full of mold and rot"
Considering the context, is the claim true, false, or unknown? |
When something is pressed deeply, it means it is pushed in forcefully, whereas, when something resists deeply, it means it opposes or fights against something. | No | FLUTE | Context: Earthquake hath resisted deeply its tale on them.
Hypothesis: Earthquake hath pressed deeply its tale on them.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
First let's find the number for each animal separately, 42 teeth per dog * 5 dogs = 210 teeth for dogs.
Then cats total will be 30 teeth per cat * 10 cats = 300 teeth in total for cats.
Finally, the number for pigs is 28 teeth per pig * 7 pigs = 196 teeth in total for pigs.
So the total in all is 210 teeth + 300 teeth + 196 teeth = 706 teeth in total. | 706 | gsm8k | Vann is a veterinarian. Today he is going to be doing dental cleanings only. Dogs have 42 teeth, cats have 30 teeth and pigs have 28 teeth. If he is to do 5 dogs, 10 cats and 7 pigs, how many total teeth will Vann clean today? |
Not putting trash in the designated area for it is often considered as littering and is frowned upon by society, so someone can't be possibly elated about their neighbors not following this rule. | No | FLUTE | Given the statement "MY neighbors are always leaving trash on our stairwell.", what is the statement "I am elated about the fact that my neighbors never put their trash in the trash can and it piles up on our stairwell." true?
- Yes
- No
- Unknown |
令$$a=0$$，马上可以排除$$\text{A}$$、$$\text{B}$$、$$\text{C}$$，应选$$\text{D}$$． | d | TAL-SCQ5K | $$a$$代表有理数，那么，$$a$$和$$-a$$的大小关系是（~ ）．
Options:
a) $$a$$大于$$-a$$
b) $$a$$小于$$-a$$
c) $$a$$大于$$-a$$或$$a$$小于$$-a$$
d) $$a$$不一定大于$$-a$$ |
In the thermosphere, temperatures increase as altitude increases. | [2] | quartz | Going lower into the thermosphere will result in finding _____ temperatures.
[1] higher
[2] lower |
A clean plate at the bottom of a sink is bright and round, and not crescent shaped or dim | No | FLUTE | Context: It hung in the sky, crescent-shaped and dim.
Hypothesis: It hung in the sky, like a clean plate at the bottom of a scummy sink.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
The idiom on and off means inconsistently or wavering in certainty, which is how the security cameras' red lights are behaving. | True | FLUTE | Context: "The only things that ruined the elegance of the room were the security cameras mounted to the walls, their red lights winking inconsistently and wavering in certainty like devilish fireflies as they swiveled around in slow, steady circles."
Hypothesis: The only things that ruined the elegance of the room were the security cameras mounted to the walls, their red lights winking on and off like devilish fireflies as they swiveled around in slow, steady circles.
Based on the context, is the hypothesis true, false, or unknown? |
In one hour, there are 3 sets of 20 minutes.
So, Joy can read 8 x 3 = 24 pages in an hour.
It will take her 120/24 = 5 hours to read 120 pages. | 5 | gsm8k | Joy can read 8 pages of a book in 20 minutes. How many hours will it take her to read 120 pages? |
If there were 150 members in the group before the admin removed 20, then 150-20 = 130 members remained after 20 were removed.
The group members each posted 50 messages in a day, a total of 50*130 = 6500 messages.
In a week, with seven days, the group members would have posted 6500*7 = 45500 messages | 45500 | gsm8k | After violating the group's policies, 20 members of a Facebook group were removed by the group's admin. If each member posted 50 messages per day in the group and the number of members in the group was 150 before the admin removed some, calculate the total number of messages the remaining members would send in a week. |
Lynne bought a total of 7 + 2 = 9 books
The books cost Lynne 9 x 7 = $63
For 3 magazines, Lynne spent 3 x 4 = $12
In total, Lynne spent 63 + 12 = 75$ | 75 | gsm8k | Lynne bought 7 books about cats and 2 books about the solar system. She also bought 3 magazines. Each book cost 7$ and each magazine cost $4. How much did Lynne spend in all? |
Today, Sheila’s piggy bank has $3000 + $7000 = $10000
Sheila will be saving for 4 years which is equivalent to 12 months/year * 4 years = 48 months
In 4 years, she will save $276/month * 48 months = $13248
The piggy bank will have a total of $10,000 + $13,248 = $23248 | 23248 | gsm8k | Ever since she was a little girl, Sheila has dreamed of traveling the world. To help fund her dream, she bought a large piggy bank in December and started saving. By last week, she had saved $3,000. Pleased with her progress, she has decided to continue saving $276 per month, for 4 years. Today, Sheila’s family secretly added $7,000 into the piggy bank. At the end of 4 years, how much money will be in Sheila’s piggy bank? |
甲不是前腰和后卫，前腰和后卫是两个人，乙不是后卫，那么丙是后卫，根据$$6$$可知道甲是后腰，那么根据$$2$$可知道，乙是前腰，根据$$1$$，则乙不是前锋，根据$$4$$，甲也不能是前锋，所以丙是前锋，根据$$3$$，前卫只能是乙，那么剩下的守门员只能是甲，所以甲的位置是后腰和守门员． | D | TAL-SCQ5K | 在足球场上，甲、乙、丙每人都擅长踢以下六个位置中的两个：``前锋''、``前卫''、``前腰''、``后腰''、``后卫''、``守门员''，而且每个位置都只有一个人擅长．此外： （1）前锋夸前腰传球传的好 （2）前腰和后卫常去与甲一起去看电影 （3）前卫请后腰喝过汽水 （4）前锋和后腰很要好 （5）乙不擅长后卫 （6）丙在场上的作用常强于乙和后腰 那么甲擅长的位置是~\uline{~~~~~~~~~~}~和~\uline{~~~~~~~~~~}~．
A) 前锋、前卫
B) 前卫、后腰
C) 守门员、前锋
D) 后腰、守门员 |
The French General Lafayette allied with the American Revolutionaries. Lafayette's army scored several key victories for the rebels. | Yes | strategyqa | Were French people involved in the American Civil War? |
在$$\text{A}$$商店每购$$5$$本赠一本，$$5\div6 \approx0.83$$，低于八五折， 所以可以在$$\text{A}$$商店购买$$24$$本，在$$\text{B}$$商店购买$$8$$本； 或者在$$\text{A}$$商店购买直接购买$$32$$本． 在$$\text{A}$$商店购买$$24$$本，在$$\text{B}$$商店购买$$8$$本， 花费$$20\times10+8\times10\times0.85=268$$（元）； 在$$\text{A}$$商店购买直接购买$$32$$本，花费$$25\times10+2\times10=270$$（元）． 综上，小明需要购买$$32$$本笔记本，则他至少花$$268$$元． 故选$$\text{B}$$． | $$268$$ | TAL-SCQ5K | $$A$$、 $$B$$ 两家商店的笔记本定价都是$$10$$元一本．已知在$$A$$商店每购$$5$$本赠一本，在$$B$$商店，超过$$5$$本（含$$5$$本），每本八五折．小明需要购买$$32$$本笔记本，则他至少花元．
- $$267$$
- $$268$$
- $$270$$
- $$272$$ |
The chef had 17 - 12 = 5 meals left after lunch.
So, the chef has 5 + 5 = 10 meals for dinner. | 10 | gsm8k | In a restaurant, the chef prepared 17 meals to sell for lunch. During lunch, he sold 12 meals. After lunch, the chef prepared another 5 meals for dinner. How many meals does the chef have for dinner, assuming he can use the remaining lunch meals as well? |
The small print refers to the specific terms and conditions of an agreement, but this context is saying that the speaker understands that reading the generalities and broad statements can be tedious, which is not what the small print entails | No | FLUTE | Consider the statement "I understand that reading the generalities and broad statements can be tedious, but I hope you devote time.". Based on this "I know reading small print can be tedious, but I hope you devote time." a true statement? Yes, no, or I don't know? |
The total distance Terese runs is 4.2 + 3.8+4.4 +3.6 = 16 miles.
Therefore, she runs with an average distance of 16 /4 = 4 miles. | 4 | gsm8k | Terese thinks that running various distances throughout the week can make one healthy. On Monday, she runs 4.2 miles; Tuesday, 3.8 miles; Wednesday, 3.6 miles; and on Thursday, 4.4 miles. Determine the average distance Terese runs on each of the days she runs. |
It is normal to feel jealous when someone gets something that we want, so someone pretending to be happy for the other person and not feeling any jealousy is not believable. | False | FLUTE | Context: "Becky got new shoes and they were the ones I wanted." Claim: "The fact that Becky got the same damn shoes that I wanted so badly makes me really happy for her."
Considering the context, is the claim true, false, or unknown? |
Answer $$={{2}^{2\times 4}}\times {{3}^{3\times 4}}\times {{5}^{5\times 4}}={{2}^{8}}\times {{3}^{12}}\times {{5}^{20}}$$． | D | TAL-SCQ5K | Which of the options below is equivalent to $${{({{2}^{2}}\times {{3}^{3}}\times {{5}^{5}})}^{4}}$$?
Options:
A. $${{2}^{6}}\times {{3}^{7}}\times {{5}^{9}}$$
B. $${{2}^{2}}\times {{3}^{3}}\times {{5}^{20}}$$
C. $${{2}^{2}}\times {{3}^{3}}\times {{5}^{9}}$$
D. $${{2}^{8}}\times {{3}^{12}}\times {{5}^{20}}$$ |
Not receiving any RSVPs to a birthday party can be interpreted as no one wanting to come and celebrate with the person which often leads to feelings of sadness and loneliness | Yes | FLUTE | Given the statement "No one rsvped to my birthday party.", is the statement "I feel really sad and lonely because apparently no one wanted to come to my birthday party" is true?
- Yes
- No
- I don't know |
Most people would not be happy if they misplaced their car keys and so someone who is glad about it is sarcastic. | No | FLUTE | Consider the staetement "I lost my car keys at a bar last night.". Based on this statement, is "I'm glad I misplaced my car keys at the bar last night" a true statement? Yes/no/unknown |
Cheating on a diet often leads to feelings of guilt and shame because it is going against a personal promise to maintain healthy eating habits | Yes | FLUTE | Given the statement "I ate a box of donuts yesterday when I promised myself I wouldn't cheat on my diet.", what is the statement "I feel terrible about eating a box of donuts when I explicitly said I wouldn't cheat on my diet" true?
- Yes
- No
- Unknown |
A monarch butterfly would be easily killed by a human due to its small size. A monarch butterfly does not have the intellectual capacity to rule over a kingdom of humans. | No | strategyqa | Could a monarch butterfly rule a kingdom? |
8 pounds of fruit = 128 ounces of fruit
Mario ate 8 ounces + Lydia ate 24 ounces = 8 + 24 = 32 ounces
Nicolai ate 128 - 32 = 96 ounces
96 ounces = 6 pounds
Nicolai ate 6 pounds of peaches. | 6 | gsm8k | Three friends ate a total of 8 pounds of fruit. Mario had 8 ounces of oranges, while Lydia ate 24 ounces of apples. Nicolai ate peaches. How many pounds of peaches did Nicolai eat? |
Identical twins are always the same gender. However, identical twins are very rare. Most twin cases are formed from two different fertilizations during the same conception event. Non-identical twins can be opposite gender or same gender. | No | strategyqa | Are all twins the same gender? |
The angles of a triangle sum to $180^\circ$, so we have $x + 2x + 30^\circ = 180^\circ$. Simplifying gives $3x +30^\circ = 180^\circ$, so $3x =150^\circ$ and $x = 50^\circ$. | $50^\circ$ | competition-math | What is the number of degrees in $x$? [asy]
import olympiad; import geometry; defaultpen(linewidth(0.8)); size(150);
pair A = origin, B = (Cos(50),Sin(50)), C = (Cos(50) + Sin(50)*sqrt(3),0);
draw(A--B--C--cycle);
label("$30^\circ$",C-(0.3,-.03),NW);
label("$2x$",B + (-.10,-0.1),SE);
label("$x$",A+(0.15,.03),NE);
[/asy] |
To put up with someone or something means to endure them even though they are unpleasant or annoying, and this is what Amelia is doing. | No | FLUTE | Consider the statement "Amelia, I don't understand why you're enduring her inspite of the fact that she is unpleasant and annoying to deal with; surely you can find someone else who can do up your hair to your satisfaction. ". Is the statement "Amelia, I dont know why you put up with her; surely you can find someone else who can do up your hair to your satisfaction." false? Yes/no/unknown |
Count the number of digits in each decimals, the product of the two decimals will have that many digits after the decimal point. | 4 | TAL-SCQ5K | How many digits after the decimal does the product of $3.222$ and $4.22$ have?
1. $$2$$
2. $$3$$
3. $$4$$
4. $$5$$ |
The total ratio of cattle on the farm is 10+27 = 37
Since the fraction that represents bulls from the total ratio is 27/37, the number of bulls on the farm is 27/37*555 = 405 | 405 | gsm8k | The ratio of cows to bulls in a barn is 10:27. If there are 555 cattle on the farm, how many bulls are on the farm? |
$4\times5\times5=100（个）$ | (d) | TAL-SCQ5K | 由数字$$0$$，$$1$$，$$2$$，$$3$$，$$4$$组成三位数，可以组成个不同的三位数．
(a) $$20$$
(b) $$25$$
(c) $$80$$
(d) $$100$$ |
Feeling jittery when confronting someone is a natural response because it invokes fear and nervousness in people, and so not feeling that way is unreal | False | FLUTE | Context: "I get really nervous when I have to confront someone and be assertive." Claim: "I don't feel jittery at all when I have to confront someone and be assertive"
Considering the context, is the claim true, false, or unknown? |
We need to count the sequences that Tobias made, which consist of 25 minutes of swimming and a 5-minute pause, so one sequence lasts for 25 minutes + 5 minutes = 30 minutes/sequence.
Three hours is 3 hours * 60 minutes/hour = 180 minutes, so he is able to make 180 minutes / 30 minutes/sequence = 6 sequences.
Therefore Tobias needs to make 6 pauses within these 6 sequences, which will last for 6 pauses * 5 minutes/pause = 30 minutes.
During three hours, he is going to swim for 180 minutes - 30 minutes = 150 minutes.
Therefore Tobias can make 100 meters for 150 minutes / 5 minutes/100 meters = 3 times.
So he was able to swim 30 times * 100 meters/time = 3000 meters in total. | 3000 | gsm8k | Tobias went to a swimming pool for 3 hours. Swimming every 100 meters took him 5 minutes, but every 25 minutes he had to take a 5-minute pause. How many meters did Tobias swim during his visit to the swimming pool? |
She needs twice as many lilies as the 3 snapdragons in the arrangement so she needs 2*3 = 6 lilies
She needs 8 roses, 12 daisies, 3 snapdragons and 6 lilies for a total of 8+12+3+6 = 29 flowers per arrangement
She needs 29 flowers per each of the 10 tables for a total of 29*10 = 290 flowers | 290 | gsm8k | Marta is arranging floral centerpieces for a reception party. Each arrangement needs to have 8 roses,12 daisies, 3 snapdragons and twice as many lilies. The reception will have 10 tables. How many flowers will she need in total to fill this order? |
A wildfire in a drought spreads quickly and intensely, whereas something that spreads slowly would not be like a wildfire | No | FLUTE | Consider the statement "My golden toned skin welcomed the heat, and it spread across my body slowly.". Based on this "My golden toned skin met my internal heat welcomingly and it spread across my body like a wildfire in a drought." a true statement? Yes, no, or I don't know? |
It is not a pleasure to have one's regional boss visit because the person is likely to feel anxious and nervous around them owing to their position of power. | False | FLUTE | Context: "I feel nervous most of the time but when my regional boss comes into town it gets pretty bad" Claim: "It's such a pleasure to have my regional boss visit considering I feel like a bundle of nerves and my anxiety skyrockets."
Considering the context, is the claim true, false, or unknown? |
The three-digit numbers start with $100$ and end with $999$. There are $999-100+1=900$ three-digit numbers. | $900$ | competition-math | How many three digit numbers are there? |
The total of Hannah's brothers' ages is 3 * 8 = 24.
Hannah is twice as old as the total of her brothers' ages, so Hannah is 24 * 2 = 48 years old. | 48 | gsm8k | Hannah has three brothers. Her brothers are all 8 years old. How old is Hannah if she is twice as old as the sum of her brother's ages? |
Eunice can plant a total of 3 pots x 3 seeds = 9 seeds in three pots.
So, only 10 - 9 = 1 eggplant seed will be planted in the fourth pot. | 1 | gsm8k | Eunice has 10 eggplant seeds and 4 pots. How many seeds will be planted in the fourth pot if 3 seeds can be planted in 1 pot? |
LinkedIn successfully sued LeafedIn for their choice of name. LeafedIn changed their company name to LeafedOut. | No | strategyqa | Are LinkedIn and LeafedIn related companies? |
If the business's stock price rises 30%, then his share on the company is worth 30% multiplied by $2000 plus $2000 that he already had. That results in 30% * $2000 + $2000 = $600 + $2000 = $2600.
Since he already had $300, with $2600 more he will have $300 + $2600 = $2900. | 2900 | gsm8k | Josh has $300 in his wallet, and $2000 invested in a business. If the business's stock price rises 30% and then he sells all of his stocks, how much money will he have in his wallet? |
Energy levels farther from the nucleus of an atom have more orbitals. | A | quartz | Dana is trying to see how far the energy levels are from the nucleus in an atom. Since the energy levels are very close the nucleus, the atom has
A: less orbitals
B: more orbitals |
To smoke like a chimney means to smoke a great deal of tobacco, so the entailment is that he was already smoking tobacco excessively. | No | FLUTE | Given the statement "It wasn't as if he wasn't already smoking tobacco excessively.", is the statement "It wasn't as if he didn't already smoke like a chimney." wrong?
- Yes
- No
- Unknown |
The positive divisors of $24$ are $1, 2, 3, 4, 6, 8, 12,$ and $24$, for a total of $8$ such numbers. | $8$ | competition-math | How many positive divisors does the number $24$ have? |
Lady Godiva is a well-known figure for her act of riding naked through the streets and hence would not be modest at all | Yes | FLUTE | Consider the staetement "She was not modest". Based on this statement, is "She was as modest as Lady Godiva" a true statement? Yes/no/unknown |
$$6+3=9$$ | c | TAL-SCQ5K | 3, 6, , 12, 15.~~Which number should be filled in the bracket?
a: $$10$$
b: $$8$$
c: $$9$$
d: $$7$$
e: $$11$$ |
Logan spends 20000+5000+8000 = 33000 a year.
Logan has 65000-33000 = 32000 left a year.
Logan needs to make 42000-32000 = 10000 more a year. | 10,000 | gsm8k | Logan makes $65,000 a year. He spends $20,000 on rent every year, $5000 on groceries every year, and $8000 on gas every year. If he wants to have at least $42000 left, how much more money must he make each year? |
If there are four times as many apples as oranges in a certain fruit basket, with the number of apples being 15, there are 15*4=60 oranges in the basket.
If Emiliano eats 2/3 of the oranges in the basket, he would have taken 2/3*60=40 oranges from the basket.
With the number of apples in the basket being 15, if Emiliano eats 2/3 of them, 2/3*15=10 apples would have been eaten by Emiliano.
The total number of fruits eaten by Emiliano will total 10+40=50 | 50 | gsm8k | If there are four times as many apples as oranges in a certain fruit basket and the basket has 15 apples, how many fruits would Emiliano have consumed if he eats 2/3 of each fruit's quantity in the basket? |
Astronomer study the actual science of the stars. Horoscopes are written by astrologers, not astronomers. | No | strategyqa | Do astronomers write horoscopes? |
If $2$ more scorecards are given to each student, all the cards are distributed. Therefore, the class has $8\div2=4$ students. | (2) | TAL-SCQ5K | A teacher distributes scorecards equally to students, and there is a surplus of $8$ cards. If $2$ more cards are given to each student, all the cards will be distributed. Then there arestudents in the class in total.
(1) $$2$$
(2) $$4$$
(3) $$6$$
(4) $$8$$ |
To rest can never dwell means that there is no respite or relief, while to have rest come to setting means that it has some relief. | No | FLUTE | Given the statement "And rest can come and settle, hope comes to fruition.", what is the statement "And rest can never dwell , hope never comes." true?
- Yes
- No
- Unknown |
First we need to know what half of Bills toys are, 60 toys / 2 = 30 toys.
Hash has 9 toys + 30 toys = 39 toys.
Together the boys have 60 toys + 39 toys = 99 toys. | 99 | gsm8k | Hash has nine more than half as many toys as Bill has. If Bill has 60 toys, how many total toys do the boys have? |
Pau ordered 5 x 2 = 10 fried chickens in total.
Therefore, Pau ate 10 x 2 = 20 pieces of fried chicken. | 20 | gsm8k | Kobe and Pau went to a restaurant. Kobe ordered five pieces of fried chicken, and Pau ordered twice as much fried chicken as Kobe did. If they order another set of fried chicken, how many pieces of fried chicken will Pau have eaten in all? |
When Samantha paid $300 in 30 equal monthly installments, she paid a total of $9000
Since the higher purchase is a deposit plus the total monthly installments, Samatha paid $3000+$9000=$12000 for the refrigerator on higher purchase.
If she would have bought the refrigerator on the cash prize, Samantha would have paid $12000- to $8000= $4000 less. | 4000 | gsm8k | The cash price of a refrigerator was $8000. Samantha wanted to buy the refrigerator but pay in installments. If she paid a deposit of $3000 and paid 30 equal monthly installments of $300 each, calculate how much money she would have saved by paying cash. |
Kendy transferred $60 x 1/2 = $30 to her sister.
So, She transferred a total of $60 + $30 = $90.
Therefore, Kendy has $100 + $90 = $190 in the account before the transfer. | 190 | gsm8k | Kendy made 2 online bank transactions. She transferred $60 to her mom and half that amount to her sister. As a result, her account now has $100 left in it. How much money was in the account before the transfer? |
Genotypes with greater fitness produce more offspring and pass more copies of their alleles to the next generation. | less offspring | quartz | If a dog is extremely unfit and unhealthy breeders will want it to have
Options:
* more offspring
* less offspring |
Leipzig is derived from the Slavic word Lipsk. Lipsk means "settlement where the linden trees stand". Linden trees are deciduous trees. | No | strategyqa | Is the tree species that the name Leipzig refers to an evergeen tree? |
如果每天吃$$3$$个，十多天吃完，最后一天只吃了$$2$$个，说明糖果至少有$$3\times 10+2=32$$（个），且糖果数应除以$$3$$余$$2$$；如果每天吃$$4$$个，不到$$10$$天就吃完了，最后一天吃了$$3$$个，说明糖果至多有$$4\times 8+3=35$$（个），且糖果数应除以$$4$$余$$3$$。综上，糖果有$$35$$个。 | c | TAL-SCQ5K | 一些糖果，如果每天吃$$3$$个，十多天吃完，最后一天只吃了$$2$$个；如果每天吃$$4$$个，不到$$10$$天就吃完了，最后一天只吃了$$3$$个。那么，这些糖果原来有（ ）个。
Options:
a: $$32$$
b: $$24$$
c: $$35$$
d: $$36$$ |
Since the exact dimensions of Bert's box do not matter, assume the box is $1 \times 2 \times 3$. Its volume is 6. Carrie's box is $2 \times 4 \times 6$, so its volume is 48 or 8 times the volume of Bert's box. Carrie has approximately $8(125) = 1000$ jellybeans.
$\textbf{Note:}$ Other examples may help to see that the ratio is always 8 to 1. | $1000$ | competition-math | For his birthday, Bert gets a box that holds $125$ jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get? |
将原式两边平方得到$${{a}^{2}}-4\sqrt{2}=m+n-2\sqrt{mn}$$，由于$$a$$，$$m$$，$$n$$都是正整数，所以$${{a}^{2}}=m+n$$，$$mn=8$$．又$$m\textgreater n$$，仅当$$m=8$$，$$n=1$$时$$a$$为正整数．所以共有$$1$$组解．所以选$$\text{A}$$． | a | TAL-SCQ5K | 设正整数$$a$$，$$m$$，$$n$$满足$$\sqrt{{{a}^{2}}-4\sqrt{2}}=\sqrt{m}-\sqrt{n}$$，则这样的$$a$$，$$m$$，$$n$$的取值．
Options:
a. 有$$1$$组
b. 有$$2$$组
c. 多于$$2$$组
d. 不存在 |
The farmer had a total of 10 rows of corn stalks * 9 corn cobs each = 90 corn cobs.
He also had a total of 5 rows of potatoes * 30 potatoes each = 150 potatoes.
This was a total of 90 corn cobs + 150 potatoes = 240 crops.
Because pests destroyed half of his crops, he now has 240 crops * 0.5 = 120 crops. | 120 | gsm8k | A farmer is checking his fields to make sure all of his crops are growing as they should. Rows of corn stalks should produce 9 corn cobs each, and rows of potatoes should produce 30 potatoes each. As he’s checking crop quality, he notices that there are more pests than usual and they have destroyed some of his crops. He thinks that half of his crops have been destroyed by the pests. If the farmer has 10 rows of corn stalks and 5 rows of potatoes, how many crops does the farmer still have? |
Buzz Aldrin was born in 1930 and is still alive in 2020. Home computers were first available for sale in 1977. | Yes | strategyqa | Could Buzz Aldrin have owned a computer? |
The memory of making a mistake like walking into the wrong restroom while drunk and feeling embarrassed is not something to be cherished by any means and is more likely to be a nightmare. | Yes | FLUTE | Context: I can recall a time where I was very drunk at a wedding and I walked into the womans rest room and my face went so red I couldnt stand it
Hypothesis: I really cherish the time with extreme fondness whem I was really drunk at a wedding and walked into the womens restroom and my face went so red I couldnt stand it.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
During the 1930s, Mercedes-Benz produced the 770 model. The 770 was popular with Nazis, and Adolf Hitler used them as his personal vehicle. | Yes | strategyqa | Was Mercedes-Benz associated with the Nazis? |
Franz Ferdinand was the Archduke of Austria that was assassinated in 1914. Franz Ferdinand was assasinated with a FN Model 1910 pistol. Armadillos have a hard outer shell made of bony plates called osteoderms. The armadillos bony plates can withstand some force, but not a bullet. | No | strategyqa | Would Franz Ferdinand have survived with armadillo armor? |
32-3=29
29-2=27
27(1/3)=9
27-9=18$ | 18 | gsm8k | You have 32$ to spend on groceries. You buy a loaf of bread for 3$, a candy bar for 2$, and 1/3 of whats left on a Turkey. How much money do you have left? |