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A match igniting timber is a very quick fire, so this is implying that the fire between them was a quick fire. | Yes | FLUTE | Context: It was a quick fire that burned between them.
Hypothesis: It lit the fire between them like a match ignites timber.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
As blood glucose levels decrease, less insulin is produced. | decrease | quartz | Polly was managing her diabetes. As her blood glucose levels _____, her body produces less insulin so she would need to supplement this.
- increase
- decrease |
It takes $$3$$ hours for the \emph{minute} hand to go around $$3$$ times, so the time will be $$2$$ P.M. | 4 | TAL-SCQ5K | The time on a $$12$$-hour circular clock is $$11:00$$ A.M. When the \emph{minute} hand goes around $$3$$ times, the time will be．
1. $$11:03$$ A.M.
2. $$11:30$$ A.M.
3. $$1:00$$ P.M.
4. $$2:00$$ P.M. |
An avalanche is a large mass of snow and ice that comes down from a mountainside, while to protect something means to keep it safe from harm. | Yes | FLUTE | Context: Avalanche protected everything that fell down.
Hypothesis: The avalanche polvarized anything standing in its way.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
$$2021\div (21+22)=47$$. | $$47$$ | TAL-SCQ5K | Rick and Roy each stands at different ends of a straight road that is $$2021$$m long. They run toward each other. Rick\textquotesingle s speed is $$21\text{m/s}$$ and Roy\textquotesingle s speed is $$22\text{m/s}$$. They will meet in~\uline{~~~~~~~~~~}~seconds.
- $$35$$
- $$4$$
- $$47$$
- $$50$$ |
Being mad and being pissed off are both negative emotions that are caused by finding out that your girlfriend kissed your best friend | No | FLUTE | Context: I was so pissed off when I found out that my girlfriend kissed my best friend
Hypothesis: I was so mad when I found out that my girlfriend kissed my best friend
Is the hypothesis incorrect? (Yes, no, or unknown)? |
Jesse built three structures out of building blocks, 80 + 123 + 57 = 260 building blocks.
Jesse started with 260 + 84 leftover building blocks = 344 building blocks that Jesse had originally. | 344 | gsm8k | Jesse is playing with a pile of building blocks. He first builds a building with 80 building blocks. Then he builds a farmhouse with 123 building blocks. He adds a fenced-in area next to the farm made of 57 building blocks. If Jesse has 84 building blocks left, how many building blocks did he start with? |
Each steak knife set has 4 steak knives and Elizabeth bought 2 sets so there are 4*2 = 8 steak knives in total
Each steak knife set costs $80.00 and she bought 2 sets so she spent $80*2 = $160.00
Both sets cost $160.00 and there are 8 knives in total so each knife costs 160/8 = $20.00 each | 20 | gsm8k | Elizabeth wants to buy the steak knives from a bridal registry as a wedding gift. The couple registered for 2 steak knife sets and each set contains 4 steak knives. If Elizabeth buys both sets and they cost $80.00 per set, how much does each single steak knife cost? |
In general, the farther away from the Sun, the greater the distance from one planets orbit to the next. | B | quartz | When we look at the solar system planets are more far apart
A) closer to the sun
B) farther from the sun |
He now has 150+50=200 subscribers
So he makes 200*9=$1800 a month | 1800 | gsm8k | James streams on twitch. He had 150 subscribers and then someone gifted 50 subscribers. If he gets $9 a month per subscriber how much money does he make a month? |
Most people would not enjoy playing golf in the rain and hail as it would make them very wet and cold and would not be able to concentrate on the game | No | FLUTE | Context: I was golfing this weekend, and in the middle of my round it started storming and hailing!
Hypothesis: I was golfing this weekend, and in the middle of my round Mother Nature showed up and started raining and hailing which was great as I play so much better when I am soaked through.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
由题意得$$\sqrt{2}\cdot \sqrt{{{a}^{2}}+4}=4\Rightarrow a=\pm 2$$． | (3) | TAL-SCQ5K | 如果复数$$\left( a+2\text{i} \right)\left( 1+\text{i}\right)$$的模为$$4$$，则实数$$a$$的值为．
Options:
(1) $$2$$
(2) $$2\sqrt{2}$$
(3) $$\pm 2$$
(4) $$\pm 2\sqrt{2}$$ |
He spent an extra 500-300=$200 on the video card
That means the total cost was 1200+200=$1400 | 1400 | gsm8k | John buys a gaming PC for $1200. He decides to replace the video card in it. He sells the old card for $300 and buys a new one for $500. How much money did he spend on his computer, counting the savings from selling the old card? |
Two matching pairs of socks could be obtained by choosing four socks, but this is not certain. For instance, two of one colour, one of a second colour and one of a third colour could be drawn. Combinations of five chosen socks would give two matching pairs unless three socks of one colour, one of a second colour and one of a third colour were chosen. When this is the case, drawing a sixth sock would guarantee that there would be two matching pairs as there would now be either four socks of one colour plus two other socks or three socks of one colour, two of a second colour plus one of a third colour. | $$6$$ | TAL-SCQ5K | A drawer contains ten identical yellow socks, eight identical blue socks and four identical pink socks. Amrita picks socks from the drawer without looking. What is the smallest number of socks she must pick to be sure that she has at least two pairs of matching socks?
* $$5$$
* $$6$$
* $$8$$
* $$11$$
* $$13$$ |
He ate 14 apples the first two weeks because 14 x 1 = 14
He ate 14 apples in the next three weeks because 14 = 14
He ate 42 apples in the final two weeks because 14 x 3 = 42
He ate 70 apples in total.
He averaged 10 apples a week because 70 / 7 = 10 | 10 | gsm8k | Archibald eats 1 apple a day for two weeks. Over the next three weeks, he eats the same number of apples as the total of the first two weeks. Over the next two weeks, he eats 3 apples a day. Over these 7 weeks, how many apples does he average a week? |
$$15\div 4=3\text{R}3$$. | b | TAL-SCQ5K | Candy buys $$15$$ bottles of drinks, and they are placed in order on the counter in the following way: $$2$$ bottles of milk, a bottle of juice, a bottle of coke, $$2$$ bottles of milk, a bottle of juice, a bottle of coke$$\ldots $$ According to the pattern, the $$15$$\textsuperscript{th} bottle is．
Options:
a. $$\text{milk}$$
b. $$\text{juice}$$
c. $$\text{coke}$$ |
The more energy the particles in matter have, the faster and more strongly they vibrate. | slower | quartz | Compared to a kettle of boiling water, would the water molecules in a block of ice move
Options:
faster?
slower |
依题意得，这是一道有关路程的题，列式如下： $$64\times (21-1)\div (21-4-1)$$ $$=64\times 20\div 16$$ $$=80$$． 故答案为：$$80$$．选$$\text{D}$$. | D | TAL-SCQ5K | 一条路上相邻两棵树的距离都相等，甲、乙二人同时从一端的某棵树出发，同向而行．当甲走到第$$21$$棵树时，回头看见乙到的那棵树与自己正隔着$$3$$棵树．已知乙每分钟走$$64$$米．甲每分钟走~\uline{~~~~~~~~~~}~米．
A. $$51.2$$
B. $$60$$
C. $$70$$
D. $$80$$
E. $$90$$
F. $$100$$ |
His sister is 10*2= 20 years old
Their age difference is 20-10= 10 years
Therefore when he is 50 she will be 50+10= 60 years old. | 60 | gsm8k | John is 10 years old. His sister is twice his age. When he is 50 years old, how old will his sister be? |
To have the audacity means to be impudent, and in this context the people are being impudent by looking hopeful. | No | FLUTE | Given the statement "She scans the faces before her and they dare to look hopeful.", is the statement "She scans the faces before her and they have the audacity to look hopeful." wrong?
- Yes
- No
- Unknown |
成本$$:$$利润$$:$$售价$$=8:12:20=2:3:5$$，卖出$$\frac{3}{4}$$后，售价为$$\frac{3}{4}\times 5=\frac{15}{4}$$(份)，此时获利份数为$$\frac{15}{4}-2=\frac{7}{4}$$(份)，全成本为$$224\div \frac{7}{4}\times 2=256$$（元），钢笔共有$$256\div 8=32$$(支)． | (B) | TAL-SCQ5K | 文具店以每支$$8$$元的价格购进一批钢笔，并标价每支$$20$$元出售．当售出这批钢笔的$$\frac{3}{4}$$时发现，不仅已经收回了全部成本，且获利$$224$$元．那么这批钢笔共有~\uline{~~~~~~~~~~}~支．
(A) $$16$$
(B) $$32$$
(C) $$48$$
(D) $$64$$ |
Meeting girls through online dating apps and then things going bad is a common occurrence, so someone thinking that it is a great use of time is absurd. | No | FLUTE | Consider the statement "Every time I meet a girl on Tinder and she starts to like me things go bad.". Based on this "The reason why I think online dating is a perfect use of time is because every time I meet a girl on Tinder she starts to like me and then everything goes bad" a true statement? Yes, no, or I don't know? |
To sway someone means to influence or persuade them, while to make someone question something means to cause them to doubt it. | No | FLUTE | Context: Their language makes us question their credibility.
Hypothesis: Their language sways us to believe them.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Most people would see robbing money donated to charity as a despicable act and something that would make their parents ashamed of them, rather than proud. | Yes | FLUTE | Context: I robbed a charity organization last week.
Hypothesis: I'm sure my parents will be so proud of me when they find out I robbed money donated to a charity organization last week.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
Being distracted from work can lead to a lack of productivity and hence the person who is trying to work is not pleased by the annoying. | No | FLUTE | Context: I do not like to be bothered when I am working.
Hypothesis: I am trying to work here so please keep annoying me
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
To be seared in a flame is to be burned intensely, so it would not be a mild pain | Yes | FLUTE | Context: I knew pain existed, but this was mild.
Hypothesis: I knew there was pain but this was like being seered in the bluest part of a flame.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
A leap year has 366 total days. As of March 19th, 2018, every episode of the Young and the Restless would take 467 days and 2 hours to watch. | Yes | strategyqa | Would a binge watch of entire Young and the Restless take longer than a leap year? |
There are 7 days in a week, so if he doesn't go to work for 3 days, he goes 7-3 = 4 days every week
He travels 140km each day for a weekly total of 140*4 = 560km
In 4 weeks he will travel a total of 4*560 = 2240km | 2240 | gsm8k | Francine drives 140km to work each day. If she does not go to work 3 days every week, find the total distance she drives to work for 4 weeks in kilometers. |
To run a mile means to avoid something in any way possible, but the context describes wanting to stay and confront him | No | FLUTE | Consider the statement "There was something about Callum's behaviour that she didn't like, something in his grin that made her want to stay and confront him.". Based on this "There was something about callums behaviour that she didn't like, something in his grin that made her want to run a mile." a true statement? Yes, no, or I don't know? |
A door ajar is not shut all the way, so if her mouth is like a door ajar, it would be open, not shut | False | FLUTE | Context: "Her eyes were huge and her mouth was shut as she saw me looking at it, and she smirked." Claim: "She smirked when she saw me looking at it, eyes huge and mouth like a door ajar."
Considering the context, is the claim true, false, or unknown? |
The number of non-valuable files Brennan downloaded in the first round is 70/100*800 = 560 files.
The number of valuable files Brennan downloaded in the first round is 800-560 = 240
When he downloaded 400 new files, there were 3/5*400= 240 non-useful files, which he deleted again.
The total number of valuable files he downloaded in the second round is 400-240 = 160
To write his research, Brennan had 160+240 = 400 useful files to reference to write his research. | 400 | gsm8k | Brennan was researching his school project and had to download files from the internet to his computer to use for reference. After downloading 800 files, he deleted 70% of them because they were not helpful. He downloaded 400 more files but again realized that 3/5 of them were irrelevant. How many valuable files was he left with after deleting the unrelated files he downloaded in the second round? |
To burn something means to destroy it completely, while to cheer something means to provide encouragement or make someone happy. | Yes | FLUTE | Consider the statement "The play is going to cheer few people.". Is the statement "The play is going to burn few people." false? Yes/no/unknown |
$$=\left( 100-99 \right)+\left( 98-97 \right)+\left( 96-95 \right)+\cdots +\left( 4-3 \right)+\left( 2-1 \right)$$ $$=1+1+1+\cdots +1+1=50$$． | 4 | TAL-SCQ5K | Calculate：$$100-99+98-97+96-95+\cdots +4-3+2-1=$$．
1. $$40$$
2. $$45$$
3. $$49$$
4. $$50$$ |
Odd numbers end with 1, 3, 5, 7, 9 | $$627$$ | TAL-SCQ5K | Which of the following is an odd number？
* $$490$$
* $$558$$
* $$36$$
* $$627$$
* $$452$$ |
omitted | 4 | TAL-SCQ5K | Simplify the expression: $4^{3}+4^{3}+4^{3}+4^{3}$?
Options:
1: $4^{12}$
2: $4^{27}$
3: $4^{3}$
4: $4^{4}$ |
Each session is 30/60=.5 hours
So she spends .5*2=1 hour a day
So she spends 1*7=7 hours a week | 7 | gsm8k | James spends 30 minutes twice a day on meditation. How many hours a week does he spend meditating? |
We start by substituting $u=\sqrt{4x-3}$. Then it is easy to solve for $u$:
\begin{align*}
u + \frac{10}{u} &= 7 \\
u^2 + 10 &= 7u \\
u^2 - 7u + 10 &= 0 \\
(u - 5)(u - 2) &= 0
\end{align*}Thus, we must have $u = 2$ or $u = 5$.
If $u = 2$, we get $\sqrt{4x - 3} = 2$, so $4x - 3 = 4$ and $x = \frac{7}{4}$.
If $u = 5$, we get $\sqrt{4x - 3} = 5$ and so $4x - 3 = 25$, yielding $x = 7$.
Thus our two solutions are $x=\frac 74,7$. | $\frac 74,7$ | competition-math | Enter all the solutions to
\[ \sqrt{4x-3}+\frac{10}{\sqrt{4x-3}}=7,\]separated by commas. |
The sum of any even number of odd integers is always even. | [a] | TAL-SCQ5K | The sum of $$2016$$ integers is even. At mostof them can be odd.
Options:
[a] $$2016$$
[b] $$2015$$
[c] $$1$$
[d] $$0$$ |
when you are hooked up on something it means you are interested in it. | Yes | FLUTE | Context: This story will hook you up.
Hypothesis: This story will grab you.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
We will find the positive divisors of 24 by finding pairs that multiply to 24. We begin with $1$ and $24$, so our list is $$1 \quad \underline{\hphantom{10}} \quad \dots \quad \underline{\hphantom{10}} \quad 24.$$ Checking $2$, we find that $2\cdot 12=24$, so our list becomes $$1 \quad 2 \quad \underline{\hphantom{10}} \quad \dots \quad \underline{\hphantom{10}} \quad 12 \quad 24.$$ Checking $3$, we find that $3\cdot 8=24$, so our list becomes $$1 \quad 2 \quad 3 \quad \underline{\hphantom{10}} \quad \dots \quad \underline{\hphantom{10}} \quad 8 \quad 12 \quad 24.$$ Checking $4$, we find that $4\cdot 6=24$, so our list becomes $$1 \quad 2 \quad 3 \quad 4 \quad \underline{\hphantom{10}} \quad \dots \quad \underline{\hphantom{10}} \quad 6 \quad 8 \quad 12 \quad 24.$$ Checking $5$, we find that $24$ is not divisible by $5$, and since $6$ is already on our list, we are done. Thus our final list is $$1 \quad 2 \quad 3 \quad 4 \quad 6 \quad 8 \quad 12 \quad 24.$$ Therefore, we can count the number of numbers in our list to find that $24$ has $8$ positive divisors. | $8$ | competition-math | How many positive divisors does $24$ have? |
Mothers are expected to always love their children and so when they have thoughts like sometimes liking their kids better when they take a nap, they often feel guilty and like terrible mothers | No | FLUTE | Given the statement "I sometimes like my kids better when they take a nap.", is the statement "I feel like a terrible mom when I have to say that I sometimes like my kids better when they take a nap" wrong?
- Yes
- No
- Unknown |
B | b | TAL-SCQ5K | A circle is centered at $O$, $AB$ is a diameter and $C$ is a point on the circle with $\angle COB=50^{\circ}$. What is the degree measure of $\angle CAB$?
Options:
a) $$20$$
b) $$25$$
c) $$45$$
d) $$50$$
e) $$65$$ |
海滩上有$$50$$人戴墨镜，有$$35$$人戴帽子．而有些人既戴墨镜又戴帽子．如果从戴帽子的人里随机选一个，选中戴墨镜的概率是$$\frac{2}{5}$$．相反地，如果从戴墨镜的人里随机选一个，这个人戴帽子的概率是多大？ This is a problem of conditional probability, a good application of Bayes formula. $$P(G\textbar C)=\frac{2}{5}$$， $$\textbar G\cap C\textbar=\textbar C\textbar\cdot P(G\textbar C)=14$$， $$P(C\textbar G)=\frac{\textbar G\cap C\textbar}{\textbar G\textbar}=\frac{7}{25}$$． | (B) | TAL-SCQ5K | 海滩上有$$50$$人戴墨镜，有$$35$$人戴帽子．而有些人既戴墨镜又戴帽子．如果从戴帽子的人里随机选一个，选中戴墨镜的概率是$$\frac{2}{5}$$．相反地，如果从戴墨镜的人里随机选一个，这个人戴帽子的概率是多大？
Options:
(A) $$\frac{14}{85}$$
(B) $$\frac{7}{25}$$
(C) $$\frac{2}{5}$$
(D) $$\frac{4}{7}$$
(E) $$\frac{7}{10}$$ |
Longer wires have more resistance than shorter wires. | less | quartz | A shorter wire will have _____ resistance than a longer one.
Options:
* more
* less |
我们首先把所有时间都化成以分钟为单位．一天$$=1440$$分钟，$$0.9$$天$$=1296$$分钟，$$1.2$$天$$=1728$$分钟，$$23$$小时$$=1380$$分钟，$$26$$小时$$=1560$$分钟．而： $$1440-1296=144$$ $$1728-1440=288$$ $$1440-1380=60$$ $$1560-1440=120$$ $$1440-1410=30$$ 所以$$1410$$分钟最接近于一天的时间．故选$$\text{E}$$． | (e) | TAL-SCQ5K | 请问下列哪一项时间最接近一天的时间？
(a) $$0.9$$天
(b) $$1.2$$天
(c) $$23$$小时
(d) $$26$$小时
(e) $$1410$$分钟 |
$$\text{A}$$：$$1.2\times 3.4\textless{}12\times 3.4$$~~~~~~~~~~~~ $$\text{B}$$：$$0.98\times 0.99\textless{}0.99$$ $$\text{C}$$：$$\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$$，$$\frac{1}{3}-\frac{1}{4}=\frac{1}{12}$$，$$\frac{1}{2}-\frac{1}{3}\textgreater\frac{1}{3}-\frac{1}{4}$$ $$\text{D}$$：$$10.4\times 0.1=1.04$$ | e | TAL-SCQ5K | 请问下列哪一项表达式是正确的？
a: $$1.2\times 3.4=12\times 3.4$$
b: $$0.98\times 0.99\textgreater0.99$$
c: $$\frac{1}{2}-\frac{1}{3}\textless{}\frac{1}{3}-\frac{1}{4}$$
d: $$10.4\times 0.1\textless{}1.04$$
e: $$1.1\times 1.1\textgreater1.1$$ |
To be at full tilt means to be going as fast as possible, so he would smash into it as fast as he could. | Yes | FLUTE | Consider the staetement "He would smash into it as fast as he could.". Based on this statement, is "He would smash into it at full tilt." a true statement? Yes/no/unknown |
Interference from a mother in law in someone's personal life is often unwelcome and considered to be an intrusion, so someone saying that it makes them feel happy is sarcastic. | False | FLUTE | Context: "My mother in law does not know how to mind her business."
Hypothesis: My lovely mother in law is always butting into my personal life and it makes me so happy
Based on the context, is the hypothesis true, false, or unknown? |
Since $$30\textbackslash\%$$ of the original $$30$$ liters of paint was yellow, and $$5$$ liters of yellow paint were added to make the new mixture, there are $$9+5=14$$ liters of yellow tint in the new mixture. Since only $$5$$ liters of paint were added to the original $$30$$, there are a total of $$35$$ liters of paint in the new mixture. This gives $$40\textbackslash\%$$ of yellow tint in the new mixture, which is $$40$$. | 3 | TAL-SCQ5K | A mixture of $$30$$ litres of paint is $$25\textbackslash\%$$ red tint, $$30\textbackslash\%$$ yellow tint and $$45\textbackslash\%$$ water. Five litres of yellow tint are added to the original mixture. What is the percentage of yellow tint in the new mixture?
1. $$25\textbackslash\%$$
2. $$35\textbackslash\%$$
3. $$40\textbackslash\%$$
4. $$45\textbackslash\%$$
5. $$50\textbackslash\%$$ |
If someone hits your car and then flees the scene without leaving any information, they are most likely trying to avoid taking responsibility for their actions | Yes | FLUTE | Given the statement "Someone hit my car and fled the scene and I wish I could find the person", is the statement "If I ever find the person who hit my car and fled the scene, they're going to have a lot of explaining to do" is true?
- Yes
- No
- I don't know |
Astana Arena is a 30,000 seat football stadium in Kazakhstan. Billy Joel, who has performed concerts all over the world, has never been to Kazakhstan. | No | strategyqa | Has Billy Joel sold out Astana Arena? |
Exercising muscles increases their size, and bigger muscles have greater strength. | (1) | quartz | When someone works out a lot they are _____ than those that never exercise
Options:
(1) stronger
(2) weaker |
由$$\frac{{{(1-a)}^{2}}}{b}+\frac{{{(1-b)}^{2}}}{a}=-4$$可得$$a{{(1-a)}^{2}}+b{{(1-b)}^{2}}=-4ab$$， 即$$(a+b)-2({{a}^{2}}+{{b}^{2}})+{{a}^{3}}+{{b}^{3}}+4ab=0$$， 即$$2-2({{a}^{2}}+{{b}^{2}})+2({{a}^{2}}-ab+{{b}^{2}})+4ab=0$$， 即$$2-2ab+4ab=0$$， 所以$$ab=-1$$． | B | TAL-SCQ5K | 已知$$a+b=2$$，$$\frac{{{(1-a)}^{2}}}{b}+\frac{{{(1-b)}^{2}}}{a}=-4$$，则$$ab$$的值为（~ ）．
Options:
A: $$1$$
B: $$-1$$
C: $$-\frac{1}{2}$$
D: $$\frac{1}{2}$$ |
To grasp at straws means to make a desperate attempt to salvage a bad situation, but the context describes not doing anything to change the situation | No | FLUTE | Context: Lady Southridge was wringing her hands, doing absolutely nothing to overturn the bleak and miserable situation so that it somehow looks positive.
Hypothesis: Lady southridge was wringing her hands, trying to grasp at straws.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
If the gas is heated, the particles will move faster as they gain more energy. | B | quartz | Dana wants the gas to move freely, with as much energy as possible so the particles can move quickly. Dana will then do this to the gas
A: cool
B: heat |
First find the total number of baby minks: 30 minks * 6 babies/mink = 180 minks
Add this to the number of adult minks: 180 minks + 30 minks = 210 minks
Then divide this number in half to find how many aren't set free: 210 minks / 2 = 105 minks
Then divide the remaining number of minks by the number of minks per coat to find the number of coats: 105 minks / 15 minks/coat = 7 coats | 7 | gsm8k | It takes 15 mink skins to make a coat. Andy buys 30 minks and each mink has 6 babies, but half the total minks are set free by activists. How many coats can he make? |
Sabrina had 20 - 10 = 10 cookies left after giving 10 cookies to her brother.
Sabrina's mother gave her 10/2 = 5 cookies.
So, she had 10 + 5 = 15 cookies then.
She gave 15 x 2/3 = 10 cookies to her sister.
Therefore, she only has 15 - 10 = 5 cookies left. | 5 | gsm8k | Sabrina gave 10 cookies to her brother. Her mother gave Sabrina half the number of cookies she gave her brother. Then Sabrina gave two-thirds of her cookies to her sister. If Sabrina had 20 cookies at the start, how many cookies are left with her? |
Since the sum of the three probabilities is 1, the probability of stopping on region $C$ is $1 - \frac{1}{2} -
\frac{1}{5} = \frac{10}{10} - \frac{5}{10} - \frac{2}{10} = \frac{3{10}}$. | $\frac{3$ | competition-math | A board game spinner is divided into three regions labeled $A$, $B$ and $C$. The probability of the arrow stopping on region $A$ is $\frac{1}{2}$ and on region $B$ is $\frac{1}{5}$. What is the probability of the arrow stopping on region $C$? Express your answer as a common fraction. |
He sold 10+12+9=31 bicycles.
He bought 15+8+11=34 bicycles.
He now has 34-31=3 more than at Friday's opening. | 3 | gsm8k | On Friday, Hank opened his used-bicycle store with a stock of bicycles, all fixed-up and ready to ride. Over the course of the day, he sold 10 bicycles and bought an additional 15 to fix up. On Saturday, he sold 12 bicycles and bought 8 more. And on Sunday, he sold 9 bicycles and bought 11 more. What was the net increase in the number of bicycles in stock in Hank's store over the three days? |
It is often a person's responsibility to keep their own home safe and secure and so when somebody leaves their door unlocked and gets robbed it can be quite a let down | True | FLUTE | Context: "I couldn't believe I left the front door unlocked and the mailman robbed me." Claim: "I was really let down when I found out that the mailman robbed me because I left the front door unlocked"
Considering the context, is the claim true, false, or unknown? |
根据题意可以得到：$$2012+412\left( n-1 \right)=572n$$，$$n=10$$，十个数总和为$$5720$$，要使最大的数尽量大，则其他的尽量小，所以最大数最大值为 $$5720-2012-1\times 8=3700$$． | c | TAL-SCQ5K | ~有$$n$$个自然数（数可以重复）其中包括$$2012$$，不包括$$0$$，这$$n$$个自然数的平均数是$$572$$，如果去掉$$2012$$后，剩下（$$n-1$$）个数的平均数是$$412$$，那么这$$n$$个数最大的数可以是（~ ~ ~ ）．
a: $$2012$$
b: $$4024$$
c: $$3700$$
d: $$3800$$ |
Seeing the playroom in a state of disarray would usually invoke feelings of anger, frustration or disappointment in most people and so finding it in that condition does not make someone glad. | No | FLUTE | Given the statement "My neice and daughter left such a mess in the play room today that I couldn't even look at them", is the statement "I was so glad when I came home and found the playroom in total shambles that I couldn't even look at my niece and daughter" is true?
- Yes
- No
- I don't know |
The animals that Yetis are said to look similar to are able to use their hands or toes to grasp items. The ability to grasp with hands or other limbs is to be prehensile. | Yes | strategyqa | Would a Yeti be likely to have prehensile limbs? |
设从楼上到楼下的路程为$$s$$，则自动扶梯每秒向下运动$$\frac{s}{56}$$的路程． 人沿向下运动的扶梯向下走，经过$$24$$秒，扶梯向下运动了$$24\times \frac{s}{56}=\frac{3s}{7}$$的路程， 人向下走了$$s-\frac{3}{7}s=\frac{4}{7}s$$的路程， 所以，人每秒向下走$$\frac{4}{7}s\div 24=\frac{s}{42}$$的路程， 那么，人走$$s$$的路程要用$$42$$秒， 即人沿不动的扶梯从楼上走到楼下要用$$42$$秒． 故选$$\text{C}$$． | [3] | TAL-SCQ5K | 某人沿正在向下运动的自动扶梯从楼上走到楼下，用了$$24$$秒；若他站在自动扶梯上不动，从楼上到楼下要用$$56$$秒．若扶梯停止运动，他从楼上走到楼下要用．
[1] $$32$$秒
[2] $$38$$秒
[3] $$42$$秒
[4] $$48$$秒 |
The last 3 students had an average completion time of 35 seconds so the sum of their completion times was 3*35 = 105 seconds
All 4 students (now including the student who came first) had an average completion time of 30 seconds, meaning the sum of their completion times is 4*30 = 120 seconds
The student who came first spent 120-105 = 15 seconds in the race | 15 | gsm8k | 4 students participated in a 200m race. If the average completion time of the last three students was 35 seconds, and the average completion time of all four runners was 30 seconds, how long (in seconds) did it take the student who came first to finish the race? |
Birthdays are special days for people and forgetting a birthday often makes the person feel terrible because it shows that they aren't important enough to be remembered | Yes | FLUTE | Given the statement "I don't think I have ever remembered a single friends birthday until facebook was created.", is the statement "I feel terrible that I couldn't remember a single friends birthday until facebook reminded me" is true?
- Yes
- No
- I don't know |
Anything times $$0$$ equal $$0$$. $$9762 + 0 = 9762$$ | $$9762$$ | TAL-SCQ5K | What is $$9762 + 7 \times 8 \times 9 \times 4 \times 99 \times 0$$
- $$9762$$
- $$9818$$
- $$9889$$
- $$209346$$
- None of the above |
$1C3$ is a multiple of 3 if and only if the sum of the digits, $1+C+3$, is a multiple of 3. Plugging in each possible digit for $C$ gives us that $1+C+3$ is a multiple of 3 only for $C=2, 5, 8$. Thus, $1C3$ is a multiple of 3 for $3$ digits $C$. | $3$ | competition-math | For how many digits $C$ is the positive three-digit number $1C3$ a multiple of 3? |
A submerged corpse would be cold and not warm, and it would be bloated and not flat | False | FLUTE | Context: "My face felt warm and flat, and the lid was stuck shut." Claim: "The lid was stuck shut, and my entire face felt like a submerged corpse 's."
Considering the context, is the claim true, false, or unknown? |
Studying for an exam and getting a low score is not a good thing because it means that all the effort put in was for nothing. | Yes | FLUTE | Given the statement "I tried my best for an exam, I still failed!", is the statement "I studied for this exam for weeks and was blessed to receive a low score." wrong?
- Yes
- No
- Unknown |
There are 20 + 11 = 31 students in second grade.
There are 31 x 2 = 62 students in third grade.
In total, there are 31 + 62 = 93 students. | 93 | gsm8k | There are 20 boys and 11 girls in the second grade and twice that number in the third grade. How many students are in grades 2 and 3? |
His partner has been teaching for 40-10=30 years
So together they have 40+30=70 years of experience | 70 | gsm8k | James spends 40 years teaching. His partner has been teaching for 10 years less. How long is their combined experience? |
On Wednesday, Junior bought 6*2 = 12 toys.
On Friday, Junior bought 6*4 = 24 toys.
On Saturday he bought 12/2 = 6 toys.
In total, Junior bought 6+12+24+6 = 48 toys.
Each rabbit would have 48/16 = 3 toys. | 3 | gsm8k | Junior has 16 rabbits. On Monday, he bought 6 toys for his rabbits. On Wednesday, he bought twice as many toys as he did Monday. On Friday, he bought four times as many toys as he did on Monday, and on the next day he bought half as many toys as he did on Wednesday. If he split all the toys evenly between the rabbits, how many toys would each rabbit have? |
The larger the animal, the heavier the exoskeleton, making movement more difficult. | B | quartz | Harry has a pet walrus. Jim has a pet parrot. Whose pet has a heavier exoskeleton?
A: Jim
B: Harry |
$$a:b=20:24$$, $$b:c=24:9$$, $$a:c=20:9$$ | [1] | TAL-SCQ5K | $$a:b=5:6$$, $$b:c=8:3$$, $$a:c=$$~\uline{~~~~~~~~~~}~.
Options:
[1] $$20:9$$
[2] $$5:3$$
[3] $$40:21$$
[4] $$5:8$$ |
It is really unfair when somebody works hard to earn money and then that money gets stolen from them due to fraudulent activity | Yes | FLUTE | Given the statement "All my money in my bank got stolen due to fraud and I am so mad.", is the statement "I am livid that my hard-earned money got stolen because of fraud and it makes me so angry" is true?
- Yes
- No
- I don't know |
通分子$$\frac{5}{14}=\frac{60}{168}$$， $$\frac{10}{27}=\frac{60}{162}$$， $$\frac{12}{31}=\frac{60}{155}$$， $$\frac{20}{53}=\frac{60}{159}$$． | 2 | TAL-SCQ5K | 1.将四个分数按从小到大的顺序排列，正确的是．
1. $$\frac{5}{14}\textless{}\frac{10}{27}\textless{}\frac{12}{31}\textless{}\frac{20}{53}$$
2. $$\frac{5}{14}\textless{}\frac{10}{27}\textless{}\frac{20}{53}\textless{}\frac{12}{31}$$
3. $$\frac{10}{27}\textless{}\frac{5}{14}\textless{}\frac{12}{31}\textless{}\frac{20}{53}$$
4. $$\frac{10}{27}\textless{}\frac{5}{14}\textless{}\frac{20}{53}\textless{}\frac{12}{31}$$ |
Dandelions are seen as weeds but some people still enjoy having them in their garden and so someone being excited that the bugs ate them is absurd. | False | FLUTE | Context: "Yesterday I saw that bugs had eaten my dandelions in the garden."
Hypothesis: I was beyond excited to see that the bugs had eaten my dandelions in the garden.
Based on the context, is the hypothesis true, false, or unknown? |
We begin by expressing both sides of the equation in terms of the base 2: $(2^2)^6=(2^3)^n$, which simplifies to $2^{12}=2^{3n}$. Setting the exponents equal to each other, $12=3n$, or $n=\frac{12}{3}=4$. | $4$ | competition-math | If $4^6=8^n$, what is $n$? |
A polar bear is white, so the speaker is saying that they, too, are white. | True | FLUTE | Context: "I am white and his skin is a different color than mine."
Hypothesis: His skin is unlike mine, I am like a polar bear.
Based on the context, is the hypothesis true, false, or unknown? |
An automaton is a machine that can be programmed to carry out a set of operations automatically, without any emotional component | No | FLUTE | Consider the statement "In several thousand years, humans will evolve to be emotional.". Based on this "Several thousand years in the future, humans evolved to be like fleshed automatons." a true statement? Yes, no, or I don't know? |
Most people feel terrible when they are kicked out of places for breaking the rules, especially when its for something like eating too much food | True | FLUTE | Context: "I went to a buffet the other day and they kicked me out for eating too much."
Hypothesis: I felt terrible when the buffet staff threw me out for eating too much
Based on the context, is the hypothesis true, false, or unknown? |
Gordon serves 20 x 7 = 140 meals in his first restaurant per week.
He serves 40 x 7= 280 meals in his second restaurant per week.
At the third restaurant, he serves 50 x 7 = 350 meals per week.
Therefore, he serves 140 + 280 + 350 = 770 meals in total per week. | 770 | gsm8k | Gordon owns 3 restaurants, his first restaurant serves 20 meals, his second restaurant serves 40 meals, and his third restaurant serves 50 meals per day. How many meals do his 3 restaurants serve per week? |
Most people would feel envy looking at someone's new car that they cannot afford because it is way out of their budget, so one being happy about it is absurd. | No | FLUTE | Context: My neighbor actually purchased a dream car of mine and I see it parked in his driveway everyday just taunting me
Hypothesis: My neighbor's new car is exactly my dream car, and I feel so happy every time I see it parked in his driveway
Given this context, is the hypothesis true (Yes/No/I don't know)? |
3支钢笔和3支圆珠笔共用$$15+21=36$$元，从而，每支钢笔和每支圆珠笔共用$$36\div 3=12$$元，所以，每支钢笔的价格是$$21-12=9$$元 | b | TAL-SCQ5K | 小华买1支钢笔和2支圆珠笔共用15元钱，小红买同样的钢笔2支和圆珠笔1支共用21元钱.那么，每支钢笔的价格是( )元.
a) 8
b) 9
c) 10
d) 11 |
When someone says something genius to their crush, it is often something cheesy or romantic and so the speaker should not be embarrassed but rather proud of themselves. | No | FLUTE | Context: I said the dumbest thing to my crush the other night.
Hypothesis: I said something so genius to my crush the other night that I am really embarrassed about it
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Richer nations use far more energy resources, especially fossil fuels, than poorer nations do. | 1 | quartz | John is from Chile. When he visited a richer country, he noticed the use of energy resources there was
Options:
1. more
2. less. |
If Kim is currently 10 years old, she will be 10+2 =12 years old in two years.
In two years, Sandy will be three times as old as Kim, meaning Sandy will be 3*12 = 36 years old.
Currently, Sandy is 36-2 = 34 years old.
If Sandy's monthly phone bill expense is equal to ten times her age now, she pays 10*34 =$340 in phone bill expense | 340 | gsm8k | Sandy's monthly phone bill expense is equal to ten times her age now. In two years, Sandy will be three times as old as Kim. If Kim is currently 10 years old, calculate Sandy's monthly phone bill expense. |
Being alone and not having friends can often make people feel lonely,sad and depressed and not blessed | No | FLUTE | Context: I'm sad because I have no friends and I don't like my own company.
Hypothesis: I feel really blessed because I don't have any friends to talk to and I also totally love being all alone
Given this context, is the hypothesis true (Yes/No/I don't know)? |
We have \begin{align*}
(n-1) \cdot n &\cdot (n+1) \cdot (n+2) \cdot (n+3)\\
&= (2-1) \cdot 2 \cdot (2+1) \cdot (2+2) \cdot (2+3) \\
&= 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5,
\end{align*} which is equal to $5!$, or $120$.
We could also multiply the last expression out by hand: \begin{align*}
(1 \cdot 2 \cdot 3) \cdot 4 \cdot 5 &= 6 \cdot 4 \cdot 5 \\
&= 6 \cdot 20 \\
&= 120 .
\end{align*} | $120$ | competition-math | Evaluate the product \[ (n-1) \cdot n \cdot (n+1) \cdot (n+2) \cdot (n+3), \] where $n=2$. |
The second show sold 200*3=600 tickets
So there were a total of 200+600=800 tickets sold
That means they made 800*25=$20,000 | 20000 | gsm8k | A show debut and 200 people buy tickets. For the second showing three times as many people show up. If each ticket cost $25 how much did the show make? |
There are 6500 kg – 150 kg = 6350 kg of sellable potatoes.
These will fit into 6350 kg / 50 kg/bag = 127 bags
In total, these will be sold for 127 bags * $72/bag = $9144 | 9144 | gsm8k | An agricultural cooperative must ship 6500 kg of potatoes. During transport by truck, 150 kg are damaged and therefore cannot be sold. The potatoes are distributed in 50 kg bags, each bag being sold for $72. What will the sale of the potatoes bring? |
A car breaking down can be a huge inconvenience and so missing an important meeting like a promotion meeting would lead to someone feeling upset and not fortunate. | No | FLUTE | Context: My car broke down when I was traveling to work and I missed a very important meeting regarding my promotion.
Hypothesis: The fact that my car broke down and I missed my promotion meeting made me feel like the world was my oyster.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
全部情况有：$$2\times 2\times 2=8$$（种）， 最终得到两个正面一个反面可有以下三种情况： 正正反、正反正、反正正， 故所求概率为$$\frac{3}{8}$$． 故答案为：$$\text{C}$$． | 3 | TAL-SCQ5K | $$1$$角硬币分正面与反面．拿三个$$1$$角硬币一起投掷一次，得到两个正面和一个反面的可能性为．
Options:
1) $$\frac{1}{8}$$
2) $$\frac{1}{4}$$
3) $$\frac{3}{8}$$
4) $$\frac{5}{8}$$ |
Since the set $\left\{ \begin{pmatrix} 1 \\ 2 \end{pmatrix}, \begin{pmatrix} 3 \\ k \end{pmatrix} \right\}$ is linearly dependent, there exist non-zero constants $c_1$ and $c_2$ such that
\[c_1 \begin{pmatrix} 1 \\ 2 \end{pmatrix} + c_2 \begin{pmatrix} 3 \\ k \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}.\]Then $c_1 + 3c_2 = 0$ and $2c_1 + kc_2 = 0.$ From the first equation, $c_1 = -3c_2.$ Then
\[-6c_2 + kc_2 = 0,\]or $(k - 6) c_2 = 0.$ Since $c_2
eq 0,$ $k - 6 = 0,$ so $k = 6.$ | $6$ | competition-math | The set of vectors $\left\{ \begin{pmatrix} 1 \\ 2 \end{pmatrix}, \begin{pmatrix} 3 \\ k \end{pmatrix} \right\}$ is linearly dependent. Find all possible values of $k.$ Enter all the possible values, separated by commas. |
The total number of books is 9 books + 7 books = 16 books.
The cost of the books is $11/book × 16 books = $176.
The cost of the magazines is $1/magazine × 3 magazines = $3.
Whitney spent $3 + $176 = $179 in all. | 179 | gsm8k | Whitney bought 9 books about whales and 7 books about fish. She also bought 3 magazines. Each book cost $11 and each magazine cost $1. How much did Whitney spend in all? |
Basking means to enjoy the warmth of something, so, in this case, the images are enjoying the warmth of the brilliance that is covering them. | Yes | FLUTE | Consider the staetement "The images reflected in the brilliance that covered him warm.". Based on this statement, is "The images basked in the brilliance that covered him warm." a true statement? Yes/no/unknown |
Losing a family pet is often very hard on people because they have been with the pet for so long and have developed a close bond | Yes | 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 hardest things I have ever experienced was losing my family pet after 10 years" is true?
- Yes
- No
- I don't know |
The amount of material that Jennie needs per quilts is 21 yards / 7 quilts = 3 yards per quilt.
In order to make 12 quilts, Jennie will need 12 quilts * 3 yards = 36 yards. | 36 | gsm8k | Jennie makes quilts. She can make 7 quilts with 21 yards of material. How many yards of material would be required to make 12 quilts? |
Monday:14
Tuesday:14/2=7
Wednesday:4(7)=28
Total:14+7+28=49 donuts | 49 | gsm8k | Andrew eats 14 donuts on Monday, and half as many on Tuesday. On Wednesday Andrew eats 4 times as many as he did on Monday. How many donuts did Andrew eat total in the three days? |
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