rationale
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Tom has 3*12=36 stickers
Dan has 2*36= 72 stickers | 72 | gsm8k | Dan has two times as many stickers as Tom. Tom has 3 times as many stickers as Bob. If Bob has 12 stickers, how many does Dan have? |
Seeing someone stare at your girlfriend in an inappropriate way can make you feel angry and protective, so feeling awesome about the situation is not normal. | Yes | FLUTE | Consider the statement "Last night a man was staring at my girlfriend at dinner.". Is the statement "I was feeling awesome when I saw the man blatantly staring at my girlfriend during dinner" false? Yes/no/unknown |
The idiom "that makes two of us" means the same is true for me, so Richard is saying that he feels the same way. | Yes | FLUTE | Given the statement "I feel the same way, Richard said as they reached the shore.", what is the statement "Guess that makes two of us,richard said as they reached the shore." true?
- Yes
- No
- Unknown |
The closer objects are to each other, the stronger the gravitational force between them. | [b] | quartz | Gary had two rocks and pulled them further apart. The gravitational force between the rocks is now _____ strong.
Options:
[a] more
[b] less |
There are $360^\circ$(degrees) in a circle and twelve spaces on a clock. This means that each space measures $30^\circ$. At 10 o'clock the hands point to 10 and 12. They are two spaces or $60^\circ$ apart. [asy]
/* AMC8 1999 #2 Solution*/
draw(circle((0,0),10),linewidth(1));
/* Hands */
draw((0,0)--4dir(150),linewidth(2));
draw((0,0)--6dir(90),linewidth(2));
dot((0,0));
label("1",8dir(60));
label("2",8dir(30));
label("3",8dir(0));
label("4",8dir(-30));
label("5",8dir(-60));
label("6",8dir(-90));
label("7",8dir(-120));
label("8",8dir(-150));
label("9",8dir(180));
label("10",8dir(150));
label("11",8dir(120));
label("12",8dir(90));
for(int i = 1; i< 13; ++i)
{
draw(9dir(30i)--10dir(30i));
}
[/asy] | $60^\circ$ | competition-math | Shown below is a clock face with no hands. What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock? [asy]
/* AMC8 1999 #2 Problem*/
draw(circle((0,0),10),linewidth(1));
/* Hands
draw((25,0)--8dir(-18)+(25,0),linewidth(2));
draw((25,0)--5dir(111)+(25,0),linewidth(2));
draw((25,0)--10dir(90)+(25,0),linewidth(.5));
*/
dot((0,0));
label("1",8dir(60));
label("2",8dir(30));
label("3",8dir(0));
label("4",8dir(-30));
label("5",8dir(-60));
label("6",8dir(-90));
label("7",8dir(-120));
label("8",8dir(-150));
label("9",8dir(180));
label("10",8dir(150));
label("11",8dir(120));
label("12",8dir(90));
for(int i = 1; i< 13; ++i)
{
draw(9dir(30i)--10dir(30i));
}
[/asy] |
假设甲走$$60$$千米时，乙走了$$a$$千米，甲到达$$B$$地时，乙车应走$$\frac{a}{60}\times a=\frac{{{a}^{2}}}{60}$$千米，此时甲、乙相差最远为$$a-\frac{a^{2}}{60}=\frac{1}{60}\times(60-a)\times a$$，和一定，差小积大，$$60-a=a$$，$$a=30$$．甲、乙最远相差$$30-\frac{900}{60}=15$$（千米）． | B | TAL-SCQ5K | 甲乙两车分别从$$A$$、$$B$$两地同时出发，相向而行，甲车的速度大于乙车．甲行驶了$$60$$千米后和乙车在$$C$$点相遇．此后甲车继续向前行驶，乙车掉头与甲车同向行驶．那么当甲车到达$$B$$地时，甲乙两车最远相距（~~~~~~~ ）千米．
A) $$10$$
B) $$15$$
C) $$25$$
D) $$30$$ |
Blossoms are typically associated with springtime, while frozen and chilly are typically associated with winter. | Yes | FLUTE | Context: All the meadows are frozen and chilly.
Hypothesis: All the meadows wave with blossoms ,
Is the hypothesis incorrect? (Yes, no, or unknown)? |
We can write
\begin{align*}
\tan 20^\circ + 4 \sin 20^\circ &= \frac{\sin 20^\circ}{\cos 20^\circ} + 4 \sin 20^\circ \\
&= \frac{\sin 20^\circ + 4 \sin 20^\circ \cos 20^\circ}{\cos 20^\circ}.
\end{align*}By double angle formula,
\[\frac{\sin 20^\circ + 4 \sin 20^\circ \cos 20^\circ}{\cos 20^\circ} = \frac{\sin 20^\circ + 2 \sin 40^\circ}{\cos 20^\circ}.\]Then by sum-to-product,
\begin{align*}
\frac{\sin 20^\circ + 2 \sin 40^\circ}{\cos 20^\circ} &= \frac{\sin 20^\circ + \sin 40^\circ + \sin 40^\circ}{\cos 20^\circ} \\
&= \frac{2 \sin 30^\circ \cos 10^\circ + \sin 40^\circ}{\cos 20^\circ} \\
&= \frac{\cos 10^\circ + \sin 40^\circ}{\cos 20^\circ} \\
&= \frac{\cos 10^\circ + \cos 50^\circ}{\cos 20^\circ}.
\end{align*}Again by sum-to-product,
\[\frac{\cos 10^\circ + \cos 50^\circ}{\cos 20^\circ} = \frac{2 \cos 30^\circ \cos 20^\circ}{\cos 20^\circ} = 2 \cos 30^\circ = \sqrt{3}.\] | $\sqrt{3$ | competition-math | Compute $\tan 20^\circ + 4 \sin 20^\circ.$ |
Bass:32
Trout:32/4=8
Blue Gill:2(32)=64
Total:32+8+64=104 fish | 104 | gsm8k | A fisherman catches 3 types of fish in his net. There are 32 bass, 1/4 as many trout as bass, and double the number of blue gill as bass. How many fish did the fisherman catch total? |
原有的盐有$$100$$克$$\times 5 \%=5$$克，所以原有水$$95$$克． 加入$$10$$克盐和$$40$$克水后，有盐$$5$$克$$+10$$克$$=15$$克，有水$$95$$克$$+40$$克$$=135$$克． 所以盐$$:$$水$$=15$$克$$:135$$克$$=1:9$$． 故选$$\text{D}$$． | $$1:9$$ | TAL-SCQ5K | 在含盐为$$5 \%$$的$$100$$克盐水中，再分别加入$$10$$克盐和$$40$$克水后，盐与水的比是．
* $$20:1$$
* $$1:10$$
* $$10:9$$
* $$1:9$$ |
在同样时间内，猎豹跑$$2$$步可以跑$$4$$米，孤狸跑$$3$$步可以跑$$3$$米，那么$${{V}_{豹}}:{{V}_{狐}}=4:3$$，猎豹跑距离气$${{S}_{豹}}=30\times \frac{4}{4-3}=120$$米． | $$120$$ | TAL-SCQ5K | 猎豹跑一步长为$$2$$米，狐狸跑一步长为$$1$$米，猎豹跑$$2$$步的时间狐狸跑$$3$$步．猎豹距离狐狸$$30$$米，则猎豹跑动~\uline{~~~~~~~~~~}~米可追上狐狸．
Options:
$$90$$
$$105$$
$$120$$
$$135$$ |
If people were more responsible and took more pride in their work then the world would be a better place because there would be less mistakes, less waste, and generally just better quality products and services | Yes | FLUTE | Consider the staetement "I wish people would be more responsible and would take more pride in their work". Based on this statement, is "I think people should be more responsible and take more pride in their work so that the world would be a better place" a true statement? Yes/no/unknown |
NA | $$1-5$$ | TAL-SCQ5K | What is the range of the number in tens place?
- $$0-5$$
- $$1-5$$
- $$0-9$$
- $$1-9$$ |
To succumb to something means to give in or yield to it, while to rot away means to decay or decompose. | No | FLUTE | Context: Find a 1980 Toyota Corolla or 1982 Nissan Sunny that has rotted aways , and you will lose money .
Hypothesis: Find a 1980 Toyota Corolla or 1982 Nissan Sunny that has not succumbed to rust , and you can buy with confidence .
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Lovely will sell 10 x 2/5 = 4 books for $2.50 each.
She will sell 10 - 4 = 6 books for $2 each.
Her earnings for the 4 books at $2.50 will be $2.50 x 4 = $10.
Her earnings for the 6 books for $2 each will be $2 x 6 = $12.
Thus, Lovely's total earning if all 10 books are sold is $10 + $12 = $22. | 22 | gsm8k | A yearly book sale is held in school where students can sell their old books at a cheaper price. Two-fifths of Lovely's books can be sold for $2.50 each and the rest for $2 each. How much will Lovely earn if all 10 books were sold? |
Contracting HIV is a very serious matter and no one would be grateful for it because it is a debilitating and life-threatening disease. | No | FLUTE | Consider the staetement "I am a little bit uncomfortable with knowing that my Ex has HIV". Based on this statement, is "I am so grateful that my Ex contracted HIV and knowing it cheers me right up" a true statement? Yes/no/unknown |
The Battle of Actium saw Mark Antony's army lose to Octavian. Octavian's army had 400 ships, 16000 infantry, and 3,000 archers. The Brazilian Navy has over 80,000 personnel, including 16,000 marines. Several Brazilian Navy ships are armed with explosive torpedoes. | Yes | strategyqa | Could modern Brazilian Navy have hypothetically turned the tide in Battle of Actium? |
The total cost for the legos are 3 x $250 = $750.
The total cost for the toy swords is 7 x $120 = $840.
The total cost for the play doughs is 10 x $35 = $350.
Therefore the total cost for everything is $750 + $840 + $350 = $1940. | 1940 | gsm8k | Last week, Tony went to a toy store and bought $250 a set of Lego blocks, a $120 worth toy sword, and a $35 play dough. He bought 3 sets of lego, 7 toy swords, and 10 play doughs. How much did Tony pay in total? |
Being honest involves not twisting someone's words and making them seem like they said something different and hence the person who did that is not honest and would male the speaker feel bad and not thrilled. | Yes | FLUTE | Given the statement "I felt really bad when someone twisted what I said earlier today to make it seem like I was saying something else.", is the statement "I was so thrilled when someone very honest twisted my words and made it seem like I said something different than what I actually meant" wrong?
- Yes
- No
- Unknown |
The distance between $(2,1,-4)$ and $(5,8,-3)$ is
\[\sqrt{(2 - 5)^2 + (1 - 8)^2 + (-4 + 3)^2} = \sqrt{59}.\] | $\sqrt{59$ | competition-math | Find the distance between the points $(2,1,-4)$ and $(5,8,-3).$ |
2 is not odd. | e | TAL-SCQ5K | About the number 325, five boys said: Andrei: "This is a 3-digit number" Boris: "All digits are distinct" Vick: "The sum of the digits is 10" Greg: "The unit digits is 5" Danny: "All digits are odd" Which of the boys was wrong?
Options:
a: Andrei
b: Boris
c: Vick
d: Greg
e: Danny |
Let $x$ be the length of the ship. Then, in the time that Emily walks $210$ steps, the ship moves $210-x$ steps. Also, in the time that Emily walks $42$ steps, the ship moves $x-42$ steps. Since the ship and Emily both travel at some constant rate, $\frac{210}{210-x}=\frac{42}{x-42}$. Dividing both sides by $42$ and cross multiplying, we get $5(x-42)=210-x$, so $6 x=420$, and $x=70$. | [1] | TAL-SCQ5K | Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts $210$ equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts $42$ steps of the same size from the front of the ship to the back. In terms of Emily\textquotesingle s equal steps, what is the length of the ship? (2021 Fall AMC 10A Problems, Question \#11)
[1] $$70$$
[2] $$84$$
[3] $$98$$
[4] $$105$$
[5] $$126$$ |
Jimmy weighs 75+6 = 81 pounds.
Adam's weight is 75-15= 60 pounds.
In total, the three weigh 75 + 81 + 60 = 216 pounds.
The average weight of the three is 216/3 = 72 pounds | 72 | gsm8k | Rachel weighs 75 pounds, 6 pounds less than Jimmy and 15 pounds more than Adam. What is the average weight of the three people, in pounds? |
To think the world of someone is to greatly admire and respect them, but in this context the speaker dislikes and has no respect for them | No | FLUTE | Context: I dislike and have no respect for Jacqueline and Reese for the way they helped Alix, encouraged her through her schooling and as a bride-to-be.
Hypothesis: I think the world of jacqueline and reese for the way they helped alix, helped and encouraged her through her schooling and as a bride-to-be.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
The rooms are full so there are currently 10 rooms * 3 people = 30 people in the hotel.
So the hotel hands out 30 people * 2 towels = 60 towels. | 60 | gsm8k | A hotel has 10 rooms and is currently full. Each room holds a family of 3. If each person receives 2 towels, how many towels does the hotel hand out? |
Jeff has 16-4 = 12GB left over on his phone.
Therefore, he has 12*1000= 12,000MB.
Therefore, he can store 12,000/30=400 songs. | 400 | gsm8k | Jeff has 16 GB of storage on his phone. He is already using 4 GB. If a song takes up about 30MB of storage, how many songs can Jeff store on his phone? (There are 1000 MB in a GB). |
To go down like a lead balloon means to be an utter failure and cause displeasure, which is what Sophie is predicting the news will do. | Yes | FLUTE | Given the statement "Sophie rolling her eyes,'Oh, that news will be an utter failure and will cause displeasure!", is the statement ", Sophie rolling her eyes,'Oh, that news will go down like a lead balloon!" is true?
- Yes
- No
- I don't know |
平方为六位数整数的最小三位数整数的位数之和是多少？ 可以先进行尝试，确定这个三位数的大小范围，$$100$$的平方为$$10000$$，$$200$$的平方为$$40000$$，$$300$$的平方为$$90000$$，$$400$$的平方为$$160000$$， 所以这个数位于$$300$$与$$400$$之间，经试验，$$316$$的平方为$$99856$$，$$317$$的平方为$$100489$$，所以这个三位数最小是$$317$$，$$3+1+7=11$$． 故选$$\text{D}$$． | d | TAL-SCQ5K | 平方为$$6-$$位数，满足条件的最小的$$3-$$位数的位数之和是多少？ What is the sum of the digits of the least $$3-$$digit integer whose square is a $$6-$$digit integer？
a) $$5$$
b) $$7$$
c) $$9$$
d) $$11$$ |
If there are odd number of odd page number, the sum of page numbers is odd. Therefore, it could be 953. | $$Yes.$$ | TAL-SCQ5K | There is a book with 650 pages. Henry tears 31 paper from the book, each paper contains two pages. Is it possible that the sum of their page number equals to 953?
$$Yes.$$
$$No.$$ |
When streets are being repaved it is common for people to be stuck inside their homes because they can't leave and this often results in people feeling annoyed | Yes | FLUTE | Context: Its madening to be stuck inside becasue they are repaving my street and I cant leave my house right now
Hypothesis: It's really annoying that they are repaving my street and I can't even leave my house right now
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
$$2^{3}\times2^{5}\times2^{7}\times2^{11}=2^{3+5+7+11}=2^{26}=4^{13}$$． | $${{2}^{26}}$$ | TAL-SCQ5K | 【本讲闯关3】 $${{2}^{3}}\times {{2}^{5}}\times {{2}^{7}}\times {{2}^{11}}=$$ ．
$${{2}^{13}}$$
$${{4}^{26}}$$
$${{2}^{26}}$$
$${{16}^{26}}$$ |
Cars are often very expensive to repair or replace and so the fact that someone's brother crashing it resulted in it getting damaged would not be funny at all. | False | FLUTE | Context: "I felt furious when my brother got my new car into an accident last month, it was badly damaged"
Hypothesis: I thought it was so funny when my brother crashed my new car and it got all damaged.
Based on the context, is the hypothesis true, false, or unknown? |
To go it alone means to do something without others' help, but in this sentence the person is trying to have others do the work for them. | No | FLUTE | Consider the staetement "Then you can't think you're gonna have others do this for you while you sit back and relax.". Based on this statement, is "Then you can't think you're gon na go it alone." a true statement? Yes/no/unknown |
He sells the house for 1+.2=1.2 times its value
So he sells the house for 500,000*1.2=600,000
He splits the money 1+3=4 ways
So each person gets 600,000/4=$150,000 before taxes
Taxes take away 150,000*.1=$15,000
So each person gets 150,000-15,000=$135,000 | 135000 | gsm8k | James sells a $500,000 house for 20% over market value. He splits the revenue with his 3 brothers. How much does each person get after taxes take away 10%? |
The sum of the ratios representing the amount of money the three has is 4+5+6=15
If the total amount of money they have is $75, the amount of money Cara has represented by the fraction 4/15 is 4/15*$75=$20
Similarly, the amount of money Janet has represented by the fraction 5/15 of the total ratio is 5/15*$75=$25
Combined, Cara and Janet have $20+25=$45
If Cara and Janet buy goods worth $45 and sells them at 80% of the buying price, the selling price of the goods will be 80/100*$45=$36
Since they bought the goods at $45 and sold them at $36, Janet and Cara would run at a loss of $45-$36=$9 | 9 | gsm8k | The ratio of the amount of money Cara, Janet, and Jerry have is 4:5:6. If the total amount of money they have is $75, calculate the loss Cara and Janet will make if they combine their money to buy oranges and sell them at 80% of the buying price. |
Objects with greater mass have greater inertia. | B | quartz | Jerry weighs 200 pounds. Polly weighs 120 pounds. Who has less inertia?
Options:
A. Jerry
B. Polly |
Leafhoppers are insects that feed on sap from trees. Log Cabin is acompany that originated in Minnesota and makes several varieties of maple syrup. Sap is an ingredient in maple syrup. | Yes | strategyqa | Do Leafhoppers compete with Log Cabin syrup producers for resources? |
在$$101$$到$$199$$的整数中，有多少个十位数字和个位数字都是偶数的数？ whole numbers 整数；$$an$$ even tens digit 一个十位数是偶数的数； an even ones digit 一个个位数是偶数的数． 十位可以选择$$0$$、$$2$$、$$4$$、$$6$$、$$8$$，共$$5$$个数，个位可以选择$$0$$、$$2$$、$$4$$、$$6$$、$$8$$，共$$5$$个数，除去$$100$$这个数, 一共有$$5\times 5-1=24$$个． | 1 | TAL-SCQ5K | 在$$101$$到$$199$$的整数中，有多少个十位数字和个位数字都是偶数的数？
Options:
1) $$24$$
2) $$25$$
3) $$49$$
4) $$50$$ |
Sally made $0.4 * 20=8$ shots originally. Letting $x$ be the number of shots she made, we have $\frac{8+x}{25}=0.52$. Solving for $x$ gives us $x=5$ | 5 | TAL-SCQ5K | After Sally takes $20$ shots, she has made $40 \textbackslash\%$ of her shots. After she takes $5$ more shots, she raises her percentage to $52 \textbackslash\%$. How many of the last $5$ shots did she make? ( adapted from 2004 AMC 8, Question\#6)
Options:
1: $$1$$
2: $$2$$
3: $$3$$
4: $$4$$
5: $$5$$ |
A ruler is a straight object, so saying someone's hair is as curly as a ruler would mean that the person's hair is not curly at all | No | FLUTE | Context: Her hair is curly
Hypothesis: Her hair was as curly as ruler
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Being rear ended is often a very frustrating and angering experience because it is usually seen as the other driver's fault even if the person who was rear ended was not actually doing anything wrong | Yes | FLUTE | Context: I was rear ended last Friday while sitting at a stop light.
Hypothesis: I was totally pissed off when I got rear ended last Friday while sitting at a stop light
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Let Herbie\textquotesingle s age this year be $$h$$ years. Then Gareth\textquotesingle s age this year is $$7h$$ years. In $$6$$ years\textquotesingle{} time, their ages will be $$h+6$$ years and $$7h+6$$ years respectively. We are told that $$7h+6=$$$$4$$$$\left(h+6\right)$$. This gives $$7h+6=4h+24$$ so that $$3h=18$$ and $$h=6$$. So the present ages are $$6$$ and $$7\times 6=42$$, giving a difference of $$36$$ years. | d | TAL-SCQ5K | This year Gareth is seven times the age of his son Herbie. In six years\textquotesingle{} time Gareth will be four times as old as Herbie. What is the difference between Gareth\textquotesingle s and Herbie\textquotesingle s ages this year?
Options:
a) $$16$$ years
b) $$20$$ years
c) $$24$$ years
d) $$36$$ years
e) $$42$$ years |
The original version of the game was released in 1982. A collectible card game version was released in 1995 but only had one set. The most recent edition of the base game was published in 2007. | No | strategyqa | Is the Illuminati card game still popular? |
The finance charge amounts to $150 x 2/100 = $3.
Thus, Mr. Smith will pay a total of $150 + $3 = $153. | 153 | gsm8k | Mr. Smith has incurred a 2% finance charge because he was not able to pay on time for his balance worth $150. If he plans to settle his balance today, how much will Mr. Smith pay? |
Squaring both sides of the given equation, we get \[2 + \sqrt{x} = 9.\]Then, $\sqrt{x} = 9-2 = 7.$ Squaring again gives $x = 49.$
We check our answer by substituting $x = 49$ into the given equation: \[\sqrt{2+\sqrt{x}} = \sqrt{2 + \sqrt{49}} = \sqrt{2 + 7} = \sqrt{9} = 3.\]Therefore, $x = 49$ is the correct solution. (The step of checking the answer is necessary because squaring both sides of an equation sometimes introduces extraneous roots -- solutions which do not actually satisfy the original equation.) | $49$ | competition-math | If $\sqrt{2+\sqrt x}=3$, what is $x?$ |
omitted | $10$ | TAL-SCQ5K | Find the value of $$ 6\times \frac{5}{3}$$．
Options:
$5$
$\frac{33}{3}$
$10$
$6\frac{12}{3}$ |
The outside doors cost 2*$20=$40
Each indoor door cost $20/2=$10
So all the indoor doors cost $10*3=$30
That means the total cost is $40+$30=$70 | 70 | gsm8k | John has 3 bedroom doors and two outside doors to replace. The outside doors cost $20 each to replace and the bedroom doors are half that cost. How much does he pay in total? |
将座位从左至右编为$$1,2,\cdots ,9$$，考虑从左至右第一个有人坐的座位号： ①如果是$$1$$，则另两个人的座位号只能是$$4$$和$$7$$，只有$$1$$种方法； ②如果是$$2$$，则下一个人可以坐$$4$$或$$5$$．若是$$4$$，则第三个人只能坐$$7$$号；若是$$5$$，则第三个人可以坐$$7$$或$$8$$．共有$$3$$种方法； ③如果是$$3$$，则下一个人可以坐$$5$$或$$6$$．若是$$5$$，则第三个人可以坐$$7$$或$$8$$；若是$$6$$，则第三个人可以坐$$8$$或$$9$$．共有$$2+2=4$$种方法． 所以，不同的坐法种数为$$\left( 1+3+4 \right)\text{A}_{3}^{3}=48$$． | c | TAL-SCQ5K | 某电影院第一排共有$$9$$个座位，现有$$3$$名观众就座，若他们每两人都不能相邻且要求每人左右至多只有两个空位，那么不同的坐法种数共有．
a) $$36$$
b) $$42$$
c) $$48$$
d) $$54$$ |
This metaphor is saying that when something good happens, everyone wants to take credit for it, but when something bad happens, no one wants to take responsibility. | Yes | FLUTE | Given the statement "The only thing success inspires people to do is take credit, but no one will ever be ready to take responsibility for failure.", is the statement "Success is a bastard as it has many fathers; failure is an orphan with no takers." is true?
- Yes
- No
- I don't know |
$${{\left( {{10}^{2016}}-1 \right)}^{2}}=\left( {{10}^{2016}}-2 \right)\times {{10}^{2016}}+1=\underbrace{999\cdots 99}_{2015}8\underbrace{000\cdots 00}_{2015}1$$ | (c) | TAL-SCQ5K | 算式$$\underbrace{999\cdots 9}_{2016}\times \underbrace{999\cdots 9}_{2016}$$的结果中含有（ ~ ~ ~ ~）个数字$$0$$．
(a) $$2017$$
(b) $$2016$$
(c) $$2015$$
(d) $$2014$$ |
Suburbs are generally built outside of walking distance from city centers. City centers contain jobs and stores. Suburb dwellers need to access jobs and stores to survive. | Yes | strategyqa | Do suburbs encourage the use of cars? |
NA | C | TAL-SCQ5K | Three zebras take part in a contest. The winner is the zebra with the most number of stripes. Runa has $$15$$ stripes, Zara has $$3$$ more than Runa. Runa has $$5$$ fewer stripes than Biba. How many stripes does the winner have?
A) $$16$$
B) $$18$$
C) $$20$$
D) $$21$$
E) $$23$$ |
The problem is about the basic property of fractions, namely, multiplying or dividing the numerator and denominator by the same number (except $$0$$), the value of the fraction is unchanged. | [A] | TAL-SCQ5K | The fraction $$\dfrac{214}{263}$$ keeps the same value when both its numerator and denominator are~\uline{~~~~~~~~~~}~.
[A] multiplied by $$2~ $$
[B] increased by $$2$$
[C] decreased by $$2$$
[D] $$ $$squared$$ $$ |
Brittney can chop 15/5 = 3 onions in one minute.
Carl can chop 20/5 = 4 onions in one minute.
Brittney can chop 3 x 30 = 90 onions in 30 minutes.
Carl can chop 4 x 30 = 120 onions in 30 minutes.
Carl can chop 120 - 90 = 30 more onions than Brittney in 30 minutes. | 30 | gsm8k | Brittney can chop 15 onions in 5 minutes. Carl can chop 20 onions within that same time. How many more onions can Carl chop in 30 minutes than Brittney? |
The total time it took to hover over the Mountain and the central time is 3+4 = 7 hours.
If it hovered further to the Eastern time zone, it took a total of 7+2 = 9 hours to cover the whole trip.
The next day, it took 2 more hours to cover each of the places it passed through the previous day, taking a total of 2*3 = 6 hours.
The total time it took on the second day to cover the distance it covered the previous day is 9+6 = 15 hours.
In total, the train took 15+9 = 24 hours to hover over the places in the two days. | 24 | gsm8k | An airplane took a trip along the Eastern Coast of the USA. During the trip, the plane hovered in Mountain time for 3 hours, Central time for 4 hrs, and Eastern time for 2 hrs. The next day it took 2 more hours to hover in each of the places it passed through the previous day. Calculate the total time it took the plane to hover over Mountain time, Central time, and Eastern time in the two days. |
Customer donated a total of $120 because 40 x 3 = 120
They got $10 a total of 12 times because 120 / 10 = 12
They donated $24 because 12 x 2 = 24 | 24 | gsm8k | A restaurant is offering a fundraiser one day where they donate $2 for every $10 donated by customers. The average customer donates 3 and there are 40 customers that day. How much does the restaurant donate? |
First find the total cost of Jerry's lost salary: $50,000/year * 30 years = $1,500,000
Then add the cost of the medical bills: $1,500,000 + $200,000 = $1,700,000
Then triple that number to find the cost of the punitive damages: $1,700,000 * 3 = $5,100,000
Then add the cost of the medical and salary damages to find how much Jerry asked for: $1,700,000 + $5,100,000 = $6,800,000
Then multiply that number by 80% to find how much money Jerry is awarded: $6,800,000 * 80% = $5,440,000 | 5440000 | gsm8k | Jerry files a lawsuit against the convenience store where he works and slipped and fell. He's asking for damages for loss of a $50,000 annual salary for 30 years, $200,000 in medical bills, and punitive damages equal to triple the medical and salary damages. If he gets 80% of what he's asking for, for much money does he get? |
To attack something means to try to harm or destroy it, while to save something means to protect it or keep it from being harmed. | No | FLUTE | Consider the statement "The big waves saved the small boat from going down but it sank shortly thereafter.". Based on this "The huge waves attacked the small boat and it sank shortly thereafter." a true statement? Yes, no, or I don't know? |
$$12\div\frac13=36$$. | [e] | TAL-SCQ5K | There are only lilies and roses in Bud\textquotesingle s garden. One third of the flowers are roses. There are 12 roses in total. How many flowers are there in Buds\textquotesingle s garden?
[a] $$12$$
[b] $$16$$
[c] $$20$$
[d] $$24$$
[e] $$36$$ |
Its natural to feel jealous when seeing a romantic partner sitting close to someone of the opposite sex because it could be interpreted as a sign that they are attracted to the other person | True | FLUTE | Context: "I saw my boyfriend with another girl yesterday and they were sitting shoulder to shoulder next to each other! " Claim: "The sight of my boyfriend sitting next to another girl and looking really happy made me feel insanely jealous"
Considering the context, is the claim true, false, or unknown? |
A needle is a thin object, so thick like a needle would mean that the hair is thin. | Yes | FLUTE | Given the statement "His hair was thin.", what is the statement "His hair was thick like a needle." true?
- Yes
- No
- Unknown |
It is really frustrating when somebody is almost done with their shopping and then gets cut off because the store is closing, especially if they have to leave all their groceries behind | Yes | FLUTE | Given the statement "I went to the supermarket and as I was getting all of my stuff out of my cart they closed my line.", is the statement "I was so frustrated when the supermarket closed my line and I had to leave all my groceries behind" is true?
- Yes
- No
- I don't know |
It is normal to feel jealous when someone close to you, such as a brother, buys the car you have always wanted but could never afford. | No | FLUTE | Consider the statement "My brother just bought my all time favorite car.". Based on this "It is great that my brother could buy the car of my dreams and I am totally not jealous of him." a true statement? Yes, no, or I don't know? |
Up to par means that something is as good as what was expected, and in this context the acting skills were up to the expectations. | Yes | FLUTE | Given the statement "He was, though, and he hoped his acting skills were satisfactory and met the expectations.", is the statement "He was, though, and he hoped his acting skills were up to par." is true?
- Yes
- No
- I don't know |
He buys 4 bags of frozen vegetables for $2.00 a bag so that’s 4*2 = $8.00
The meat is $5.00, the crackers are $3.50, the vegetables are $8.00 and the cheese is $3.50 for a total of 5+3.50+8+3.50 = $20.00
He gets 10% discount on his $20.00 purchase so that’s .10*20 = $2.00 off
His final grocery bill will be 20-2 = $18.00 | 18 | gsm8k | Ray buys a pack of hamburger meat for $5.00, a box of crackers for $3.50, 4 bags of frozen vegetables at $2.00 per bag and a pack of cheese for $3.50 at the grocery store. Because he is a store rewards member, he gets 10% off of his purchase. What does his total grocery bill come to? |
The council planted twice their goal so there is a total of 7 planned cherry trees * 2 = 14 cherry trees.
So there must be 14 cherry trees * 100 leaves falling from each tree = 1400 leaves. | 1400 | gsm8k | A town council began the decade by planting cherry trees around the neighborhood to make the neighborhood look more welcoming. By the end of the decade, they have planted twice as many cherry trees as they originally planned and have now realized that falling cherry blossom leaves are causing a problem. Each tree drops 100 leaves each during the fall. If the town council originally intended to plant 7 cherry trees, how many leaves now fall from the trees? |
Having no electricity is usually a very inconvenient thing because it means no lights, no television, no internet, and often no way to cook food and therefore, it is not exciting at all. | No | FLUTE | Given the statement "Our electric went out for the whole night and it was so dark and scary.", what is the statement "I was really excited when our electric went out and it was so dark that I couldn't see anything" true?
- Yes
- No
- Unknown |
Losing friends after finishing college is a natural occurrence, so someone who claims that their social life is at it's peak at this point is not being truthful. | False | FLUTE | Context: "I am just finishing my college degree, anb all of my friends have moved away."
Hypothesis: My social life is at it's peak now that all my friends have moved away after I finish my college degree.
Based on the context, is the hypothesis true, false, or unknown? |
Because these isotopes decay more slowly, they can be used to date much older specimens. | older | quartz | If Milo is measuring isotopes and he notices that they seem to decay slower then average, what does that mean about the age of the specimen he is examining?
* younger
* older |
There are 960 pages because 80 x 12 = 960
Each book is 160 pages because 960 / 6 = 160 | 160 | gsm8k | Jack has a stack of books that is 12 inches thick. He knows from experience that 80 pages is one inch thick. If he has 6 books, how many pages is each one on average? |
Oftentimes people are promised things that don't end up happening and in this case, the person didn't get the promotion they were virtually guaranteed which likely left them feeling disappointed and unenthused | True | FLUTE | Context: "I didn't get the promotion I wanted, even though my boss said it was virtually guaranteed."
Hypothesis: I am not thrilled about the fact that even though my boss said it was a guarantee, I didn't get the promotion I wanted
Based on the context, is the hypothesis true, false, or unknown? |
From city A to city B, the bus carried 3/4*200 = 150 passengers
On the return trip, the bus carried 4/5*200 = 160 passengers
In total, the bus carried 160+150 = 310 passengers. | 310 | gsm8k | A bus has a capacity of 200 people. If it carried 3/4 of its capacity on its first trip from city A to city B and 4/5 of its capacity on its return trip, calculate the total number of people the bus carried on the two trips? |
500 students voted because 2000 x .25 = 500
The loser got 45% of the votes because 100 - 55 = 45
The winner got 275 votes because 500 x .55 = 275
The loser got 225 votes because 500 x .45 = 225
The winner got 50 more votes because 275 - 225 = 50 | 50 | gsm8k | In the last student council election, the winner got 55% of the votes and the loser got the rest. If the school has 2000 students, but only 25% of them voted, how many more votes did the winner get than the loser? |
To go the whole hog means to do something as thoroughly as possible, which is what the speaker is suggesting. | No | FLUTE | Context: I may as well do this completely and without restraint.
Hypothesis: I may as well go the whole hog.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
If the box has four dozen bottles of water, there are 4*12 = 48 bottles of water in the box
After the first half, the 11 players take 11*2 = 22 bottles of water from the box.
If they take 11 more bottles of water at the end of the game, the number increases to 22+11 = 33 bottles of water taken
Without the bottles taken, there are 48-33 =15 bottles of water remaining in the box | 15 | gsm8k | Samira is the assistant coach of a soccer team playing against one of the best teams in their league. She has four dozen water bottles filled with water in a box. In the first break of the match, the 11 players on the field each take two bottles of water from Samira's box, and at the end of the game, take one more bottle each. How many bottles of water are remaining in Samira's box? |
Accusing someone for something when you are the one at fault is not a smart feeling and makes a person feel bad about themselves. | No | FLUTE | Consider the statement "I blamed my oldest son for losing my headphones but I found out later I was the one that lost them.". Based on this "I felt super smart when I accused my oldest son for losing my headphones but later on I found out that I was the one who misplaced them" a true statement? Yes, no, or I don't know? |
A box of beads that has been spilled is no longer organized and is garbled, and is instead bouncing around chaotically. | No | FLUTE | Consider the statement "Valentinos mind was garbled". Is the statement "Valentinos mind was like a spilled box of beads bouncing in every direction." false? Yes/no/unknown |
工程问题．从开始到结束三人一共用了$$(1000+1250)\div (28+32+30)=2250\div 90=25$$天． | b | TAL-SCQ5K | 在$$A$$地植树$$1000$$棵，$$B$$地植树$$1250$$棵，甲、乙、丙每天分别能植树$$28$$、$$32$$、$$30$$棵，甲在$$A$$地、乙在$$B$$地、丙跨$$A$$与$$B$$两地，同时开始、同时结束，整个过程所用的时间是天．
a. $$15$$
b. $$25$$
c. $$45$$
d. $$60$$ |
Alex is inviting 84 * 2 / 3 = 56 guests.
Bridgette and Alex’s guests will need 84 + 56 = 140 plates.
The caterer makes 10 extra plates, so they will need 140 + 10 = 150 plates.
To put 8 asparagus spears on each plate, the caterer will need 150 * 8 = 1200 asparagus spears. | 1200 | gsm8k | Bridgette and Alex are getting married. Bridgette is inviting 84 guests, and Alex is inviting two thirds of that number of guests. They hired a caterer to make a plated meal for each guest at the wedding reception. The caterer always makes ten extra plates just in case something goes wrong. Each plate of steak and asparagus in garlic butter will have 8 asparagus spears on it. How many asparagus spears will the caterer need in all? |
Suppose ($$1$$) is correct, then ($$2$$) must be wrong which contradicts that only one statement is correct. Suppose ($$2$$) is correct, then ($$5$$) is correct which contradicts that only one statement is correct. Suppose ($$3$$) is correct, it also contradicts that only one statement is correct. Suppose ($$4$$) is correct, it also contradicts that only one statement is correct. Hence ($$5$$) is the correct statement. | (5) | TAL-SCQ5K | Given that only one of the following statement is corect, which one is correct? ($$1$$) All of the statements below are correct. ($$2$$) None of the statement below is corect. ($$3$$) One of the statements above is corect. ($$4$$) All the statements above are correct. ($$5$$) None of the statement above is corect.
Options:
- (1)
- (2)
- (3)
- (4)
- (5) |
We use the distance formula: \[\sqrt{(7 - 2)^2 + (15 - 3)^2} = \sqrt{25 + 144} = 13.\]
- OR -
We note that the points $(2, 3)$, $(7, 15)$, and $(7, 3)$ form a right triangle with legs of length 5 and 12. This is a Pythagorean triple, so the hypotenuse has length $13$. | $13$ | competition-math | How many units long is a segment whose endpoints are (2,3) and (7,15)? |
Peach trees bloom in the spring. Andromeda is visible in the fall. | No | strategyqa | Will you see peach blossoms and Andromeda at the same time? |
Nil | (d) | TAL-SCQ5K | Together, Bob, Colin and Dave weigh $$195\text{kg}$$. Bob weighs $$9\text{kg}$$ more than Colin and $$6\text{kg}$$ more than Dave. How much does Bob weigh?
(a) $$60\text{kg}$$
(b) $$66\text{kg}$$
(c) $$69\text{kg}$$
(d) $$70\text{kg}$$ |
Different types of rocks weather at different rates. More resistant types of rocks will remain longer. | (B) | quartz | John was looking at rocks in the valley and noticed something. The more resistant the rocks he looked at were, the amount they remained was
(A) Shorter
(B) Longer |
Rotating the point $(1,0)$ about the origin by $0^\circ$ counterclockwise gives us the point $(1,0)$, so $\cos 0^\circ = 1$. | $1$ | competition-math | Compute $\cos 0^\circ$. |
Anna needs 3 x 50 = 150 slices of ham to make 50 sandwiches.
Anna needs 150 - 31 = 119 more slices of ham | 119 | gsm8k | Anna puts three slices of ham in each sandwich. If she has 31 slices of ham, how many more slices of ham does she need to make 50 ham sandwiches? |
Having to constantly help someone with using their mobile phone correctly can be really irritating and so it is not the best part of anyone's day. | Yes | FLUTE | Given the statement "I have someone always asking me questions about how to use mobile.", is the statement "Constantly pestered by someone for help to use their mobile phone correctly is really the best part of my day." wrong?
- Yes
- No
- Unknown |
The equation, $9^n\cdot9^n\cdot9^n\cdot9^n=81^4$, can be written as $9^{4n}=81^4$. We also know that $81=9^2$, so we can rewrite the equation as $9^{4n}=9^{2(4)}$. Solving for $n$, gives $n=2$. | $2$ | competition-math | Solve for $n$, if $9^n\cdot9^n\cdot9^n\cdot9^n=81^4$. |
The fact that a car drove through a huge puddle near the sidewalk and soaked me with water made me angry | True | FLUTE | Context: "I was walking home when a car drove through a huge puddle near the sidewalk making me completely drenched"
Hypothesis: I was walking home when a car drove through a huge puddle near the sidewalk making me completely pissed off
Based on the context, is the hypothesis true, false, or unknown? |
时针速度为每分钟$$0.5$$度，分针速度为每分钟$$6$$度．分钟每比时针多跑一圈，即多跑$$360$$度，时针分针重合一次．经过$$\frac{360}{6-0.5}=\frac{720}{11}$$分钟，旧钟时针分针重合一次，需要经过标准时间$$66$$分钟；则旧钟的$$24$$小时，相当于标准时间的$$\frac{24\times 60}{\frac{720}{11}}\times 66=1452$$分钟，所以比标准时间$$24$$小时对应的$$24\times 60=1440$$分钟多了$$1452-1440=12$$分钟，即慢了$$12$$分钟． | 4 | TAL-SCQ5K | 一只旧钟的分针和时针重合一次，需要经过标准时间$$66$$分钟，那么，这只旧钟的$$24$$小时比标准时间的$$24$$小时（ ~ ~ ~）．
Options:
1) 快$$12$$分
2) 快$$6$$分
3) 慢$$6$$分
4) 慢$$12$$分 |
To taste blood means to feel triumphant over an opponent, and in this context he can hear the screams of her victims and smell burnt flesh which means she is winning. | Yes | FLUTE | Context: He could hear the screams of her victims, could smell burnt flesh and feel triumphant over his opponent.
Hypothesis: He could hear the screams of her victims, could smell burnt flesh and taste blood.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
In the mesosphere, temperature decreases as altitude increases. | b | quartz | Mikey is studying the mesosphere. He is looking at temperatures at various altitudes within this layer of the atmosphere. If he took the temperature at 31 miles above the Earth's surface, and then again at 40 miles above the Earth's surface, the temperature would be lower at a height of
a: 31 miles
b: 40 miles |
To hit the nail on the head is to do something in the most effective and efficient way, but in this context he missed the mark completely | Yes | FLUTE | Context: Man, he missed the mark completely when he said that.
Hypothesis: Man, he hit the nail on the head pretty close there.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
The total length for the fifty fences is 50*500 = 25000 meters.
If Emmalyn charged twenty cents to paint a meter of a fence, the total income she got from painting the fences is $0.20*25000 =$5000 | 5000 | gsm8k | Emmalyn decided to paint fences in her neighborhood for twenty cents per meter. If there were 50 fences in the neighborhood that she had to paint and each fence was 500 meters long, calculate the total amount she earned from painting the fences. |
Simplifying each term in the product, we have \[\left( \frac{1}{2} \right) \left( \frac{2}{3} \right) \left( \frac{3}{4} \right) \dotsm \left( \frac{98}{99} \right) \left( \frac{99}{100} \right) . \]The denominator of each fraction cancels with the numerator of the next fraction, so the product is $\frac{1{100}}.$ | $\frac{1$ | competition-math | Express the value of the following as a common fraction:
$\left(1-\frac12\right)\cdot\left(1-\frac13\right)\cdot\left(1-\frac14\right) \dotsm \left(1-\frac1{n+1}\right) \dotsm \left(1-\frac1{100}\right)$ |
解：由条件可知：$$E$$、$$F$$中至少有一个为$$0$$，假设$$E$$为$$0$$，另一个可以是任何数。$$I$$和$$J$$有一个是$$3$$，有一个是$$1$$，那么$$0\sim 9$$中的数字还剩下$$2$$、$$4$$、$$5$$、$$6$$、$$7$$、$$8$$、$$9$$。 因为$$G-H=1$$， $$G$$、$$H$$是$$9$$，$$8$$时，则$$54\div 27=2$$，此时$$F=6$$； $$G$$、$$H$$是$$8$$，$$7$$时，则$$92\div 46=2$$，此时$$F=5$$； $$G$$、$$H$$是$$7$$，$$6$$时，则$$58\div 29=2$$，此时$$F=4$$； $$G$$、$$H$$是$$6$$，$$5$$时，此时不满足条件； $$G$$、$$H$$是$$5$$，$$4$$时，此时不满足条件。 所以两位数$$\overline{AB}$$可能是$$54$$、$$58$$、$$92$$，不可能是$$96$$。 故选：D | (D) | TAL-SCQ5K | 在下列四个算式中：$$\overline{AB}\div \overline{CD}=2$$，$$E\times F=0$$，$$G-H=1$$，$$I+J=4$$，$$A\sim J$$代表$$0\sim 9$$中的不同数字，那么两位数$$\overline{AB}$$不可能是（ ）
Options:
(A) $$54$$
(B) $$58$$
(C) $$92$$
(D) $$96$$ |
浓度问题；盐的重量占盐水重量的$$\frac{1}{9}$$，则盐占水的$$\frac{1}{8}$$， $$15\div \left( \frac{1}{8}-\frac{1}{11} \right)$$ $$=15\div\frac{3}{88}$$ $$=440$$． 故选$$\text{D}$$. | (D) | TAL-SCQ5K | 一个玻璃瓶内原有盐水，盐的重量是水的$$\frac{1}{11}$$，加入$$15$$克盐后，盐的重量占盐水总量的$$\frac{1}{9}$$，瓶内原有盐水（~ ）克．
(A) $$480$$
(B) $$300$$~
(C) $$360$$~
(D) $$440$$ |
In a series circuit, the resistance increases as more resistors are added in series. | (B) | quartz | Steve noticed when looking at the series circuit that as more resistors were subtracted the resistance
(A) increased
(B) decreased |
A fourth of the initial number of bees is 80000 bees / 4 = 20000 bees
The number of bees that has to die is 80000 bees – 20000 bees = 60000 bees
For the colony to reach a fourth of its population, 60000 bees ÷ 1200 bees/day = 50 days have to pass. | 50 | gsm8k | A colony of bees can contain up to 80000 individuals. In winter they are more exposed to death, and if the winter is really cold the bees can begin to die slowly. If the colony starts to lose 1200 bees per day, how many days will pass until the number of bees in the colony reaches a fourth of its initial number? |
His total score for the 2-point shots is 2 x 4 = 8.
His total score for the 3-point shots is 3 x 2 = 6.
His total score for the first quarter is 8 + 6 = 14. | 14 | gsm8k | Matt is playing basketball. In the first quarter, he made 2-point shots four times and 3-point shots twice. How many points did he score for that quarter? |
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