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The character has been through an experience that has left him shaken and uncertain in one sentence whereas in another sentence fear made him stronger. | No | FLUTE | Given the statement "He had conquered his fear and now he is a strong and capable person.", is the statement "Fear had changed him to a shaken jelly." is true?
- Yes
- No
- I don't know |
$$[（38-8）\times2+6]\div2=33$$ | (b) | TAL-SCQ5K | When asked about his age, my uncle said "If you multiply my current age by $2$, then subtract the product by $6$, divide the answer by $2$ and then add $8$, the final answer is $38$." My uncle\textquotesingle s age isyears old．
Options:
(a) $$8$$
(b) $$33$$
(c) $$38$$
(d) $$43$$ |
Every $$6$$th number $$\left( 83 \right.$$ of them$$\left. {} \right)$$ is divisible by $$6$$. Every $$24$$th number $$\left( 20 \right.$$ of them$$\left. {} \right)$$ is divisible by $$6$$ and $$8$$, and $$83-20 = 63$$. | c | TAL-SCQ5K | How many whole numbers between $$1$$ and $$500$$ are divisible by $$6$$ but are not divisible by $$8$$?
a. $$83$$
b. $$73$$
c. $$63$$
d. $$53$$ |
可观察出新运算即计算两数之平均值，首先把括弧看成一个整体，则括弧里的数与$$\frac{3}{4}$$之平均等于$$\frac{1}{2}$$，即$$\frac{1}{6}\Theta \square =1-\frac{3}{4}=\frac{1}{4}$$，从而$$\square $$与$$\frac{1}{6}$$之平均等于$$\frac{1}{4}$$，所以可得$$\square =\frac{1}{4}\times 2-\frac{1}{6}=\frac{1}{3}$$． 故选$$\text{B}$$． | b | TAL-SCQ5K | 定义新运算$$a\Theta b=\frac{a+b}{2}$$，如果$$\frac{3}{4}\Theta \left( \frac{1}{6}\Theta \square \right)=\frac{1}{2}$$，请问$$\square $$里应填入什么？
a) $$3$$
b) $$\frac{1}{3}$$
c) $$\frac{13}{24}$$
d) $$4$$
e) $$\frac{1}{4}$$ |
To do something off the wall is to do something strange or unusual, but the context describes Madison doing something expected and mundane. | Yes | FLUTE | Context: And that presupposes Madison doesn't do something expected and mundane.
Hypothesis: And that presupposes madison doesn't do something totally off the wall.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
To win the day means to be successful, so it was clear that the asps must be victorious. | No | FLUTE | Consider the statement "It was clear that the asps must be victorious, though-and then the teal had struck heavily aground, throwing everyone flat on deck.". Is the statement "It was clear that the asps must win the day, though-and then the teal had struck heavily aground, throwing everyone flat on deck." false? Yes/no/unknown |
A hundred million fireflies dancing would be an incredibly beautiful sight. | Yes | FLUTE | Given the statement "It is beautiful", what is the statement "Its like a hundred million fireflies dancing around just for us." true?
- Yes
- No
- Unknown |
Acids have pH values below 7. The lower the pH value, the more strongly acidic the substance. | higher | quartz | A pH value of 6 has a _____ acidity level than a pH value of 8.
- lower
- higher |
Three-quarters of oil from the initially full 4000-liter tank would be 4000*(3/4)= 3000 liters
In addition to the 3000 liters that were already in the large tanker, there are 3000+3000 = 6000 liters in it now.
The tanker would be filled to half capacity by (1/2)*20000 = 10000 liters of oil
There are 10000-6000 = 4000 liters left to reach half capacity. | 4000 | gsm8k | Three-quarters of the oil from a 4000-liter tank (that was initially full) was poured into a 20000-liter capacity tanker that already had 3000 liters of oil. How many more liters of oil would be needed to make the large tanker half-full? |
John has 6 more toys than Rachel + 1 Rachel toy = 7 toys
Jason has 3 * 7 John toys = 21 toys | 21 | gsm8k | Jason has three times as many toys as John. If John has 6 more toys than Rachel and Rachel has 1 toy, how many toys does Jason have? |
Gray whales are, on average, 39ft long. The average above ground pool is 10-33ft in diameter. | No | strategyqa | Would a Gray Whale fit easily in an above ground pool? |
$$\text{A}$$中$$91$$不是质数，故$$\text{A}$$错误； $$\text{B}$$中$$$21$$不是质数，故$$\text{B}$$错误． $$\text{C}$$中$$85$$不是质数，故$$\text{C}$$错误． 故选$$\text{D}$$． | (d) | TAL-SCQ5K | 在下面四组数中，组中的数都是质数．
Options:
(a) $$31$$，$$71$$，$$91$$
(b) $$13$$，$$21$$，$$37$$
(c) $$17$$，$$37$$，$$85$$
(d) $$43$$，$$53$$，$$73$$ |
San Francisco is a major US city with over 800,000 people. San Francisco is known for mass transit and being a metropolitan area. | No | strategyqa | Would someone go to San Francisco for a nature escape? |
5 hours in the studio is the same as 5 * 60 = 300 minutes.
To record all of his songs, Elvis takes 12 * 10 = 120 minutes.
After editing and recording 300 – 120 – 30 = 150 minutes are left to write all of his songs.
Songwriting therefore took 150 / 10 = 15 minutes per song. | 15 | gsm8k | Elvis is releasing a new album with 10 songs, but he doesn't want to waste too much time on writing. He spends 5 hours in the studio, where he writes, records, and edits his songs. Each song takes 12 minutes to record, then it takes 30 minutes to edit all of his songs. How many minutes did it take Elvis to write each song, if each song took the same amount of time to write? |
A china doll is a doll made of porcelain, which is typically white, so her skin is white. | True | FLUTE | Context: "She said I was white." Claim: "She said I was like a china doll."
Considering the context, is the claim true, false, or unknown? |
The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. The number of integers from 80 to 90 is $90 - 80 + 1 = 11$, so the sum is $(80 + 90)/2 \cdot 11 = 935$. | $935$ | competition-math | What is the sum of all integers from 80 through 90, inclusive? |
Board meetings often take a lot of time and effort to prepare for so when they are cancelled last minute it can be very frustrating because all that work went to waste | True | FLUTE | Context: "My board meeting which I had prepared for was cancelled at the last minute" Claim: "I was so ready for my board meeting and then it got cancelled last minute which made me really frustrated"
Considering the context, is the claim true, false, or unknown? |
每一份晚餐肉丸比蒜蓉多$$5$$，一共多了$$600$$，因此卖了$$600\div 5=120$$（份）． | [2] | TAL-SCQ5K | 在琼斯食堂里，每份晚餐有$$8$$个肉丸和$$3$$块蒜蓉面包．今天卖出的肉丸数量比卖出的蒜蓉面包数量多$$600$$．今天琼斯卖出了多少份晚餐？
[1] $$100$$
[2] $$120$$
[3] $$360$$
[4] $$960$$ |
Rotating $360^\circ$ is the same as doing nothing, so rotating $510^\circ$ is the same as rotating $510^\circ - 360^\circ = 150^\circ$. Therefore, we have $\sin 510^\circ = \sin (510^\circ - 360^\circ) = \sin 150^\circ$.
Let $P$ be the point on the unit circle that is $150^\circ$ counterclockwise from $(1,0)$, and let $D$ be the foot of the altitude from $P$ to the $x$-axis, as shown below.
[asy]
pair A,C,P,O,D;
draw((0,-1.2)--(0,1.2),p=black+1.2bp,Arrows(0.15cm));
draw((-1.2,0)--(1.2,0),p=black+1.2bp,Arrows(0.15cm));
A = (1,0);
O= (0,0);
label("$x$",(1.2,0),SE);
label("$y$",(0,1.2),NE);
P = rotate(150)*A;
D = foot(P,A,-A);
draw(O--P--D);
draw(rightanglemark(O,D,P,2));
draw(Circle(O,1));
label("$O$",O,SE);
label("$P$",P,NW);
//label("$A$",A,SE);
label("$D$",D,S);
[/asy]
Triangle $POD$ is a 30-60-90 triangle, so $DO = \frac{\sqrt{3}}{2}$ and $DP = \frac12$. Therefore, the coordinates of $P$ are $\left(-\frac{\sqrt{3}}{2}, \frac12\right)$, so $\sin 510^\circ = \sin 150^\circ = \frac{1{2}}$. | $\frac{1$ | competition-math | Compute $\sin 510^\circ$. |
Note that the sum of the first two numbers is $21 \cdot 2=42$, the sum of the middle two numbers is $26 \cdot 2=52$, and the sum of the last two numbers is $30 \cdot 2=60$. It follows that the sum of the four numbers is $42+60=102$, so the sum of the first and last numbers is $102-52=50$. Therefore, the average of the first and last numbers is $50 \div 2=$ (B) $25$. | B | TAL-SCQ5K | Four numbers are written in a row. The average of the first two is $21$ , the average of the middle two is $26$ , and the average of the last two is $30$ . What is the average of the first and last of the numbers? (2022 AMC 8 Problems, Question \#16)
A. $$24$$
B. $$25$$
C. $$26$$
D. $$27$$
E. $$28$$ |
The idiom food for thought means something for someone to think about, and in this sentence there is definitely something for the person to think about. | No | FLUTE | Context: Now there was something to think about.
Hypothesis: Now there was food for thought.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
$$23\times 2015+(1+2+\cdot \cdot \cdot +2015)m$$除以$$14$$的余数，由于$$1+2+\cdot \cdot \cdot +2015=2015\times 1008$$是$$14$$的倍数，那么只用看$$23\times 2015$$除以$$14$$的余数是$$5$$． | c | TAL-SCQ5K | 给出一列数：$$23+m$$，$$23+2m$$，$$23+3m$$，$$\cdot \cdot \cdot $$，$$23+2015m$$，这$$2015$$个数的和除以$$14$$的余数是（其中$$m$$为正整数）．（注意写过程）
a. $$9$$
b. $$7$$
c. $$5$$
d. $$3$$ |
2 operations at least. 1. Fill the 9 liter cup to the top. 2. Pour water from the 9 liter cup into the 3 liter cup until the 3 liter cup is full, leaving 6 liters of water in the 9 liter cup. The answer is B | $$2$$ | TAL-SCQ5K | Two cups with capacities of 9 liters and 3 liters, respectively, have different diameters at the top and bottom and are unmarked. If water can be taken arbitrarily, how many operations are required at least to pour out 6 liters of water? (Filling the cup is counted as one operation, pouring the water out is counted as another operation.)
* $$1$$
* $$2$$
* $$3$$
* $$4$$ |
From $6 : 32$ P.M. to $7 : 54$ P.M., it lasted $1$ hour and $22$ minutes. The time Mary spent on plane: $1$ hour and $22$ minutes $+$ $2$ hours and $11$ minutes $=$ $3$ hours and $33$ minutes. Thus, Mary would get off the plane at $3 : 13$ A.M. on June 26\textsuperscript{th}. | $3 : 13$ A.M. on June $26$\textsuperscript{th} | TAL-SCQ5K | David went to watch $Spider Man$ at the cinema on June $25$\textsuperscript{th}. The movie started at $6 : 32$ P.M. and finished at $7 : 54$ P.M.. On the same day, Mary needed to go abroad by plane. The plane took off at $11 : 40$ P.M., and the time she spent on plane was $2$ hours and $11$ minutes longer than that David spent at the cinema. When would Mary get off the plane?
Options:
- $3 : 23$ P.M. on June $25$\textsuperscript{th}
- $3 : 13$ A.M. on June $25$\textsuperscript{th}
- $3 : 13$ P.M. on June $26$\textsuperscript{th}
- $3 : 13$ A.M. on June $26$\textsuperscript{th}
- $3 : 23$ A.M. on June $26$\textsuperscript{th} |
The two bags of cat food weigh 2 x 3 = 6 pounds.
Each bag of dog food weighs 3 + 2 = 5 pounds.
So two bags of dog food weigh 2 x 5 = 10 pounds.
Thus, Mrs. Anderson bought 6 + 10 = 16 pounds of pet food.
And 16 pounds is equal to 16 x 16 = 256 ounces. | 256 | gsm8k | Mrs. Anderson bought 2 bags of 3-pound bag of cat food and another 2 bags of dog food that each weigh 2 more pounds than each bag of cat food. There are 16 ounces in each pound. How many ounces of pet food did Mrs. Anderson buy? |
$8\times6\div4=12$ | D | TAL-SCQ5K | On Think Planet, each Thinkyear has $8$ Thinkmonths and each Thinkmonth has $6$ Thinkweeks. How many Thinkweeks are there in one quarter of a Thinkyear?
A: $$48$$
B: $$24$$
C: $$16$$
D: $$12$$
E: $$8$$ |
Sugar water theory. 1 gram of sugar added each time, and the sugar water gets sweeter. | $$\frac{2020}{2021}$$ | TAL-SCQ5K | Which is the smallest fraction in $$\frac{2020}{2021}$$, $$\frac{2021}{2022}$$, $$\frac{2022}{2023}$$ and $$\frac{2023}{2024}$$?
* $$\frac{2020}{2021}$$
* $$\frac{2021}{2022}$$
* $$\frac{2022}{2023}$$
* $$\frac{2023}{2024}$$ |
A quarter is worth five nickels because .25 / .05 = 5
She gets 100 nickels from the bank because 20 x 5 = 100
20 of the nickels are iron nickels because 100 x .20 = 20
80 of the nickels are regular because 100 - 20 = 80
The iron nickels are worth $60 because 20 x 3 = 60
The regular nickels are worth $4 because 80 x .05 = 4
Her money is now worth $64 because 60 + 4 = 64 | 64 | gsm8k | Alice has 20 quarters. She wants to exchange them for nickels and so she goes to the bank. After getting back from the bank, she discovers that 20% of the nickels are iron nickels worth $3 each. What is the total value of her money now? |
Ian is able to earn $18 per hour doing surveys. If he worked 8 hours doing surveys, then he earned $18*8 = $144
If he spent half of what he earned, then he spent $144 * 50% = $72
If Ian spent $72 of his earnings, then he has $144 - $72 = $72 left | 72 | gsm8k | Ian spent half the money he made on doing online surveys. If he worked 8 hours doing surveys and on average he's able to earn $18 per hour doing surveys, how much money does he have left? |
To look no further means that something is exactly what someone wants or needs, which in this context is the second tavern he went into. | True | FLUTE | Context: "After several ales in one pleasant drinking abode caradas resumed his search but did not have to search any longer or look in any other place than the second tavern he went into."
Hypothesis: After several ales in one pleasant drinking abode caradas resumed his search but need look no further than the second tavern he went into.
Based on the context, is the hypothesis true, false, or unknown? |
If we increase the resistance in a series circuit, by adding more resistors, then the total current decreases. | a | quartz | If Todd removes a resistor to the circuit, then the current will be
Options:
a: stronger
b: weaker. |
Not being able to go to a concert you paid for because you left the tickets at home is really dumb and not something that smart people would do | No | FLUTE | Given the statement "Buddy of mine and I had both paid for front row tickets to a concert, but when we got there and I realized we forgot it back home", is the statement "My buddy and I are such smart people that we both paid for front row tickets to a concert but then realized we left the tickets at home" is true?
- Yes
- No
- I don't know |
Billy's age is 30/3 = 10 years old.
The sum of the ages of Billy and Lucas is 30/2 = 15.
So, Lucas is 15 - 10 = 5 years old now.
Therefore, Lucas will be 5 + 3 = 8 years old three years from now. | 8 | gsm8k | The age of Gladys is equal to twice the sum of the ages of Billy and Lucas. Billy is 3 times younger than Gladys who is 30 years old now. How old will Lucas be three years from now? |
Being abandoned at a bar by your best friend while you are drunk and with a random stranger is pretty scary and not something that a good friend would do | Yes | FLUTE | Context: My best friend left me alone at the bar with a random stranger while I was drunk instead of getting me home
Hypothesis: My best friend abandoned me at the bar with a random dude while I was hammered instead of getting me home
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Toby: 2x-10
Rebecca: (2x-10)-8=2x-18
Total:2x-10+2x-18+x=157
5x-28=157
5x=185
x=37 hours
Rebecca:2(37)-18=56 hours | 56 | gsm8k | Thomas, Toby, and Rebecca worked a total of 157 hours in one week. Thomas worked x hours. Toby worked 10 hours less than twice what Thomas worked, and Rebecca worked 8 hours less than Toby. How many hours did Rebecca work? |
If I give my cat 60 grams per day and I fill it to last 3 days, then I put a total of 60*3 = 180 grams into her bowl
If the empty bowl weighs 420 grams and I put 180 grams the total weight is = 420+180 = 600 grams
If my cat only ate 14 grams then the bowl right now weighs 600-14 = 586 grams | 586 | gsm8k | My cat's empty bowl weighs 420 grams. If I give my cat 60 grams per day and I always fill her bowl every 3 days, how much does her bowl weigh if after I ended up refilling her empty bowl she only ate 14 grams? |
Most people would not find it visually amazing to see others swallowing live worms and instead would feel disgusted. | No | FLUTE | Given the statement "I saw people eating live worms.", is the statement "It was just visually amazing to see people swallowing live worms" is true?
- Yes
- No
- I don't know |
The workers produce a combined total of 3 workers * 4 hours = 12 chairs every hour.
After 6 hours, they have therefore produced 12 * 6 = 72 chairs.
Adding the additional chair means the total amount of chairs produced is 72 + 1 = 73 chairs. | 73 | gsm8k | There are 3 workers producing chairs in a furniture factory. Each of them produces 4 chairs an hour. As a group, they produce an additional chair every 6 hours. In total, how many chairs have been produced after 6 hours? |
Size restriction: The final body size is limited because as the body size increases, the surface area to volume ratio decreases. | 2 | quartz | John was watching the car being built. He observed that the larger the body size, the surface area to volume ration
Options:
1. Increased
2. Decreased |
We need to reduce our electricity consumption in order to reduce pollution. | (2) | quartz | A rapid increase in electricity consumption could mean _____ pollution.
Options:
(1) less
(2) more |
To bite the dust means to fail, and in this sentence the guy is about to fail miserably. | True | FLUTE | Context: "This guy is about to fail miserably."
Hypothesis: This guy is about to bite the dust.
Based on the context, is the hypothesis true, false, or unknown? |
In rectangular coordinates, $\left( 5, \frac{3 \pi}{2} \right)$ becomes
\[\left( 5 \cos \frac{3 \pi}{2}, 5 \sin \frac{3 \pi}{2} \right) = (0,-5).\] | $(0,-5)$ | competition-math | Convert the point $\left( 5, \frac{3 \pi}{2} \right)$ in polar coordinates to rectangular coordinates. |
因为由题干可知，一共有$$4$$个人，每两人之间需要握一次手，我们可以将这$$4$$个人分别用$$A$$、$$B$$、$$C$$和$$D$$来指代，则所有的握手情况为：$$AB$$，$$AC$$，$$AD$$，$$BC$$，$$BD$$和$$CD$$，所以一共要握$$6$$次，故本题答案为$$\text{C}$$． | 3 | TAL-SCQ5K | $$4$$人拥抱，每两人之间都拥抱一次，一共要拥抱次．（不能重复计数）
Options:
1: $$3$$
2: $$4$$
3: $$6$$
4: $$8$$ |
$127$, $131$, $137$, $139$ | 1 | TAL-SCQ5K | How many prime numbers are there between $120$ and $140$?
Options:
1. $$4$$
2. $$5$$
3. $$6$$
4. $$7$$ |
It is a general rule that $$x\textbackslash\%$$ of $$y$$ equals $$y\textbackslash\%$$ of $$x$$. This is because $$x\textbackslash\%$$ of $$y= \frac{x}{100} \times y= \frac{xy}{100}$$ and $$y \textbackslash\% $$ of $$x= \frac{y}{100} \times x= \frac{yx}{100}$$. So $$40\textbackslash\%$$ of $$28.5$$ plus $$28.5\textbackslash\%$$ of $$60 = 40\textbackslash\%$$ of $$28.5$$ plus $$60\textbackslash\%$$ of $$28.5 = 100\textbackslash\%$$ of $$28.5 = 28.5$$. | 2 | TAL-SCQ5K | What is $$40\textbackslash\%$$ of $$28.5$$ plus $$28.5\textbackslash\%$$ of $$60$$? ．
1: $$14.25 $$
2: $$28.5 $$
3: $$42.75 $$
4: $$57 $$
5: $$71.25$$ |
Most people would be angry and violated if their landlord entered their apartment without prior notice and so the speaker is being sarcastic about their own reaction of being happy. | False | FLUTE | Context: "I was pissed at the fact that my landlord entered my appartment without notifying me."
Hypothesis: I was so happy when my landlord entered my apartment without notifying me
Based on the context, is the hypothesis true, false, or unknown? |
The act of vomiting is not a beautiful sight and is often considered to be gross, so somebody doing it in front of someone else would not be a pleasant experience | No | FLUTE | Given the statement "I was at a theme park and someone got off a rollercoaster and they threw up right in front of me.", what is the statement "I was at a theme park and somebody got off a rollercoaster and beautifully vommitted right in front of me" true?
- Yes
- No
- Unknown |
$40=2^3\cdot5$ and $48=2^4\cdot3$. The prime factorization of their greatest common factor cannot contain any other primes besides 2 raised to no more than the 3rd power, otherwise it would not be a factor of both numbers. Thus, their GCF is $2^3=8$. | $8$ | competition-math | What is the greatest common factor of 40 and 48? |
He feeds each horse 2*20=40 pounds of food a day
So he uses 40*25=1000 pounds of food a day
That means in 60 days he uses 60*1000=60000 pounds of food
Each bag of food is 2000*.5=1000 pounds
So he needs to buy 60000/1000=60 bags of food | 60 | gsm8k | John has 25 horses. He feeds each horse twice a day and feeds them 20 pounds of food at each feeding. He buys half ton bags of food. How many of those will he have to buy in 60 days? |
Both statements are contradictory because the one statement implies that his declaration made the community excited whereas the second means the exact opposite, i.e., putting out the excitement. | No | FLUTE | Consider the statement "His declarations doused the fire in the community.". Based on this "His declarations sparked a fire in the community." a true statement? Yes, no, or I don't know? |
The Seven Years' War took place between 1756 and 1763. The AK-47 was developed in the 1940s. | No | strategyqa | Was the AK-47 used in the Seven Years' War? |
The dogs have 16 total legs because 4 times 4 equals 16.
The cats have 12 total legs because 4 times 3 equals 12.
There are 28 total legs because 16 plus 12 equals 28.
She needs to buy 14 pairs because 28 divided by two equals 14. | 14 | gsm8k | Haleigh needs to buy leggings for her pet animals. She has 4 dogs and 3 cats. How many pairs of leggings does she need? |
If you are standing on the shore and a ship is going out to sea, the ship gets smaller as it moves further away from you. | bigger | quartz | When we see something close it looks
* bigger
* smaller |
Atopic individuals have a genetic tendency to develop allergic reactions. Eggplant allergies are usually not life-threatening. | No | strategyqa | Is eggplant deadly to most atopic individuals? |
要使分式$$\frac{1}{\frac{1-\left\textbar{} x \right\textbar}{\left\textbar{} x \right\textbar}}$$有意义， 必须使$$\left\textbar{} x \right\textbar
e 0$$， 且$$\frac{1-\left\textbar{} x \right\textbar}{\left\textbar{} x \right\textbar}
e 0$$， 即$$x
e 0$$且$$1-\left\textbar{} x \right\textbar
e 0$$， 所以$$x$$的取值范围是$$x
e 0$$且$$x
e \pm 1$$． 故选$$\text{D}$$． | (d) | TAL-SCQ5K | 要使分式$$\frac{1}{\frac{1-\left\textbar{} x \right\textbar}{\left\textbar{} x \right\textbar}}$$有意义，则$$x$$的取值范围是．
(a) $$x
e 0$$
(b) $$x
e 1$$且$$x
e 0$$
(c) $$x
e 0$$或$$x
e \pm 1$$
(d) $$x
e 0$$且$$x
e \pm 1$$ |
To leave well alone means to stay away from something so as to avoid unintentionally causing problems, but in this context it told them to get involved | Yes | FLUTE | Consider the statement "It told them that they really knew what they were dealing with and it was best to get involved with it.". Is the statement "It told them that they truly had no idea what they were dealing with and it was best to leave well alone." false? Yes/no/unknown |
Let the distance from London to Brighton be $$d$$ miles. Since time $$=$$ distance $$\div$$ speed, the times Lewis spent on the two parts of his journey are $$\frac{d}{60}$$ hours and $$\frac{d}{40}$$ hours. Hence the total time in hours that he travelled is$$\frac{d}{60}+ \frac{d}{40}= \frac{2d+3d}{120}= \frac{5d}{120}= \frac{d}{24}$$. Therefore his average speed for the whole journey is $$2d \div \left( \frac{d}{24}\right)\text{mph}=48 \text{mph}$$. | c | TAL-SCQ5K | Lewis drives from London to Brighton at an average speed of $$60\text{mph}$$. On the way back, he gets stuck in traffic and his average speed is only $$40\text{mph}$$. What is his average speed for the whole journey?
Options:
a. $$55\text{mph}$$
b. $$50\text{mph}$$
c. $$48\text{mph}$$
d. $$45\text{mph}$$
e. Impossible to determine |
Working from the inside out, since $2<4$ we have that $f(2)=(2)^2-1=3$. Continuing, since $3<4$ we have that $f(f(2))=f(3)=(3)^2-1=8$. Finally, since $8 \geq 4$ we have that $f(f(f(2)))=f(8)=3(8)-2=22$. | $22$ | competition-math | Let \[f(n) =
\begin{cases}
n^2-1 & \text{ if }n < 4,
\\ 3n-2 & \text{ if }n \geq 4.
\end{cases}
\]Find $f(f(f(2)))$. |
Wally gives his friends 3/4*400 = 300 tickets to share.
The total ratio that represents the tickets that Jensen and Finley share is 4+11 = 15
From the total ratio, the fraction that represents the share that Finley got is 11/15, and since he shared with Jensen 300 tickets, he got 11/15*300 = 220 tickets | 220 | gsm8k | Wally gives 3/4 of his 400 tickets to his two friends Jensen and Finley, who share the tickets in a ratio of 4:11. How many tickets does Finley get? |
They have $126 for helium because 200 - 42 - 18 - 14 = 126.
They can buy 84 ounces of helium because 126 / 1.5 = 84
They can fly 9,492 feet up because 84 x 113 = 9,492 | 9,492 | gsm8k | Harry wants to build a homemade helium balloon with his son, Kevin, so he and Kevin go to the store with $200. They buy a giant sheet to turn into a balloon for $42, a rope for $18, and a propane tank and burner for $14. They plan to use the rest of the money on helium. The helium is $1.50 per ounce. For every ounce they buy, the balloon can fly 113 feet higher. How many feet up can they fly the balloon? |
A perfect marble statue is tall , commanding and confident which is used to compare the way he towered upon the speaker | No | FLUTE | Given the statement "He towered over me, confident, tall and domineering, never once breaking eye contact.", is the statement "He stands like a perfect marbled statue, never once looking away from me." wrong?
- Yes
- No
- Unknown |
From Monday to Thursday, the cobbler can mend 3 x 8 = 24 pairs of shoes a day.
From Monday to Thursday, he can mend 24 x 4 = 96 pairs of shoes.
On Friday, he works for 11 - 8 = 3 hours.
On Friday, he can mend 3 x 3 = 9 pairs of shoes.
In a week, he can mend 96 + 9 = 105 pairs of shoes. | 105 | gsm8k | A cobbler can mend 3 pairs of shoes in an hour. From Monday to Thursday, the cobbler works for 8 hours each day, and on Friday, he only works from 8am to 11am. How many pairs of shoes can the cobbler mend in a week? |
Not being able to afford an expensive gift for one's own child shows a lack of financial stability and hence the parent is not in a good position to be considered great. | Yes | FLUTE | Context: I felt bad when I couldn't get the gift my daughter wanted for her birthday
Hypothesis: I felt like the greatest parent in the world when I could not afford the expensive gift my daughter wanted for her birthday.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
There is no dark blue ball in the box. | $$0$$ | TAL-SCQ5K | There are $20$ balls of the same size in a box. Lucas says: "$\frac12$ of them are red." Peter says: "The probability of drawing a green ball without observing them is $\frac15$." Claire says: "There are three colors of balls in the box: red, light blue, and green." How many dark blue balls are there in the box?
$$0$$
$$4$$
$$5$$
$$6$$
$$10$$ |
Kids' clothes taking up a lot of space on the floor and not being put away in the closet or hamper creates a mess and is something that no one would love. | No | FLUTE | Context: I hate when my kids leave their clothes all over the floor
Hypothesis: I just love it when my kids leave their clothes all over the floor
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Larger telescopes can collect more light and see finer details than smaller telescopes. | [a] | quartz | The reason scientists use huge telescopes is because they collect
Options:
[a] more light
[b] less light |
$\frac{1\times2\times3\times4\times5}{5\times4\times3\times2\times1}=1$ | e | TAL-SCQ5K | What is the product of five fractions, whose denominators are $5-1$ in descending order, and the numerators are $1-5$ in ascending order？
Options:
a) $\frac1{25}$
b) $\frac1{2}$
c) $\frac1{5}$
d) $$0$$
e) $$1$$ |
Often times when people make new dishes they are taking a risk because they are not sure how it will taste | No | FLUTE | Consider the statement "I tried to make a new dish last night for dinner but when it tasted too gross I had to throw it out.". Is the statement "I made an experimental dish last night that unfortunately tasted so vile that I had to throw it all out" false? Yes/no/unknown |
The product of the matrices is
\[\begin{pmatrix} 3 & -8 \\ a & 11 \end{pmatrix} \begin{pmatrix} 11 & b \\ 4 & 3 \end{pmatrix} = \begin{pmatrix} 1 & 3b - 24 \\ 11a + 44 & ab + 33 \end{pmatrix}.\]We want this to be the identity matrix, so $3b - 24 = 0,$ $11a + 44 = 0,$ and $ab + 33 = 1.$ Solving, we find $(a,b) = (-4,8).$ | $(-4,8)$ | competition-math | The matrices
\[\begin{pmatrix} 3 & -8 \\ a & 11 \end{pmatrix} \quad \text{and} \quad \begin{pmatrix} 11 & b \\ 4 & 3 \end{pmatrix}\]are inverses. Enter the ordered pair $(a,b).$ |
Consider the worst case scenario: first 3 are drawn, all of different colors, when the fourth is drawn, no matter which color is drawn, a pair of the same color will definitely be matched. Continue to draw the fifth one. The worst case is that the last color socks are drawn again, and at this point there are three socks of the same color and one sock of each of the other two colors. If you continue to draw the sixth one, no matter which color you draw, you will be able to form two pairs of socks of the same color. So the answer is to draw 6 times. | (B) | TAL-SCQ5K | A drawer contains ten identical yellow socks, eight identical blue socks and one hundred 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?
Options:
(A) $$5$$
(B) $$6$$
(C) $$8$$
(D) $$11$$
(E) $$13$$ |
If we increase the resistance in a series circuit, by adding more resistors, then the total current decreases. | (b) | quartz | Increasing the resistance in a series circuit will lead to _____ total current.
(a) more
(b) less |
The wind blows through the branches of this huge tree, which means that the wind is flowing through the leaves of the tree. | Yes | FLUTE | Given the statement "The wind blows through the branches of this huge tree.", what is the statement "The wind floats through the leaves." true?
- Yes
- No
- Unknown |
甲、丙$$6$$分钟相遇的路程：$$\left( {100 + 75} \right) \times 6 = 1050$$$$($$米$$)$$； 甲、乙相遇的时间为：$$1050 \div \left( {80 - 75} \right) = 210$$$$($$分钟$$)$$； 东、西两村之间的距离为：$$\left( {100 + 80} \right) \times 210 = 37800$$$$($$米$$)$$． | a | TAL-SCQ5K | 有甲、乙、丙$$3$$人，甲每分钟走$$100$$米，乙每分钟走$$80$$米，丙每分钟走$$75$$米．现在甲从东村，乙、丙两人从西村同时出发相向而行，在途中甲与乙相遇$$6$$分钟后，甲又与丙相遇． 那么，东、西两村之间的距离是多少米？
Options:
a. $$37800$$
b. $$38800$$
c. $$39900$$
d. 太难了，容我在喝一杯$$82$$年的雪碧压压惊 |
相互给，总和不变，给完后三人的钱数都是$$1800\div 3=600$$，望望得到希希的钱后是$$600\div \frac{4}{5}=750$$，给希希$$150$$后，星星是$$600$$，那么说明星星给出$$\frac{1}{3}$$后是$$450$$，那么星星原来是$$450\div \frac{2}{3}=675$$（元），那么给了希希$$225$$元，希希得到后有$$600\div \frac{3}{4}=800$$（元），那么希希原有$$800-225=575$$（元）．那么望望原有$$1800-675-575=550$$（元），所以希希原来的钱比望望原来的钱多$$25$$元． | a | TAL-SCQ5K | 星星、希希、望望三人过年期间一共收了$$1800$$元压岁钱，如果星星把自己的钱数的$$\frac{1}{3}$$给希希，然后希希把自己现有钱数的$$\frac{1}{4}$$给望望，望望再把自己现有钱数的$$\frac{1}{5}$$给星星，此时二个人手中的钱就一样多了，那么希希原来的钱数比望望原来的钱数多（~ ）．
a) $$25$$
b) $$35$$
c) $$100$$
d) $$125$$ |
The seven deadly sins are:pride, greed, wrath, envy, lust, gluttony, and sloth. Under Columbus, every native of fourteen years of age or upward was to pay a large hawk's bell of gold dust or cotton and those who could not pay were punished. in just two years under Columbus's governorship, over 125,000 of the 250,000–300,000 natives in Haiti were dead. | Yes | strategyqa | Did Christopher Columbus condone multiple deadly sins? |
The more cylinders a car engine has, the more powerful its engine can be. | b | quartz | Mona is designing a car in a factory. If she decides to remove cylinders from the car's engine, what happens to the power that engine can output?
a) increased
b) decreased |
It is understandable to be angry when a dog destroys something that is valuable or important to someone, like a favorite pair of shoes | Yes | FLUTE | Consider the statement "My dog chewed my favorite pair of shoes last week I was so irritated with her.". Based on this "I was so mad when my dog destroyed my favorite pair of shoes last week" a true statement? Yes, no, or I don't know? |
To give someone a bloody nose means to inflict damage or defeat on someone, but in this sentence the political newcomer was the one who was defeated. | No | FLUTE | Context: Everyone agreed that the political newcomer was defeated and humiliated by the congressman during their first televised debate.
Hypothesis: Everyone agreed that the political newcomer gave the congressman a bloody nose during their first televised debate.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
The length of each side of the square is $\sqrt{144} = 12\text{cm}$. | (C) | TAL-SCQ5K | A square has an area of $144\text{cm}^{2}$, what is the length of each side of the square?
(A) $10\text{cm}$
(B) $11\text{cm}$
(C) $12\text{cm}$
(D) $13\text{cm}$ |
In the final 40 seconds, the Fireflies scored seven 3-point baskets to improve their score by 3*7=21 points.
Thus, the Fireflies final total was 74+21=95 points.
In the final 40 seconds, the hornets scored an additional two 2-point baskets to improve their score by 2*2=4 points.
Thus, the Hornets final total was 86+4=90 points.
The final difference in points between the two teams was 95-90=5 points. | 5 | gsm8k | With 40 seconds left to play in the basketball game, the Dunkinville Hornets were leading the Fredingo Fireflies by a score of 86 to 74. In the remaining seconds in the game, the Fireflies scored 7 three-point baskets while holding the Hornets to only 2 two-point baskets to win the game. How many more points did the Fireflies score in the game than did the Hornets? |
The closer the field lines are drawn together, the stronger the field being described. | B | quartz | John was in his office looking at the diagrams. He saw that as the lines were sparser, the fields were
Options:
A. Stronger
B. Weaker |
Blues incorporated spirituals, work songs, field hollers, shouts, chants, and rhymed simple narrative ballads and was derived from African-Americans. Blues music uses instruments like slide guitar, harmonica, piano, and bass drums. Depeche Mode are a British pop synth group. Depeche Mode uses computer synthesizers to create their unique sound as well as heavy rock guitars. Depeche Mode was influenced by The Cure, and Ultravox, new wave rock bands. | No | strategyqa | Were Depeche Mode heavily influenced by blues music? |
We have $6 \# 2 = 6+\frac{6}{2} = 6+3 = 9$. | $9$ | competition-math | The operation $\#$ is defined as $a \# b = a + \frac{a}{b}$. What is the value of $6 \# 2$? |
Most people would want their neighbors to be considerate and not make noise at night which would disrupt their sleep and under no conditions would it make them happy. | No | FLUTE | Given the statement "Everynight after 11pm my neighbor is out in the parking lot, in and out of her vehicle making noise.", what is the statement "I am really elated that my considerate neighbor is up all night and disrupting my sleep with her noise" true?
- Yes
- No
- Unknown |
Pigments in the skin act like a filter that can prevent the skin from making vitamin D. As a result, people with darker skin need more time in the sun than people with lighter skin to make the same amount of vitamin D. | Mike | quartz | Two friends are headed to the beach, Mike and John. Mike is white, and John is black. Both want to make the same amount of vitamin D through sun exposure. The person who will take less time to make the amount of vitamin D is
Mike
John |
The typical person has 10 toes spread across their two feet. Larry King has been married 8 times. You can count each marriage on each toe. | Yes | strategyqa | Could Larry King's marriages be counted on two feet? |
$8 + 3 = 11$ | $$11$$ | TAL-SCQ5K | Louis had $8$ sticks. He broke three of them into two pieces. How many sticks does he have now?
Options:
* $$9$$
* $$10$$
* $$11$$
* $$12$$
* $$13$$ |
The original price is x.
The discount is 100% - 25% remaining = 75% discount.
The discount is 75%, so the original price is x - .75x = .25x.
The sale price is $6, so $6 = .25x, which is the same as 6/.25 = x.
X = $24. | 24 | gsm8k | Macy's is selling shirts that have been reduced to $6. This price is at 25% of the original price. What was the original price? |
To put on a pedestal means to see someone or something as perfect, and in this context the speaker wants to go back to seeing the actor as perfect. | Yes | FLUTE | Consider the staetement "I'd do anything to go back to you just being an amazing actor that I worshipped and saw as perfect.". Based on this statement, is "I'd give anything to go back to you just being an amazing actor that I put on a pedestal." a true statement? Yes/no/unknown |
It takes $$144$$ workers $$60$$ hours to paint a bridge. That\textquotesingle s $$144\times60=8640$$ worker-hours. For $$108$$ workers, the job takes $$8640\div108=80$$ hours. | $$80$$ | TAL-SCQ5K | It takes $$144$$ workers $$60$$ hours to paint a bridge. Working at the same rate, how many hours would $$108$$ workers require to do the job?
* $$45$$
* $$65$$
* $$80$$
* $$96$$ |
Ivan the Terrible was the 1st Tsar of Russia. Ivan the Terrible died in 1584. The first confirmed person to fly was Jean Francois Pilatre de Rozier in 1783. | No | strategyqa | Has Ivan the Terrible flown to Europe? |
When you add the first two days you get 14+25=39 marigolds
On the third day they sold 25*2=50 marigolds
During the three day sale 39+50=89 marigolds were sold | 89 | gsm8k | On the first day of the garden center sale, 14 marigolds were sold. The next day 25 more marigolds were sold. On the third day the center sold two times the number of marigolds it did on the day before. How many marigolds were sold during the sale? |
This is counting the number of ways that six distinct objects can be put in order, so there are $6! = 720$ different arrangements. | $720$ | competition-math | How many ways are there to arrange the letters of the word $\text{BA}_1\text{N}_1\text{A}_2\text{N}_2\text{A}_3$, in which the three A's and the two N's are considered different? |
The idiom means facing two equally unpleasant dangerous or risky alternatives, and the entailment captures this by saying that he is caught between two difficult choices where both options will lead to negative consequences. | Yes | FLUTE | Context: Mr. Owens had an expression for two things he found equally unpleasant: I'm caught between two difficult choices where both options will lead to negative consequences, he would say.
Hypothesis: Mr. Owens had an expression for two things he found equally unpleasant: I'm between the devil and the deep blue sea,he would say.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
$\textbackslash$2$, as the producer surplus is calculated as the difference between the price the good is sold for and the cost of production, which is $\textbackslash$10$ - $\textbackslash$8$ = $\textbackslash$2$. | $\textbackslash$ 2$ | TAL-SCQ5K | In a competitive market, a producer is able to sell their good for $\textbackslash$ 10$ per unit, while the cost of producing each unit is $\textbackslash$ 8$. What is the producer surplus in this scenario?
- $\textbackslash$ 2$
- $\textbackslash$ 8$
- $\textbackslash$ 10$
- $\textbackslash$ 12$ |
由$${{\complement }_{U}}\left { P\cup Q \right }=\left { 6 \right }\Rightarrow {{a}^{2}}+{{b}^{2}}+a+b=6$$，显然只有答案$$D$$符合． | D | TAL-SCQ5K | 已知集合$$P=\left { 1,\left\textbar{} a \right\textbar{} \right }$$，$$Q=\left { 2, {{b}^{2}} \right }$$为全集$$U=\left { 1, 2, 3, {{a}^{2}}+{{b}^{2}}+a+b \right }$$的子集，且$${{\complement }_{U}}\left { P\cup Q \right }=\left { 6 \right }$$，则下面结论正确的是．
A. $$a=3$$，$$b=1$$
B. $$a=3$$，$$b=-1$$
C. $$a=-3$$，$$b=1$$
D. $$a=-3$$，$$b=-1$$ |
Let $x$ be the number of cookies that Lee can make with three cups of flour. We can set up the proportion $\frac{18}{2} = \frac{x}{3}$. Solving for $x$, we find that $x = 27$. | $27$ | competition-math | Lee can make 18 cookies with two cups of flour. How many cookies can he make with three cups of flour? |
He needs to save up $100 because 14,600 - 14,500 = 100
He earned $60 off trips because 40 x 1.5 = 60
He earned $40 off groceries because 100 - 60 = 40
He delivered $800 in groceries because 40 / .05 = 800 | 800 | gsm8k | Alex is saving up for a new car. He already has $14,500 saved up and the car costs $14,600. He decides that to make the last of the money he will deliver groceries for people in the neighborhood. He charges $1.5 per trip and then 5% of the price of the groceries. If he makes 40 trips and has saved up enough, how many dollars' worth of groceries did he deliver? |
Making promises and not following through with them is a sign of untrustworthiness and so someone who is satisfied with that behavior from their landlord is not being rational. | No | FLUTE | Context: Before signing the contract the landlord made promises that he will do some reparations but he never kept his word.
Hypothesis: The landlord made so many promises but never followed through with any of them, which totally makes me feel satisfied
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
From $8:30$ to $10:15$ = $1$ hr $45$ min, $1$ hr $45$ min = $105$ min, three $30$-minute parts = $90$ min, $105 - 90$ = $15$ min. | [2] | TAL-SCQ5K | A certain play has three $30$-minute parts and two intermission among them. The play started at $8:30$ and ended at $10:15$. How many minutes long were the intermissions in total? (Adapted from 2010 Math Kangaroo Problem, Level 1-2, Question \#19)
Options:
[1] $$10$$
[2] $$15$$
[3] $$20$$
[4] $$25$$ |