rationale
stringlengths 0
3.73k
| target
stringlengths 1
162
| source
stringclasses 6
values | prompt
stringlengths 16
2.02k
|
|---|---|---|---|
To think outside the box means to consider new and innovative ideas, but the speaker is suggesting sticking to traditional and outdated ideas | False | FLUTE | Context: "Stick to traditional and outdated ideas for once." Claim: "think outside the box for once."
Considering the context, is the claim true, false, or unknown? |
It is not fair that some people get to travel to amazing places for work while others don't get to travel at all. | False | FLUTE | Context: "All of my friends have these great jobs and travel so often it isn't fair."
Hypothesis: It is absolutely fair how all my friends get to travel to all these amazing places for work and I get to hang out at home
Based on the context, is the hypothesis true, false, or unknown? |
The television discount is $480 x 5/100 = $24.
So, the television price is $480 - $24 = $456.
The outstanding balance is $456 – $150 = $306
The monthly payment is $306 / 3 = $102 | 102 | gsm8k | Isabelle’s parents bought a new television for $480. The seller gives them a 5% discount. They pay a first installment of $150 and will pay the rest in 3 monthly installments. What is the amount of a monthly payment? |
College is often seen as a very important step in life and the decision to drop out of college is a big one that usually requires parental approval | No | FLUTE | Context: Last month I found out my son decided to drop out of college without telling me.
Hypothesis: I was devastated when I found out last month that my son decided to drop out of college without telling me
Is the hypothesis incorrect? (Yes, no, or unknown)? |
$3\times2\times1=6$ $4\times3\times2=24$ $24\times6=144$ | $$144$$ | TAL-SCQ5K | How many ways are there to rearrange the letters in the word \textquotesingle BEAUTY\textquotesingle{} if the vowels are never together?
* $$24$$
* $$48$$
* $$144$$
* $$480$$
* $$720$$ |
The interest rates for car loans are currently quite high and so someone who is elated about it is not rational because they are celebrating something that is unfavorable. | False | FLUTE | Context: "The way interest rates are these days I'm so scared to go get a car loan" Claim: "I am elated about the way interest rates are these days and that I might not be able to afford a car loan."
Considering the context, is the claim true, false, or unknown? |
1 day = 24 hours，$$1$$ hour = 60 minutes，$$1$$ minute = 60 seconds，$$24$$ days = (24 \times 24) hours = [(24\times 24) \times 60] minutes = 24\times 24\times 60\times 60 seconds | E | TAL-SCQ5K | Which of the following calculations shows how to work out the number of seconds in~~24 days?
A) 24 \times 24~
B) 24 \times 60
C) 24 \times 24 \times 60
D) 24 \times 60 \times 60
E) 24 \times 24 \times 60 \times 60 |
Most people would not be pleased upon returning to their car and noticing that someone had caused damage to it, but rather would feel frustrated or angry. | No | FLUTE | Context: I was mad when I returned to my car and noticed someone put a dent in my door
Hypothesis: I was so pleased when I returned to my car and noticed someone put a dent in my door.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Areas near the equator are warmer than areas near the poles because they receive more direct sunlight. | more | quartz | A person moving south from the North Pole will receive _____ direct sunlight.
Options:
* more
* less |
$$A\subseteq B$$，$$A
e \varnothing $$．$$\Rightarrow $$$$3\leqslant 2a+1\leqslant 3a-5\leqslant 22$$，$$\Rightarrow $$$$6\leqslant a\leqslant 9$$． 故选$$B$$． | (B) | TAL-SCQ5K | 若非空集合$$A=\left { x\textbar2a+1\leqslant x\leqslant 3a-5 \right }$$，$$B=\left { x\textbar3\leqslant x\leqslant 22 \right }$$，则能使$$A\subseteq A\cap B$$成立的所有$$a$$的集合是（~ ~ ）．
Options:
(A) $$\left { a\textbar{} 1\leqslant a\leqslant 9 \right }$$
(B) $$\left { a\textbar{} 6\leqslant a\leqslant 9 \right }$$
(C) $$\left { a\textbar a\leqslant 9 \right }$$
(D) $$\varnothing $$ |
$3+8=4+7=5+6=11$ | [D] | TAL-SCQ5K | There is a cube whose six faces are marked with $3$, $4$, $5$, $6$, $7$, and $8$. If the sum of every two numbers that are on the opposite faces are the same, the number on the opposite face of $4$ is~\uline{~~~~~~~~~~}~
[A] $$3$$
[B] $$5$$
[C] $$6$$
[D] $$7$$
[E] $$8$$ |
Arnel shared 5 x 8 = 40 pencils with his friends.
So, he had 10 + 40 = 50 pencils in all.
Therefore, each box had 50/10 = 5 pencils inside. | 5 | gsm8k | Arnel had ten boxes of pencils with the same number of pencils in each box. He kept ten pencils and shared the remaining pencils equally with his five friends. If his friends got eight pencils each, how many pencils are in each box? |
A saw is a very harsh tool, and it is used to cut through hard materials, so a voice that is like a saw would be harsh as well | Yes | FLUTE | Consider the statement "Yevsen's voice was gentle.". Is the statement "Yevsen's voice was like a saw cutting through metal." false? Yes/no/unknown |
Uncle Ben has 440 chickens - 39 roosters = 401 hens.
Uncle Ben has 401 hens - 15 that don't lay eggs = 386 hens that lay eggs.
The egg-laying hens each lay 3 eggs * 386 hens = 1158 eggs. | 1158 | gsm8k | Uncle Ben has 440 chickens on his farm. 39 are roosters and the rest are hens. 15 of his hens do not lay eggs, and the rest do. If each egg-laying hen lays 3 eggs, how many eggs will Uncle Ben have? |
The elastic force increases the more the material is stretched or compressed. | 1 | quartz | If a product is stretched, elastic force will
Options:
1. increase
2. decrease |
Green = 16 + 12 = 28
Green + Red = 28 + 16 = 44
There are 44 apples in the bowl. | 44 | gsm8k | There are 12 more green apples than red apples in a bowl. There are 16 red apples. How many apples are there in the bowl? |
When someone is said to be 'cranky' it usually means that they are in a bad mood and are snapping at people more easily which can be irritating for those around them | Yes | FLUTE | Consider the statement "My wife is so cranky today". Based on this "My wife has been extra crabby today and it's kinda getting on my nerves" a true statement? Yes, no, or I don't know? |
$1+3+5+\ldots+2017+2019-2 -4-6-\ldots-2016-2018$ $=1+(3-2)+(5-4)+\cdots +(2017-2016)+(2019-2018)$ $=1+1+1+\cdots +1+1$ $=1010$ | d | TAL-SCQ5K | What is the value of $1+3+5+\ldots+2017+2019-2 -4-6-\ldots-2016-2018$? (Adapted from $2018$ AMC 8 Problem, Question \#5)
a. $$1007$$
b. $$1008$$
c. $$1009$$
d. $$1010$$
e. $$1011$$ |
She has 24 students and her muffin recipe only makes 6 muffins so she needs to bake 24/6 = 4 batches of muffins
She brings muffins on the 1st of the month for 9 months and it takes 4 batches to feed all of her students so she bakes 9*4 = 36 batches of muffins | 36 | gsm8k | As a special treat, Georgia makes muffins and brings them to her students on the first day of every month. Her muffin recipe only makes 6 muffins and she has 24 students. How many batches of muffins does Georgia make in 9 months? |
Warmer molecules vibrate faster than cooler ones. | B | quartz | Lisa is heating soup on the stove. The molecules will begin to vibrate _____ as the soup heats up.
Options:
A) slower
B) faster |
A kangaroo is known for its quick and powerful jumps, which is similar to the way the person describes their arm moving. | Yes | FLUTE | Consider the staetement "I hit her in the face quickly and repetitively before I could process what my arm was doing.". Based on this statement, is "In one quick motion my arm turns, before I can grasp what direction it's about to maneuver, I'm bopping lexy in the face like a cartoon kangaroo ." a true statement? Yes/no/unknown |
第$$3$$个数为$$17$$，第$$4$$个数为$$14.5$$，第$$5$$个数为$$15.75$$，第$$6$$个数为$$15.125\cdot \cdot \cdot \cdot \cdot \cdot $$整数部分一直都是$$15$$，所以第$$10$$个数的整数部分为$$15$$． | 3 | TAL-SCQ5K | 有一列数，第$$1$$个数是$$22$$，第$$2$$个数是$$12$$，从第$$3$$个开始，每个数是它前面两个数的平均数，这列数的第$$10$$个数的整数部分（~ ）．
1: $$13$$
2: $$14$$
3: $$15$$
4: $$16$$ |
The remainder of $$A$$ $$\div9$$ is $$7$$, and $$2A=A+A$$. Therefore the remainder of $$2A\div9$$ is $$7+7=14$$. $$14= 9+5$$, therefore the remainder is $$5$$. | 3 | TAL-SCQ5K | A student wrote down a natural number. When she divided the number by $$9$$, the remainder was $$7$$. What is the~~remainder when twice that number is divided by $$9$$?
1. $$1$$
2. $$2$$
3. $$5$$
4. $$6$$
5. $$7$$ |
To stream something means to flow continuously and rapidly, while to ebb something means to recede or diminish. | No | FLUTE | Consider the staetement "Her passion is ebbing through the air.". Based on this statement, is "Her passion is streaming through the air." a true statement? Yes/no/unknown |
Waves with shorter wavelengths have more energy. | b | quartz | When the ocean has waves one after the other they have
a: less energy
b: more energy |
To be sporting something means to be wearing it or displaying it, while to be wearing all sorts of color except for yellow would suggest that she was not wearing yellow. | No | FLUTE | Given the statement "She was wearing all sorts of color except yellow.", what is the statement "She was sporting yellow that day." true?
- Yes
- No
- Unknown |
Gus eats 2 + 3 = 5 eggs for breakfast and lunch.
Including dinner, he eats a total of 5 + 1 = 6 eggs. | 6 | gsm8k | Gus eats 2 eggs-omelet for breakfast. He has an egg salad sandwich made with 3 eggs for lunch. He then has an egg drop soup made with 1 egg for dinner. How many eggs did Gus eat altogether? |
\[
x^2+5x-6=(-1)^2+5(-1)-6=1-5-6=-10.
\] | $-10$ | competition-math | What is the value of the expression $x^2+ 5x-6$, when $x =-1$? |
Mortdecai collects a total of 8x2 = 16 dozens of eggs.
He sells a total of 3 + 5 = 8 dozens of eggs.
So, 16 - 8 = 8 dozens of eggs are left.
After using 4 dozens of eggs to make a pie, 8 - 4 = 4 dozens of eggs are left.
Since there are 12 in 1 dozen, then Mortdecai donates 4 x 12 = 48 pieces of eggs to the charity. | 48 | gsm8k | In a week, Mortdecai collects 8 dozen eggs every Tuesday and Thursday, and he delivers 3 dozen eggs to the market and 5 dozen eggs to the mall. He then uses 4 dozen eggs to make a pie every Saturday. Mortdecai donates the remaining eggs to the charity by Sunday. How many eggs does he donate to the charity? |
Each gust blows the leaf forward 5 feet, so 11 gusts will blow it forward 5 * 11 = 55 feet.
Each swirl after a gust blows it back 2 feet, so 11 swirls will blow it back 2 * 11 = 22 feet.
After 11 gusts, the leaf has traveled 55 - 22 = 33 feet down the sidewalk. | 33 | gsm8k | A leaf is being blown down a sidewalk by swirling gusts of wind. For every five feet that a gust blows it forward, the wind swirls and blows it back two feet. How many feet has it traveled down the sidewalk after 11 gusts of wind? |
Amateur detectives are known for being suspicious about everyone and everything, looking for clues that will help them solve a case. | Yes | FLUTE | Consider the statement "You are starting to get suspicious about everyone around you being a robot subtly testing you.". Based on this "Everyone is a robot subtly testing you, but you are starting to get like an amateur detective." a true statement? Yes, no, or I don't know? |
If Audrey was asleep for 10 hours last night and dreamed for 2/5 of the time, she dreamed for 2/5*10 = 4 hours.
The total time Audrey slept without dreaming is 10-4 = 6 hours. | 6 | gsm8k | Audrey was asleep for 10 hours last night and dreamed for 2/5 of the time. How much of the night was she not dreaming? |
由题意，把函数$$y=\sin \left( 2x+\frac{ \pi }{6} \right)-1$$的图象按向量$$\overrightarrow{a}=\left( \frac{ \pi }{6},1 \right)$$平移， 可得$$y=\sin \left[ 2\left( x-\frac{ \pi }{6} \right)+\frac{ \pi }{6} \right]=\sin \left( 2x-\frac{ \pi }{6} \right)$$， 再把所得图象上各点的横坐标缩短为原来的$$\frac{1}{2}$$， 可得$$y=\sin \left( 4x-\frac{ \pi }{6} \right)$$，故选$$\text{B}$$. | (2) | TAL-SCQ5K | 把函数$$y=\sin \left( 2x+\frac{ \pi }{6} \right)-1$$的图象按向量$$\overrightarrow{a}=\left( \frac{ \pi }{6},1 \right)$$平移，再把所得图象上各点的横坐标缩短为原来的$$\frac{1}{2}$$，则所得图象的函数解析式是．
Options:
(1) $$y=\sin \left( 4x+\frac{2 \pi }{3} \right)-2$$
(2) $$y=\sin \left( 4x-\frac{ \pi }{6} \right)$$
(3) $$y=\sin \left( 2x+\frac{ \pi }{6} \right)$$
(4) $$y=\cos \left( 4x+\frac{2 \pi }{3} \right)$$ |
Two bracelets need 50 x 2 = 100 beads.
So they will need 9 x 100 = 900 beads in all. | 900 | gsm8k | Nine members of the crafts club are making 2 necklaces each. It takes 50 beads to make each necklace. How many beads will they need in all? |
The higher the pH value is, the stronger the base. | Larger | quartz | John was looking at some chemicals in the chemistry lab. He saw that the higher the ph value was, the base became
Options:
- Larger
- Smaller |
After eating 15 green macaroons, the number is reduced to 40 green macaroons - 15 green macaroons = 25 green macaroons
If Fran ate 15 green macaroons, he also ate 2 red/green * 15 green macaroons = 30 red macaroons.
The total number of red macaroons remaining is 50 red macaroons - 30 red macaroons = 20 red macaroons
The total number of macaroons Fran has left are 20 macaroons + 25 macaroons = 45 macaroons | 45 | gsm8k | Fran baked 50 red macaroons and 40 green macarons. How many macaroons will remain if Fran ate 15 green macaroons and twice as many red macaroons as green macaroons? |
The coach has 8 liters * 1000 ml/liter = 8,000 ml of water.
She pours 200 ml/player x 30 players = 6,000 ml of water in total for all the athletes.
The water spill means 6,000 ml + 250 ml = 6,250 ml of water was used.
There was 8,000 ml - 6,250 ml = 1,750 ml of water left. | 1750 | gsm8k | There are 30 players on a football team. The coach has 8 liters of water. She pours 200 milliliters of water for every player so they can get hydrated. Unfortunately, there was a water spill and 250ml of water was spilled. How much water was left over? |
Let $p$ be the number of Popsicles Megan can finish in 4 hours and 30 minutes. If we convert that period of time into minutes, we find that 4 hours and 30 minutes is equal to $(4)(60)+30=270$ minutes. From here, we can set up the proportion \begin{align*} \frac{x}{270}& =\frac{1}{15}
\\\Rightarrow \qquad x& =\left(\frac{1}{15}\right)(270)
\\\Rightarrow \qquad x& =18
\end{align*} | $18$ | competition-math | On a hot day, Megan likes to eat a Popsicle every 15 minutes. Assuming she keeps up that rate of consumption, how many Popsicles can Megan finish in 4 hours and 30 minutes? |
$$6$$ pens = $$5$$ pencils, we use $\times6$ which give us $36$ pens = $30$ pencils | $$30$$ | TAL-SCQ5K | If $$6$$ pens cost as much as $$5$$ pencils, then $$36$$ pens cost as much as pencils.
Options:
* $$6$$
* $$30$$
* $$21$$
* $$98$$ |
Starting with $100, he paid $20 to Colin, leaving him with $100-$20=$80.
Twice as much as $20 is 2*$20=$40.
Thus, he paid $40 to Helen, leaving him with $80-$40=$40.
Half as much to Benedict as he had paid to Helen is $40/2=$20.
Thus, he paid $20 to Benedict, leaving him with $40-$20=$20 after paying off all debts. | 20 | gsm8k | Ian won $100 in the lottery. He decided to use the money to pay off debts. He paid $20 to Colin. He then paid twice as much to Helen, as he had paid to Colin. Then finally, he paid half as much to Benedict, as he had paid to Helen. How much money, in dollars, does he have left after paying off debts? |
This means that when the forest trees burned, everything was red from the fire. | No | FLUTE | Consider the statement "All fire-flush 'd when forest trees burned.". Is the statement "All fire-flush 'd when forest trees smoldered." false? Yes/no/unknown |
$$18\div15\textbackslash\% = 120$$ grams. | $$120$$ grams | TAL-SCQ5K | A $$15\textbackslash\%$$ sugar solution contains $$18$$ grams of pure sugar. How many grams of solution are there?
- $$90$$ grams
- $$100$$ grams
- $$120$$ grams
- $$150$$ grams |
By using multiple stages, empty fuel containers could drop away. This reduced the mass of the rocket so that it could fly higher. | 1 | quartz | David is getting ready to fly into space on a rocket. As the rocket shoots upwards, part of the mass falls away, allowing the rocket to go
1: higher
2: lower |
Let’s use r for the cost of each necklace
4*12+8*r=80
48+8*r=80
8*r=80-48=32
8r=32
r=4 dollars for each ring | 4 | gsm8k | Linda makes and sells necklaces at craft fairs. At her most recent fair she sold 4 necklaces and 8 rings for a total of $80. If each necklace costs $12, how much does each ring cost? |
Marnie bought 50 x 5 = 250 beads from the 5 bags of 50 beads.
She also bought 100 x 2 = 200 beads from the 2 bags of 100 beads.
She has a total of 250 + 200 = 450 beads.
Hence, she will be able to make 450/50 = 9 bracelets. | 9 | gsm8k | Marnie makes bead bracelets. She bought 5 bags of 50 beads and 2 bags of 100 beads. If 50 beads are used to make one bracelet, how many bracelets will Marnie be able to make out of the beads she bought? |
乘车时间是$$40-6=34$$分，假设全是地铁是$$30$$分钟，时间差是$$34-30=4$$ 分钟，需要调整到公交推迟$$4$$分钟，地铁和公交的时间比是$$3:5$$，设地铁时间是多份，公交是$$5$$份时间，$$4\div \left( 5-3 \right)=2$$，公交时间为$$5\times 2=10$$分钟． | C | TAL-SCQ5K | 小明家距学校，乘地铁需要$$30$$分钟，乘公交车需要$$50$$分钟．某天小明因故先乘地铁，再换乘公交车．用了$$40$$分钟到达学校，其中换乘过程用了$$6$$分钟，那么这天小明乘坐公交车用了分钟．
A. $$6$$
B. $$8$$
C. $$10$$
D. $$12$$
E. $$14$$ |
Since $7^2 < 50 < 8^2$ and $15^2 < 250 < 16^2$, the squares between 50 and 250 are $8^2,9^2,10^2,\ldots,15^2$. So there are $15 - 8 + 1 = 8$ such squares. | $8$ | competition-math | How many perfect squares are between 50 and 250? |
Paintball is a shooting sport that uses paint pellets in lieu of bullets. Crossbow is a shooting sport that uses 'bolts' or arrows instead of bullets. | No | strategyqa | Do all shooting sports involve bullets? |
The more tightly packed the particles inside the material are, the more dense we say they are. | [b] | quartz | Sasha is throwing bottles into the lake. Some bottles are filled with sand, and some only have a tiny bit of sand in them. The bottles filled with sand will sink first because they are
[a] less dense
[b] more dense |
American Summits donated 45 x 2 = 90 bottled waters.
Hormel donated 45 x 3 = 135 spams.
Boudin Bakery donated 135 x 1/3 = 45 sourdoughs.
Del Monte Foods donated 90 - 30 = 60 canned fruits.
Therefore, a total of 45 + 90 + 135 + 45 + 60 = 375 different food. | 375 | gsm8k | Five food companies sponsored a local food bank. Foster Farms donated 45 dressed chickens; American Summits donated twice the number of bottled water than the number of dressed chicken donated by Foster Farms; Hormel donated three times the number of dressed chickens that Foster Farms donated; Boudin Butchers donated one-third of the number of dressed chickens that Hormel donated; Del Monte Foods donated 30 fewer bottles of water than American Summits. How many food items did the companies donate in total? |
设每册$$n$$道题，则有 $$\left { \begin{matrix}351\textgreater4n 689\textless{}8n \end{matrix} \right.\Rightarrow \left { \begin{matrix}n\textless{}87\frac{3}{4} n\textgreater86\frac{1}{8} \end{matrix} \right.$$ 故$$n$$只能为$$87$$． | d | TAL-SCQ5K | ~小明收集了$$10$$册数学题，每册的题目数相同，并且连续编号（例如，第$$2$$册中的第一个题目比第$$1$$册中最后一个题的编号大$$1$$），一天他发现编号为$$351$$的数学题在第$$5$$册上，编号为$$689$$的数学题在第$$8$$册上，那么每册各有（~ ~ ~ ）个数学题．
a. $$70$$
b. $$71$$
c. $$85$$
d. $$87$$ |
If $r = \sec \theta = \frac{1}{\cos \theta},$ then $x = r \cos \theta = 1.$ Thus, the graph of $r = \sec \theta$ is simply the line $x = 1.$
If $r = \csc \theta = \frac{1}{\sin \theta},$ then $y = r \sin \theta = 1.$ Thus, the graph of $r = \csc \theta$ is simply the line $y = 1.$
[asy]
unitsize(2 cm);
fill((0,0)--(1,0)--(1,1)--(0,1)--cycle,gray(0.7));
draw((-0.3,1)--(1.3,1),red);
draw((1,-0.3)--(1,1.3),red);
draw((-0.3,0)--(1.3,0));
draw((0,-0.3)--(0,1.3));
[/asy]
Hence, the region we are interested in is simply the square with vertices $(0,0),$ $(1,0),$ $(1,1),$ and $(0,1),$ which has area $1.$ | $1$ | competition-math | Find the area of the region bounded by the graph of $r = \sec \theta,$ the graph of $r = \csc \theta,$ the $x$-axis, and the $y$-axis. |
丽人服装厂去年产值$$240$$万元， 比前年增加$$\frac{1}{5}$$，则这两个年产值共有$$240\div \left( 1+\frac{1}{5} \right)+240$$． 故选$$\text{C}$$． | c | TAL-SCQ5K | 丽人服装厂去年产值$$240$$万元，比前年增加$$\frac{1}{5}$$，丽人服装厂这两年产值共有多少万元？应列式为．
a. $$240+240\times \frac{1}{5}$$
b. $$240+240\times \left( 1+\frac{1}{5} \right)$$
c. $$240+240\div \left( 1+\frac{1}{5} \right)$$ |
进三次位数字和少$$3\times 9=27$$，则$$36+25-27=34$$． | b | TAL-SCQ5K | 有$$A$$、$$B$$两个整数，$$A$$的各位数字之和为$$36$$，$$B$$的各位数字之和为$$25$$，且两数相加时进位三次，那么$$A+B$$的各位数字之和是．
a) $$33$$
b) $$34$$
c) $$35$$
d) $$36$$ |
He works 30/2=15 days
So he works 15*12=180 hours in the month
He got a 20*.3=$6 an hour raise
So he gets paid 20+6=$26 an hour
That means he makes 26*180=$4680 | 4680 | gsm8k | John works 12 hours every other day. He gets a 30% raise from his former $20 an hour job. How much does he make in a 30 day month? |
Emily bought 9 packs of candy necklaces * 8 candy necklaces in a pack = 72 candy necklaces.
Her classmates took 72 candy necklaces – 40 candy necklaces left = 32 candy necklaces
Since each pack contained 8 necklaces, this means 32 / 8 = 4 packs of candy necklaces were opened. | 4 | gsm8k | Emily bought 9 packs of candy necklaces to give her classmates at school for Valentine’s Day. Each pack had 8 candy necklaces in it. Emily opened one pack at a time. After her classmates took as many as they wanted, there were 40 candy necklaces left. How many packs did Emily open for her classmates? |
①当$$x\textgreater0$$，$$y\textgreater0$$时，原方程组为$$\begin{cases}x+y=12 x+y=6 \end{cases}$$显然无解； ②当$$x ~\textless{} ~0$$，$$y\textgreater0$$时，原方程组为$$\begin{cases}-x+y=12 x+y=6 \end{cases}$$，解得$$\begin{cases}x=-3 y=9 \end{cases}$$； ③当$$x\textgreater0$$，$$y ~\textless{} ~0$$时，原方程组为$$\begin{cases}x+y=12 x-y=6 \end{cases}$$，解得$$\begin{cases}x=9 y=3 \end{cases}$$，舍去； ④当$$x ~\textless{} ~0$$，$$y ~\textless{} ~0$$时，原方程组为$$\begin{cases}-x+y=12 x-y=6 \end{cases}$$显然无解； 综上，只有$$1$$组解．故选$$\text{A}$$． | (A) | TAL-SCQ5K | 方程组$$\begin{cases}\left\textbar{} x \right\textbar+y=12 x+\left\textbar{} y \right\textbar=6 \end{cases}$$的解的个数为．
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$4$$ |
Stealing money from anyone is wrong and unethical, but doing it from one's own daughter is really disgraceful and not something to be proud of. | False | FLUTE | Context: "I stole money from my daughter's piggy bank and now she's wondering where her money went"
Hypothesis: I feel really proud of myself for stealing money from my daughter's piggy bank without her having any clue.
Based on the context, is the hypothesis true, false, or unknown? |
When Brooke gets twelve more balloons, his total becomes 12+8 = 20
When Tracy adds 24 more balloons to her 6, her total number of balloons becomes 24+6 = 30
When half of Tracy's balloons pop, she remains with 1/2*30 =15
The combined total balloons for the two is 15+20 = 35 balloons | 35 | gsm8k | If Brooke adds eight balloons to his current 12, and Tracy adds 24 to her current 6, how many balloons will they have in total if Tracy pops half of her balloons? |
根据题意分析可知，假设$$20$$道题全部做对， 则得：$$20\times5=100$$（分），现在比满分少了$$100-76=24$$（分）， 又因为答错或不答一题比答对一题少$$1+5=6$$（分）， 也就是做错了：$$24\div6=4$$（题）， 所以做对了：$$20-4=16$$（题）， 故选答案$$\text{D}$$． | $$16$$ | TAL-SCQ5K | 【补3】小明参加$$\text{YMO}$$竞赛，共有$$20$$道赛题，答对一题给$$5$$分，答错一题或不答扣$$1$$分．小明得了$$76$$分．小明答对了题．
Options:
* $$13$$
* $$14$$
* $$15$$
* $$16$$ |
Angelo and Melanie think they should dedicate 3 hours to each of the 2 chapters, 3 hours x 2 chapters = 6 hours total.
For the worksheets they plan to dedicate 1.5 hours for each worksheet, 1.5 hours x 4 worksheets = 6 hours total.
Angelo and Melanie need to start with planning 12 hours to study, at 4 hours a day, 12 / 4 = 3 days.
However, they need to include time for breaks and lunch. Every hour they want to include a 10-minute break, so 12 total hours x 10 minutes = 120 extra minutes for breaks.
They also want to include 3 10-minute snack breaks, 3 x 10 minutes = 30 minutes.
And they want to include 30 minutes for lunch each day, so 120 minutes for breaks + 30 minutes for snack breaks + 30 minutes for lunch = 180 minutes, or 180 / 60 minutes per hour = 3 extra hours.
So Angelo and Melanie want to plan 12 hours to study + 3 hours of breaks = 15 hours total.
They want to study no more than 4 hours each day, 15 hours / 4 hours each day = 3.75
They will need to plan to study 4 days to allow for all the time they need. | 4 | gsm8k | Angelo and Melanie want to plan how many hours over the next week they should study together for their test next week. They have 2 chapters of their textbook to study and 4 worksheets to memorize. They figure out that they should dedicate 3 hours to each chapter of their textbook and 1.5 hours for each worksheet. If they plan to study no more than 4 hours each day, how many days should they plan to study total over the next week if they take a 10-minute break every hour, include 3 10-minute snack breaks each day, and 30 minutes for lunch each day? |
The integer is $1$, since $1^2=1<2$. | $1$ | competition-math | What is the only integer whose square is less than its double? |
If the second tallest building is half as tall as the first one's height of 100 feet, it is 100/2= 50 feet tall.
If the third tallest building is half as tall as the second one's height of 50 feet, it is 50/2= 25 feet tall.
If the fourth building is one-fifth as tall as the third one, it is 25/5= 5 feet tall.
Therefore, all four buildings put together would be 100+50+25+5= 180 feet tall. | 180 | gsm8k | The tallest building in the world is 100 feet tall. If the second tallest is half that tall, and the third tallest is half as tall as the second, and the fourth is one-fifth as tall as the third, how tall are all 4 buildings put together? |
Gripped with illness is used here to mean that something happend suddenly and violently, here, in this case, the man was hit with an illness that killed him quickly. | Yes | FLUTE | Consider the statement "He was stricken with a terrible illness that killed him so fast he had no chance to do anything.". Based on this "He was gripped with a terrible illness that killed him quickly." a true statement? Yes, no, or I don't know? |
Rachel's age is 8 x 2 = 16.
Collete's age is 8 / 2 = 4.
Therefore the difference between their age is 16 - 4 = 12. | 12 | gsm8k | Rachel is twice as old as Rona and Collete's age is half the age of Rona's. If Rona is 8 years old, what is the difference between the age of Collete and Rachel? |
Final Fantasy VI is a video game. Video games are played using a video game console and television. Video game consoles and televisions require electricity in order to function. | Yes | strategyqa | Does Final Fantasy VI require electricity to play? |
$135_7 = 1\cdot7^2 + 3\cdot7^1 + 5\cdot7^0 = 49 + 21 + 5 = 75.$ | $75$ | competition-math | Convert $135_7$ to a base 10 integer. |
深圳和广州的路程为$$60$$千米，则从深圳到广州用时$$60\div30=2$$小时，从广州到深圳用时$$60\div60=1$$小时，总共用时$$1+2=3$$小时，平均速度$$=60\times2\div3=40$$千米$$/$$小时． 答案：$$B$$． | b | TAL-SCQ5K | 某人开车往返于深圳和广州之间，从深圳去广州每小时行$$30$$千米，从广州返回深圳每小时行$$60$$千米．那么他往返深圳和广州的平均速度是千米$$/$$时．
a) $$35$$
b) $$40$$
c) $$45$$
d) $$50$$
e) $$55$$ |
First find the total increase in Bob's earnings: $0.50/hour * 40 hours/week = $20/week
Then find the weekly decrease in Bob's housing assistance: $60/month / 4 weeks/month = $15/week
Then subtract the lost assistance from the increased wages to find Bob's net increase in money: $20/week - $15/week = $5/week | 5 | gsm8k | Bob gets rent assistance because he's low-income. If he gets a raise of $0.50/hour and works 40 hours a week, how much more will he actually earn a week if his housing benefit is reduced by $60/month? |
The full box is harder to move because it has greater mass and therefore greater inertia. | 1 | quartz | If Jimbo is creating a ball from clay and he adds more clay to the ball, what does he do to the ball's inertia?
1: increases it
2: decreases it |
Taxes being raised is not a good thing because it means people will have to pay more money and hence would not be excited about it. | Yes | FLUTE | Context: I really get mad when my taxes are raised.
Hypothesis: I'm so excited about my taxes being raised that I could scream
Is the hypothesis incorrect? (Yes, no, or unknown)? |
We can start by pairing the terms in this expression and factoring them as a difference of squares: \begin{align*}
&\phantom{=} \,\,\, (19^2-17^2)+(15^2-13^2)+(11^2-9^2)+(7^2-5^2)+(3^2-1^2) \\
&= 2(19 + 17) + 2(15 + 13) + 2(11 + 9) + 2(7 + 5) + 2(3 + 1)\\
&= 2(19 + 17 + 15 + 13 + 11 + 9 + 7 + 5 + 3 + 1) \\
&= 2(100) \\
&= 200.
\end{align*} | $200$ | competition-math | What is the value of $19^2-17^2+15^2-13^2+11^2-9^2+7^2-5^2+3^2-1^2?$ |
Warm air is less dense than cool air, so it rises higher in the troposphere. | (2) | quartz | If Mona cools down the air she is putting into her weather balloon, what will happen to the height that it can rise into the troposphere?
(1) increase
(2) decrease |
The total ratio representing the age of the three siblings is 4+3+7 = 14
Halima's age is represented by the fraction 4/14, which means she is 4/14*126 = 36 years old.
Beckhams age, from the total age of the three, is 3/14*126 = 27
The difference in age between Halima and Beckham is 36-27 = 9 | 9 | gsm8k | The ratio representing the age of Halima, Beckham, and Michelle is 4:3:7, respectively. If the total age for the three siblings is 126, calculate the age difference between Halima and Beckham. |
Forgetting to pay a credit card bill is not a great thing because it leads to late fees and penalties which makes the individual disappointed. | No | FLUTE | Consider the staetement "I forgot to pay my credit card bill, I'm so disappointed with myself.". Based on this statement, is "I feel great that I forgot to pay my credit card bill and now have to deal with the consequences" a true statement? Yes/no/unknown |
Now there are twice as many dogs as cats, and if the number of cats is 20, there are 2*20=40 dogs.
Before twenty new ones were born, the number of dogs in the neighborhood originally was 40-20=20
If the number of dogs in the neighborhood was originally half the number of cats in the neighborhood, there were 20*2=40 cats in the neighborhood. | 40 | gsm8k | If the number of dogs in the neighborhood was originally half the number of cats in the neighborhood before twenty new dogs were born, and now there are twice as many dogs as cats, how many cats were in the neighborhood, to begin with, if there are 20 cats now? |
由题意，得： $$2m=2$$，$$n-1=1$$． ∴$$m=1$$，$$n=2$$． ∴$$m-2n=1-2\times 1=-1$$． 故选$$\text{C}$$． | $$-1$$ | TAL-SCQ5K | 单项式$$3{{x}^{2m}}{{y}^{n-1}}$$与单项式$$-\frac{1}{2}{{x}^{2}}y$$是同类项，则$$m-2n$$的值为．
- $$1$$
- $$0$$
- $$-1$$
- $$-3$$ |
由面积法知：点$$P$$到等边三角形三边的距离之和等于这个等边三角形的高，而$$b=\frac{1}{2}\cdot \frac{a}{3}\cdot h$$，所以$$h=\frac{6b}{a}$$． 故选$$\text{C}$$． | [3] | TAL-SCQ5K | 用一根长为$$a$$米的细绳围成一个等边三角形，测得它的面积是$$b$$平方米．在这个等边三角形内任取一点$$P$$，则点$$P$$到等边三角形三边的距离的和等于．
Options:
[1] $$\frac{2b}{a}$$米
[2] $$\frac{4b}{a}$$米
[3] $$\frac{6b}{a}$$米
[4] $$\frac{8b}{a}$$米 |
Half an hour after $6:30$ is $7:00$ $7+1=8$ | [2] | TAL-SCQ5K | Vansen left for school at $6:30$ am. He took half an hour to walk from his house to school. Ron reached school $1$ hour later than Vansen. At what time did Ron reach school? (adapted from 2009 Math Kangaroo Problem, Level 3-4, Question \#8)
Options:
[1] $7:00$ am.
[2] $8:00$ am.
[3] $8:45$ am.
[4] $9:00$ am.
[5] $10:00$ am. |
Natalie: 10000/2=5000$
10000-5000=5000
Rick:5000(.60)=3000$
5000-3000=2000$ left for Lucy. | 2000 | gsm8k | Natalie's father has saved up $10,000 to split up between his kids. Natalie will get half, as she is the oldest. Rick will get 60 percent of the remaining money, and Lucy will get whatever is left after Natilie and Rick get paid. How much money does Lucy get? |
Tom’s rabbit is 8 / 2 = 4 years old.
His dog is 4 x 3 = 12 years old. | 12 | gsm8k | Tom’s cat is 8 years old. His rabbit is half the age of his cat. His dog is three times as old as his rabbit. How old is the dog? |
A Banana Republic is a small country with a corrupt government and a weak economy, and this sentence is describing a cheap and low-quality window. | No | FLUTE | Context: She checked her reflection in the cheap and low-quality window.
Hypothesis: She checked her reflection in the Banana Republic window.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
Coworkers coming in late everyday can lead to a lot of disruption in the work schedule and so someone considering it to be delightful is highly unrealistic. | No | FLUTE | Context: My coworker comes into work late everyday and it drives me crazy
Hypothesis: It's really delightful when my coworker comes in late everyday and disrupts the work schedule
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Lilibeth picks 6 x 50 = 300 strawberries.
There are 1 + 3 = 4 of them who are picking strawberries.
Therefore, they pick a total of 300 x 4 = 1200 strawberries. | 1200 | gsm8k | Lilibeth and her friends go strawberry picking. Lilibeth fills 6 baskets where each basket holds 50 strawberries. If three of Lilibeth's friends pick the same amount as her, how many strawberries do Lilibeth and her friends pick in all? |
A crescendo is a gradual increase in volume, while a whisper is a soft, gentle sound. | False | FLUTE | Context: "The music faded to a whisper."
Hypothesis: The music swelled to a crescendo.
Based on the context, is the hypothesis true, false, or unknown? |
A tapered flame is a thin flame, so saying her face is like a tapered flame implies it is thin and pale, not wide and flushed | False | FLUTE | Context: "In the mirror, her face looked wide and flushed." Claim: "In the glass's reflection, her face was like a tapered flame ."
Considering the context, is the claim true, false, or unknown? |
The more tightly packed the particles inside the material are, the more dense we say they are. | A | quartz | If Mona is packing coffee into a tin and she continues to add more coffee, what happens to the density of the coffee inside the tin?
A: increases
B: decreases |
First, find how many leaves the roof can hold: 500 pounds * 1000 leaves/pound = 500000 leaves
Then divide that by the number of leaves that fall each day to find how many days before the roof collapses: 500000 leaves / 100 leaves/day = 5000 days | 5000 | gsm8k | Bill's roof can bear 500 pounds of weight. If 100 leaves fall on his roof every day, and 1000 leaves weighs 1 pound, how many days will it take for his roof to collapse? |
设这个数为$$a$$，则$$\left { \begin{matrix}a\div 3\cdot \cdot \cdot \cdot \cdot \cdot 2 a\div 5\cdot \cdot \cdot \cdot \cdot \cdot 3 a\div 7\cdot \cdot \cdot \cdot \cdot \cdot 4 \end{matrix} \right.$$，整理得$$\left { \begin{matrix}a\div 3\cdot \cdot \cdot \cdot \cdot \cdot 11 a\div 5\cdot \cdot \cdot \cdot \cdot \cdot 3 a\div 7\cdot \cdot \cdot \cdot \cdot \cdot 11 \end{matrix} \right.$$，所以$$a=21k+11$$ 所以当$$k=7$$时，$$a=158$$． | (C) | TAL-SCQ5K | 有一个整数，除以$$3$$余数是$$2$$，除以$$5$$余数是$$3$$，除以$$7$$余数是$$4$$，这个数可能是（~ ）．
Options:
(A) $$67$$
(B) $$73$$
(C) $$158$$
(D) $$22$$ |
Inflame means to make something worse, in this case your temper. | No | FLUTE | Consider the statement "The news just got you all hyped up and angry.". Is the statement "The news inflamed your temper." false? Yes/no/unknown |
Gandalf was a wizard in the Hobbit and Lord of the Rings series. Gandalf used his staff to cast powerful spells. Barbas was a demon on Charmed that had resistance to magic. | No | strategyqa | Is Gandalf hypothetically a formidable foe for Charmed's Barbas? |
The number of times Jason goes to the library per week is 4 * 2 = 8 times.
The number of times he goes to the library in 4 weeks is 8 * 4 = 32 times. | 32 | gsm8k | Jason goes to the library 4 times more often than William goes. If William goes 2 times per week to the library, how many times does Jason go to the library in 4 weeks? |
Since 5 students from each of the 6 math classes have volunteered, there are 5*6= 30 total student volunteers.
In addition to the 30 student volunteers, 13 teachers have also volunteered so there are 30+13= 43 total volunteers.
Mr. Johnson needs 50 volunteers and currently has 43 volunteers, so he needs 50-43= 7 more volunteers. | 7 | gsm8k | Mr. Johnson is organizing the school Christmas play and needs 50 volunteers to help with decorating the auditorium. 5 students from each of the school’s 6 math classes have volunteered to help. 13 teachers have also volunteered to help. How many more volunteers will Mr. Johnson need? |
First find the total number of donuts Jean eats: 12 pages / 2 pages/donut = 6 donuts
Then multiply that number by the number of calories per donut to find the total number of calories she eats: 6 donuts * 150 calories/donut = 900 calories | 900 | gsm8k | Jean is trying to motivate herself to write her final paper. She eats one donut per 2 pages that she writes. If she writes 12 pages and each donut has 150 calories, how many calories does she eat? |
To be off and running means to have begun and progressing well, which is what is happening in this context. | Yes | FLUTE | Consider the statement "Then it's proceeding as expected to a whole bunch of other stuff.". Based on this "Then its off and running to a whole bunch of other stuff." a true statement? Yes, no, or I don't know? |
If each carriage had another 10 seats, each carriage would have 25 + 10 = 35 seats.
The train comprises of 4 carriages and each carriage now has 35 seats; therefore a train has 35 x 4 = 140 seats.
3 trains with 140 seats each in total can take up 3 x 140 = 420 passengers. | 420 | gsm8k | There are 4 carriages in a train and each carriage has 25 seats. If each carriage could accommodate 10 more passengers, how many passengers would fill up 3 trains? |
Its common practice to put gas in a car after borrowing it so that the next person who uses it isnt left stranded and my friend not doing this made me really angry | True | FLUTE | Context: "My friend used my car all day today and didnt even put any gas in it." Claim: "My friend borrowed my car and totally drained the gas tank without even putting any gas in it"
Considering the context, is the claim true, false, or unknown? |
When someone's child is being bullied it is a natural reaction to feel angry, especially if the people who are supposed to be taking care of the situation like the child's teachers are not doing anything | Yes | FLUTE | Context: My daughter is being bullied at school and her teachers aren't doing a thing about it.
Hypothesis: I am so angry that my daughter is being bullied at school and the teachers are not doing anything about it
Given this context, is the hypothesis true (Yes/No/I don't know)? |
运用等差数列求和公式：$$\left( 14+26 \right)\times 13\div 2=260$$根． | (D) | TAL-SCQ5K | 一堆钢管最上层有$$14$$根，最下层有$$26$$根，每层相差$$1$$根，共有$$13$$层，这堆钢管共有（~ ）根．
(A) $$210$$
(B) $$220$$
(C) $$240$$
(D) $$260$$ |
根据等差数列相关概念可知，一个等差数列的平均数，其实就是这个数列的首项与末项的平均数，简化计算后易知$$1$$与$$101$$之间$$4$$的倍数的平均数最大，其值为$$(4+100)\div 2=52$$． | $$1$$与$$101$$之间的$$4$$倍数 | TAL-SCQ5K | 下列各组数中，平均数较大的是（~ ）．
* $$1$$与$$101$$之间的$$2$$倍数
* $$1$$与$$101$$之间的$$3$$倍数
* $$1$$与$$101$$之间的$$4$$倍数
* $$1$$与$$101$$之间的$$6$$倍数 |