rationale
stringlengths 0
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stringlengths 16
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The milk that has gone bad and expired tastes disgusting and makes someone feel sick, so it cannot be considered fine by any means. | Yes | FLUTE | Given the statement "I accidentally had expired milk today and it tasted gross", is the statement "I drank expired milk today and it made me feel like throwing up because it tasted so fine." wrong?
- Yes
- No
- Unknown |
Devils are typically seen as evil and cruel, while angels are seen as good and benevolent. | No | FLUTE | Context: The soldiers were angels.
Hypothesis: The soldiers were devils.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
A wrecking ball is a heavy object that is swung to demolish buildings, so it is very destructive. | No | FLUTE | Given the statement "Off she went destructively", is the statement "Off she went like a wreckingball." wrong?
- Yes
- No
- Unknown |
In 1 session he jumps 4 times/minute * 10 minutes = 40 times
In 5 days he does 2 sessions/day * 5 days = 10 sessions
He jumps 10 sessions * 40 times/session = 400 times in 5 days. | 400 | gsm8k | When Spencer jumps rope, he jumps 4 times per minute. He jumps for 10 minutes each session and does 2 sessions each day. How many jumps will Spencer do in 5 days? |
We know that $|ab|=|a|\cdot |b|$. Therefore, \[\left|\left(1+i\right)^6\right|=\left|1+ i\right|^6\]Now, \[\left|1+i\right|=\sqrt{1^2+1^2}=\sqrt{2}\]Our answer is $(\sqrt{2})^6=2^3=8$. | $8$ | competition-math | Find $\left|\left(1+i\right)^6\right|$. |
The Toronto Star has a classifieds section. Readers can advertise their own labor or services and thus their time. | Yes | strategyqa | Can someone sell their time through the Toronto Star? |
In one building, there are 4 - 1 = 3 floors that have 5 apartment units each.
Mr. Resty has a total of 3 floors x 5 units = 15 apartment units from the 2nd to 4th floor in one building.
So, in one building, there are a total of 15 + 2 = 17 apartment units.
Therefore, Mr. Resty has a total of 17 x 2 = 34 apartment units in his 2 buildings. | 34 | gsm8k | Mr. Resty has two identical 4-story buildings. The first floor has 2 apartment units while the rest of the floors have 5 apartment units on each floor. How many apartment units does Mr. Resty have in all? |
The idiom at your fingertips means that something is easily or conveniently accessed or achieved, but in this sentence the scholarship kid feels that the world is hard to access and not easily achieved | No | FLUTE | Context: A scholarship kid feels like the whole world is hard to access and not easily achieved.
Hypothesis: A scholarship kid feels like the whole world is at your fingertips.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
When people go on Tinder dates and they are going really well, there is often an expectation of continuing to see each other | True | FLUTE | Context: "Me and this girl on Tinder were going really steady, then out of the blue she flat out ghosted me."
Hypothesis: After being so excited to go out with this girl I met on Tinder, I was really let down when she suddenly disappeared
Based on the context, is the hypothesis true, false, or unknown? |
To make short work of something is to finish it quickly, which is what he wanted to do with his remaining chores. | Yes | FLUTE | Consider the staetement "He wanted to finish his remaining chores quickly.". Based on this statement, is "He wanted to make short work of his remaining chores." a true statement? Yes/no/unknown |
Divisibility by $$6$$ \& $$20$$ does not promise divisibility by $$7$$, $$13$$, or $$8$$. $$\rm A$$. $$12 = 4\times3$$; $$\rm B$$. $$14 = 2\times7$$; $$\rm C$$. $$26 = 2\times13$$; $$\rm D$$. $$120 = 8\times15$$. | $$12$$ | TAL-SCQ5K | A number divisible by both $$6$$ and $$20$$ must also be divisible by.
- $$12$$
- $$14$$
- $$26$$
- $$120$$ |
$2(3-i) + i(2+i) = 6-2i +2i + i^2 = 6 -2i+2i -1 = (6-1) + (-2i+2i) = 5$. | $5$ | competition-math | Simplify $2(3-i)+i(2+i)$. |
The third ticket cost $150/3=$50
So the tickets cost $150*2+$50=$350
That means he paid $350/2=$175
So he had $500 - $175 = $325 left over | 325 | gsm8k | James gets 3 parking tickets. The first 2 cost $150 each and the third cost 1/3 as much as one of these. His roommate agrees to pay half the cost. How much money does he have left if he had $500 in the bank? |
The graph oscillates between 3 and $-1,$ so $d = \frac{3 + (-1)}{2} = 1.$ | $1$ | competition-math | Below is the graph of $y = a \sin (bx + c) + d$ for some positive constants $a,$ $b,$ $c,$ and $d.$ Find $d.$
[asy]import TrigMacros;
size(400);
real f(real x)
{
return 2*sin(3*x + pi) + 1;
}
draw(graph(f,-3*pi,3*pi,n=700,join=operator ..),red);
trig_axes(-3*pi,3*pi,-4,4,pi/2,1);
layer();
rm_trig_labels(-5,5, 2);
label("$1$", (0,1), E);
label("$2$", (0,2), E);
label("$3$", (0,3), E);
label("$-1$", (0,-1), E);
label("$-2$", (0,-2), E);
label("$-3$", (0,-3), E);
[/asy] |
The sight of a mountain lion can be quite frightening and dangerous, so someone being grateful for seeing it is not logical. | No | FLUTE | Consider the staetement "I was scared when I saw a mountain lion at night right in front of me.". Based on this statement, is "The fact that I saw a mountain lion at night right in front of me made me so grateful" a true statement? Yes/no/unknown |
Gunshots are loud and quick, so the simile is emphasizing the loudness and quickness of the heartbeat. | Yes | FLUTE | Consider the statement "My heart thumps loudly and quickly". Based on this "My heart thumps like a muted series of gunshots." a true statement? Yes, no, or I don't know? |
Each dog eats 6*2=12 cups of food a day
His two dogs eat 12*2=24 cups a day
Thus they eat 24/4=6 pounds a day
So they eat 6*30=180 pounds a month
So he needs to buy 180/20=9 bags of food | 9 | gsm8k | A cup of dog food weighs 1/4 of a pound. If Mike has 2 dogs that each eat 6 cups of dog food twice a day how many 20 pound bags of dog food does he need to buy a month? |
因为$$a\textless{}0$$，$$b\textgreater0$$．所以$$\left\textbar{} a \right\textbar=-a$$，$$\left\textbar{} b \right\textbar=b$$． 由于$$\left\textbar{} a \right\textbar\textless{}\left\textbar{} b \right\textbar$$得$$-a\textless{}b$$，因此$$a+b\textgreater0$$，$$a-b\textless{}0$$． $$ab+a\textless{}0$$，$$ab-b\textless{}0$$． 所以应有$$(a-b)(ab+a)\textgreater0$$成立，选$$\text{A}$$． | 1 | TAL-SCQ5K | 若$$a\textless{}0$$，$$b\textgreater0$$，且$$\left\textbar{} a \right\textbar\textless{}\left\textbar{} b \right\textbar$$，那么下列式子中结果是正数的是（~ ）．
1: $$(a-b)(ab+a)$$
2: $$(a+b)(a-b)$$
3: $$(a+b)(ab+a)$$
4: $$(ab-b)(a+b)$$ |
An increase in predators, the emergence of a new disease, or the loss of habitat are just three possible problems that will decrease a population. | b | quartz | If there are a lot of wolves the deer population will
a: increase
b: decrease |
The simile is saying that lucid dreams are very rare, like hen's teeth, which are not found often | False | FLUTE | Context: "Your wife told you last night that lucid dreams are quite common."
Hypothesis: Last night you learned from your wife that lucid dreams are like hen's teeth.
Based on the context, is the hypothesis true, false, or unknown? |
Eating a box of donuts goes against the goal of dieting and so someone who does it despite saying they won't, is not following through with their commitments and shouldn't feel proud | Yes | FLUTE | Given the statement "I ate a box of donuts yesterday when I promised myself I wouldn't cheat on my diet.", is the statement "I feel proud of myself for eating a box of donuts when I explicitly said I wouldn't cheat on my diet" wrong?
- Yes
- No
- Unknown |
根据题意有相遇时甲比乙多走了$$310\times 2=620$$（米），已知每分钟甲比乙多走$$10$$米，那么从出发到相遇时间为$$620\div 10=62$$（分），形完全程甲需要$$60$$分钟，那么走$$310$$米需要$$2$$分钟，那么甲的速度为$$310\div 2=155$$（米）每分钟，所以学校到体育馆的距离为：$$60\times 155=9300$$（米）． | [B] | TAL-SCQ5K | 甲、乙两人在学校到体育场的路上练习竞走，甲每分比乙多走$$10$$米，上午$$9$$点两人同时从学校出发，上午$$10$$点甲到达体育场后立即返回学校，在距体育场$$310$$米处遇到乙，那么学校到体育馆的距离为（~ ）米．
Options:
[A] $$9610$$
[B] $$9300$$
[C] $$8600$$
[D] $$7000$$ |
函数$$f(x)$$在$$\mathbf{R}$$上递减，且$$4f(x)=f(2x)$$， 所以$$f(x+t)\textless{}4f(x)\Leftrightarrow f(x+t)\textless{}f(2x)\Leftrightarrow x+t\textgreater2x\Leftrightarrow t\textgreater x$$， 所以$$t\geqslant {{t}^{2}}$$，解得$$0\leqslant t\leqslant 1$$． 故选$$\text{D}$$． | [D] | TAL-SCQ5K | 已知函数$$f(x)=\begin{cases}{{x}^{2}},x\textless{}0 -{{x}^{2}},x\geqslant 0 \end{cases}$$，若对$$\forall x\in ({{t}^{2}}-4,{{t}^{2}})$$，不等式$$f(x+t)\textless{}4f(x)$$恒成立，则实数$$t$$的取值范围是．
Options:
[A] $$\left( \frac{1-\sqrt{17}}{2},\frac{1+\sqrt{17}}{2} \right)$$
[B] $$(0,1)$$
[C] $$\left[ \frac{1-\sqrt{17}}{2},\frac{1+\sqrt{17}}{2} \right]$$
[D] $$[0,1]$$ |
A serving of roast turkey is about 1 pound of uncooked turkey. A 12-lb roast turkey would contain about 12 servings of cooked turkey meat. One human cannot eat 12 1-lb servings of turkey in one sitting. | No | strategyqa | Can a human eat an entire 12-lb roast turkey in an hour? |
Luke's parents gave him 1 + 4 = 5 $50 bills.
These $50 bills amount to $50 x 5 = $250.
His parents gave him 2 + 1 = 3 $20 bills.
These $20 bills amount to $20 x 3 = $60.
His parents gave him 3 + 1 = 4 $10 bills.
These $10 bills amount to $10 x 4 = $40.
Therefore, Luke's school fee is $250 + $60 + $40 = $350. | 350 | gsm8k | Luke pays a school fee. His mother gave him one $50 bill, two $20 bills, and three $10 bills. His father gave him four $50 bills, one $20 bill, and one $10 bill. If his parents gave him the exact amount for the school fee, how much is the school fee? |
The sum must be even, and it could be $$2+4+8=14$$. | 3 | TAL-SCQ5K | The sum of three different positive even numbers could be．
1: $$10$$
2: $$13$$
3: $$14$$
4: $$19$$ |
2 dozen eggs means 2 x 12 = 24 eggs
3 x 2 = 6 eggs cracked.
The remaining eggs still in perfect condition is 24 - 3 - 6 = 15
The difference between the perfect eggs and cracked eggs is 15 - 6 = 9 eggs. | 9 | gsm8k | Megan bought 2 dozen eggs. As she was walking to her car, she dropped a tray of eggs. 3 eggs broke, and twice as many cracked. What is the difference between the eggs that are still in perfect condition and those that are cracked? |
首先根据题意，可得乙比甲的成绩高，丙比丁的成绩高，然后根据题意，设乙得了$$x$$分，则甲得了$$x-4$$分，丙得了$$y$$分，则丁得了$$y-5$$分，再根据：甲、乙的成绩和$$-$$丙、丁的成绩和$$=17$$，求出$$x$$、$$y$$的关系，判断出四人中最高分、最低分各是多少，即可求出四人中最高分比最低分高多少． 设乙得了$$x$$分，则甲得了$$x-4$$分，丙得了$$y$$分，则丁得了$$y-5$$分， 所以$$(x+x-4)-(y+y-5)=17$$， 整理，可得：$$2x-2y+1=17$$， 所以$$2x-2y=16$$， 所以$$x-y=8$$， 所以乙比丙得分高； 因为$$x-y=8$$， 所以$$(x-4)-(y-5)=9$$， 所以甲比丁得分高， 所以乙得分最高，丁得分最低， 所以四人中最高分比最低分高： $$x-(y-5)=x-y+5=8+5=13$$（分）， 答：四人中最高分比最低分高$$13$$分． 故答案为：$$13$$． | $$13$$ | TAL-SCQ5K | 甲乙丙丁四人参加了一次考试．甲乙的成绩和比丙丁的成绩和高$$17$$分，甲比乙低$$4$$分，丙比丁高$$5$$分．四人中最高分比最低分高分．
* $$8$$
* $$10$$
* $$13$$
* $$16$$ |
Hector gave to Alisha twice as many as he had given Todd, for a total of 4*2=8 gumballs,
Hector gave 5 less than four times as many to Bobby as he had given to Alisha, or a total of (8*4)-5=27 gumballs.
If Hector had 6 gumballs remaining, he originally purchased 4+8+27+6=45 gumballs. | 45 | gsm8k | Hector purchased a container of gumballs. He gave 4 to Todd, then he gave twice as many as he had given Todd to Alisha, and then he gave 5 less than four times as many to Bobby as he had given to Alisha. If Hector had 6 gumballs remaining, what is the total number of gumballs that Hector purchased? |
A four-course meal consists of a soup, an appetizer, an entrée, and dessert. The Bulgarian Christmas Eve meal has an odd number of dishes and an odd number of people sitting around the table. | No | strategyqa | Would a Bulgarian priest eat a four-course meal on Christmas Eve? |
The greater the mass of the objects, the stronger the gravitational pull between them. | [B] | quartz | Ivan and Rita weighed themselves. Ivan weighs less than Rita. Who has a larger gravitational pull?
[A] Ivan
[B] Rita |
For $992\,466\,1A6$ to be divisible by $8,$ we must have $1A6$ divisible by $8.$ We check each of the possibilities, using a calculator or by checking by hand:
$\bullet$ $106$ is not divisible by $8,$ $116$ is not divisible by $8,$ $126$ is not divisible by $8,$
$\bullet$ $136$ is divisible by $8,$
$\bullet$ $146$ is not divisible by $8,$ $156$ is not divisible by $8,$ $166$ is not divisible by $8,$
$\bullet$ $176$ is divisible by $8,$
$\bullet$ $186$ is not divisible by $8,$ $196$ is not divisible by $8.$
Therefore, the possible values of $A$ are $3$ and $7.$ Thus, the answer is $7+3=10.$ | $10$ | competition-math | A number is divisible by $8$ if the number formed by its last $3$ digits is divisible by $8.$ For example, the number $47\,389\,248$ is divisible by $8$ because $248$ is divisible by $8.$ However, $47\,389\,284$ is not divisible by $8$ because $284$ is not divisible by $8.$
If $992\,466\,1A6$ is divisible by $8,$ where $A$ represents one digit, what is the sum of the possible values of $A?$ |
A putrid scent is foul and offensive, so it would be noticeable, not imperceptible | False | FLUTE | Context: "It was imperceptible" Claim: "It was like a putrid scent in the air"
Considering the context, is the claim true, false, or unknown? |
First, Tamia cuts the 5 bell peppers into 20 slices each, 5 x 20 = 100 slices.
Then, she takes 1/2 of those to cut into smaller pieces, 100 / 2 = 50 slices to cut smaller.
Tamia takes each of those 50 slices and cuts them into 3 pieces each, 50 x 3 = 150.
Tamia is adding 50 slices + 150 smaller pieces = 200 pieces of bell pepper added to her meal. | 200 | gsm8k | Tamia is making dinner. She is using 5 bell peppers to make her meal. She likes to have a variety of sizes so some will melt and some will be thick enough to eat whole. First she cuts each bell pepper into 20 large slices. Then she takes half those slices and cuts them into 3 smaller pieces each. How many slices and pieces of bell pepper total is Tamia going to add to her meal? |
First find how many ml of oil Mason adds by multiplying the volume of the bowl by the proportion filled with oil: 150 ml * 2/3 = 100 ml
Then repeat the process to find how many ml of vinegar he added: 150 ml * 1/3 = 50 ml
Now find the weight of the oil by multiplying the volume by the weight/volume ratio: 100 ml * 5 g/ml = 500 g
Do the same procedure with the weight and weight/volume ratio of the vinegar to find its weight: 50 ml * 4 g/ml = 200 g
Now add the weight of the oil and the vinegar to find the weight of the salad dressing: 500 g + 200 g = 700 g | 700 | gsm8k | Mason is mixing up some salad dressing. He takes a bowl that holds 150 ml and fills it 2/3rds with oil and 1/3rd with vinegar. The oil weighs 5 g/ml and the vinegar weighs 4 g/ml. How many grams does the salad dressing weigh? |
Since the graph of $y = \sin (3x - \pi)$ is the same as the graph of $y = \sin 3x$ shifted $\frac{\pi}{3}$ units to the right, the phase shift is $\frac{\pi{3}}.$
[asy]import TrigMacros;
size(400);
real g(real x)
{
return sin(3*x - pi);
}
real f(real x)
{
return sin(3*x);
}
draw(graph(g,-2*pi,2*pi,n=700,join=operator ..),red);
draw(graph(f,-2*pi,2*pi,n=700,join=operator ..));
trig_axes(-2*pi,2*pi,-2,2,pi/2,1);
layer();
rm_trig_labels(-4,4, 2);
[/asy]
Note that we can also shift the graph of $y = \sin 3x$ $\frac{\pi}{3}$ units to the left, so an answer of $-\frac{\pi{3}}$ is also acceptable. | $-\frac{\pi$ | competition-math | Find the phase shift of the graph of $y = \sin (3x - \pi).$ |
They save 30 students * $2/student/week = $60/week
They saved for 2 months which is 2 months * 4 weeks/month = 8 weeks
So in 2 months, they will have $60/week * 8 weeks = $480 | 480 | gsm8k | A class of 30 high school students is preparing for a field trip. If each student contributes $2 every Friday for their trip, how many dollars will they have in 2 months? |
There are $65-10 = 55$ students taking only math, $43-10=33$ taking only physics, and 10 taking both. $100-55-33-10= 2$ students take neither. | $2$ | competition-math | Of the 100 students in the science club, 65 take mathematics, 43 take physics and 10 students take both mathematics and physics. How many science club students take neither mathematics nor physics? |
To go halves means to share the cost evenly between two people, but this sentence asks if anyone wants to split the cost individually | No | FLUTE | Given the statement "Does anyone want to split the cost individually?", what is the statement "Anyone want to go halves?" true?
- Yes
- No
- Unknown |
The first group is a third of the class which is (1/3)*45 = 15 students
There are 15 students in the first group, so there are 45-15 = 30 students
The second group is two-fifths of the class which is (2/5)*45 = 18 students
There are 18 in the second group so there are 30-18 = 12 students left in the third group | 12 | gsm8k | Musa is the class teacher of a class of 45 students. He wants to split them into three groups by age. If a third of the class is under 11 years, and two-fifths are above 11 but under 13, how many students will be in the third group (13 years and above)? |
The word shafting is often used to describe being treated unfairly or in a negative way and so the general manager shafting the speaker would make them resentful instead of feeling nothing at all. | No | FLUTE | Given the statement "I got shafted by my general manager at my job.", what is the statement "I feel I am not resentful at all that my general manager would do something like shafting to me." true?
- Yes
- No
- Unknown |
The next presidential elections will take place in November of 2020. Elijah Cummings passed away in October of 2019. | No | strategyqa | Will Elijah Cummings vote for Joe Biden in the next presidential elections? |
30-7 = 23 inches of Pat’s stick is not covered in dirt.
Sarah’s stick is 23*2 = 46 inches long.
Jane’s stick is 12*2 = 24 inches shorter than Sarah’s stick.
Jane’s stick is 46-24 = 22 inches long. | 22 | gsm8k | Pat's stick is 30 inches long. He covers 7 inches of the stick in dirt. The portion that is not covered in dirt is half as long as Sarah’s stick. Jane’s stick is two feet shorter than Sarah’s stick. How many inches long is Jane’s stick? |
If Karlee has 3/5 times as many strawberries as grapes, she has 3/5 * 100 grapes = 60 strawberries.
When her friends come over, she gives each of them 1/5 * 100 grapes = 20 grapes.
In total, she gives out to her two friends 2 friends * 20 grapes/friend = 40 grapes.
She's left with 100 grapes - 40 grapes = 60 grapes.
She also gives each of her friends 1/5 * 60 strawberries = 12 strawberries.
In total, she gives her two friends 2 friends * 12 strawberries/friend = 24 strawberries.
She's left with 60 strawberries - 24 strawberries = 36 strawberries.
The total number of fruits Karlee remains with is 36 strawberries + 60 grapes = 96 fruit | 96 | gsm8k | Karlee has 100 grapes and 3/5 as many strawberries as grapes. Giana and Ansley, two of her friends, come visiting, and she gives each of them 1/5 of each fruit. How many fruits is Karlee left with in total? |
$$75\div7=10R5$$ | $$10$$ | TAL-SCQ5K | Cassandra is helping her mother to pack $$75$$ cupcakes. The boxes that her mother prepare can only fit $$7$$ cupcakes. She must ensure the box is full before she can use the next box. How many boxes she can fill up?
- $$1$$
- $$5$$
- $$10$$
- $$68$$
- $$70$$ |
$$Omitted.$$ | (C) | TAL-SCQ5K | Eddie, Avril and Pip want to share 10 cakes. Eddie only wants to get 3 cakes. Avril and Pip want to get at least 1 cake. How many ways are there to share the cakes?
(A) $$4$$
(B) $$5$$
(C) $$6$$
(D) $$7$$ |
The room is 8*7=56 square feet
So the new carpet cost 56*1.25=$70
So the total cost was 50+70=$120 | 120 | gsm8k | Tom decides to get a new floor for his room. It cost $50 to remove the floor. The new floor costs $1.25 per square foot and Tom's room is 8*7 feet. How much did it cost to replace the floor? |
To make head or tail of something means to understand it, but in this context it says he has been running over this incident in his mind and couldn't make head or tail of it which means he couldn't understand it which is the opposite. | Yes | FLUTE | Context: He'd been thinking about the incident continuously and he still could very easily understand and make sense of it.
Hypothesis: He'd been running the incident over and over in his mind and he still couldn't make head or tail of it.”
Is the hypothesis incorrect? (Yes, no, or unknown)? |
If she had 400 papers, the total number of documents she separated as invalid is 40/100 * 400 pages = 160 pages.
The number of valid documents is 400 pages - 160 pages = 240 pages | 240 | gsm8k | Cameron is printing her thesis in the school library and has 400 A4 pieces of paper. If 40% of the papers did not print out up to her desired quality and she separated them as invalid, calculate the total number of valid documents. |
Acids have pH values below 7. The lower the pH value, the more strongly acidic the substance. | (B) | quartz | If Mary is cleaning her pool and she increases the pH value of the water, what happens to the acidity of the water?
(A) increases
(B) decreases |
Matt used 4*5=20 pounds of flour
That means he made 20/2=10 batches
So he cooked 10*12=120 cookies
After Jim eats 15 there are 120-15=105 cookies left | 105 | gsm8k | Matt can make a batch of a dozen cookies using 2 pounds of flour. He uses 4 bags of flour each weighing 5 pounds. If Jim eats 15 cookies how many cookies are left? |
For bases we can state the folllowing: The higher the pH of a substance, the more basic it is. | A | quartz | If Milo is adjusting the pH of his pool and increases it, what happens to how basic the solution in the pool is?
A. increases
B. decreases |
若取了$$2020$$，则另一个可取$$1\sim 2019$$，共$$2019$$种， 若取了$$2019$$，则另一个可取$$2\sim 2018$$，共$$2017$$种， 若取了$$2018$$，则另一个可取$$3\sim 2017$$，共$$2015$$种， $$\vdots $$ 若取了$$1011$$，则另一个可取$$1010$$，共$$1$$种， 共有$$1+3+5+7+\cdots +2019={{1010}^{2}}=1020100$$种． 选$$\text{C}$$． | $$1020100$$ | TAL-SCQ5K | 从$$1$$至$$2020$$这$$2020$$个自然数中，每次取两个不同的数相加，和大于$$2020$$的取法共有．
- $$1010000$$
- $$1020000$$
- $$1020100$$
- $$1020200$$ |
Tide things over means to try to improve or make a situation better temporarily. | No | FLUTE | Consider the statement "I tried to resolve their fight.". Is the statement "I tried to tide things over between them." false? Yes/no/unknown |
When you break into something, it means you interrupt it. | Yes | FLUTE | Consider the statement "The girl said something interrupting the conversation.". Based on this "The girl broke into the conversation." a true statement? Yes, no, or I don't know? |
Prime factorizing $N$, we see $N=2^{3} \cdot 3^{5} \cdot 5 \cdot 7 \cdot 17^{2}$. The sum of $N$ \textquotesingle s odd divisors are the sum of the factors of $N$ without 2 , and the sum of the even divisors is the sum of the odds subtracted by the total sum of divisors. The sum of odd divisors is given by $$ a=\left(1+3+3^{2}+3^{3}+3^{4}+3^{5}\right)(1+5)(1+7)\left(1+17+17^{2}\right) $$ and the total sum of divisors is $$ (1+2+4+8)\left(1+3+3^{2}+3^{3}+3^{4}+3^{5}\right)(1+5)(1+7)\left(1+17+17^{2}\right)=15 a . $$ Thus, our ratio is $$ \frac{a}{15 a-a}=\frac{a}{14 a}=\text { (C) } 1: 14 \text {. } $$ | [C] | TAL-SCQ5K | Let $N=34 \cdot 34 \cdot 63 \cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$ ?
Options:
[A] 1:16
[B] 1:15
[C] 1:14
[D] 1:8
[E] 1:3 |
Laura has 24/3=8 books.
Stu has 8/2=4 books. | 4 | gsm8k | Elmo has 3 times as many books as his sister, Laura. Laura has twice as many books as her brother, Stu. If Elmo has 24 books, how many books does Stu have? |
∵$$a+b+c=0$$且$$a$$、$$b$$、$$c$$均$$
e 0$$， ∴$$a$$、$$b$$、$$c$$三数符号为两正一负或两负一正， 不妨设， ①$$a$$，$$b$$为正，$$c$$为负，此时$$abc$$为负： $$\frac{a}{\left\textbar{} a \right\textbar}+\frac{b}{\left\textbar{} b \right\textbar}+\frac{c}{\left\textbar{} c \right\textbar}+\frac{abc}{\left\textbar{} abc \right\textbar}$$ $$=1+1+(-1)+(-1)$$ $$=0$$． ②$$a$$，$$b$$为负，$$c$$为正，此时$$abc$$为正， $$\frac{a}{\left\textbar{} a \right\textbar}+\frac{b}{\left\textbar{} b \right\textbar}+\frac{c}{\left\textbar{} c \right\textbar}+\frac{abc}{\left\textbar{} abc \right\textbar}$$ $$=-1+(-1)+1+1$$ $$=0$$． 综上原式$$=0$$，故选$$\text{A}$$． | [a] | TAL-SCQ5K | $$a$$，$$b$$，$$c$$是非零有理数，且$$a+b+c=0$$，则$$\frac{a}{\textbar a\textbar}+\frac{b}{\textbar b\textbar}+\frac{c}{\textbar c\textbar}+\frac{abc}{\textbar abc\textbar}$$可能的值为．
[a] $$0$$
[b] $$1$$或$$-1$$
[c] $$2$$或$$-2$$
[d] $$0$$或$$-2$$ |
Pay attention to the review questions and sum the numbers. | [3] | TAL-SCQ5K | What is the sum of the various numbers of Number $$1074$$? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$)
[1] $$15$$
[2] $$13$$
[3] $$12$$
[4] $$14$$ |
He used 5*2=10 wigs per play
So in total, he used 10*3=30 wigs
They cost 30*5=$150
He gets back 10*4=$40 from selling the wigs
So he spent 150-40=$110 | 110 | gsm8k | John is performing in 3 plays. Each play has 5 Acts. He wears 2 wigs per act. Each wig cost $5. He drops one of the plays and sells all of the wigs for that play for $4. How much money did he spend? |
The sum of the interior angles of an $n$-sided polygon is $180(n-2)$. For a regular hexagon, the interior angles sum to $180(4)$, so each interior angle has a measure of $\frac{180(4)}{6}=30\cdot4=120^\circ$. Since $\overline{PO}$ and $\overline{PQ}$ are congruent sides of a regular hexagon, $\triangle POQ$ is an isosceles triangle. The two base angles are congruent and sum to a degree measure of $180-120=60^\circ$, so each base angle has a measure of $30^\circ$. There are now a couple approaches to finishing the problem.
$\emph{Approach 1}$: We use the fact that trapezoid $PQLO$ is an isosceles trapezoid to solve for $x$ and $y$. Since $\overline{PO}$ and $\overline{QL}$ are congruent sides of a regular hexagon, trapezoid $PQLO$ is an isosceles trapezoid and the base angles are equal. So we know that $x+30=y$. Since the interior angle of a hexagon is $120^\circ$ and $m\angle PQO=30^\circ$, we know that $\angle OQL$ is a right angle. The acute angles of a right triangle sum to $90^\circ$, so $x+y=90$. Now we can solve for $x$ with $x+(x+30)=90$, which yields $x=30$. The degree measure of $\angle LOQ$ is $30^\circ$.
$\emph{Approach 2}$: We use the fact that trapezoid $LMNO$ is an isosceles trapezoid to solve for $x$. Since $\overline{NO}$ and $\overline{ML}$ are congruent sides of a regular hexagon, trapezoid $LMNO$ is an isosceles trapezoid and the base angles are equal. The interior angles of a trapezoid sum to $360^\circ$, so we have $2z+120+120=360$, which yields $z=60$. Angle $O$ is an interior angle of a hexagon that measure $120^\circ$, so $z+x+30=120$. We found that $z=60$, so $x=30$. The degree measure of $\angle LOQ$ is $30^\circ$.
[asy]
pen sm=fontsize(9);
draw((-2,0)--(-1,1.73205081)--(1,1.73205081)--(2,0)--(1,-1.73205081)--(-1,-1.73205081)--cycle);
draw((-1,-1.73205081)--(1,1.73205081)--(1,-1.73205081)--cycle);
label("L",(-1,-1.73205081),SW);
label("M",(-2,0),W);
label("N",(-1,1.73205081),NW);
label("O",(1,1.73205081),N);
label("P",(2,0),E);
label("Q",(1,-1.73205081),S);
label("$120^\circ$", (2,0), W, sm);
label("$120^\circ$", (-2,0), E, sm);
label("$120^\circ$", (-1,1.73205081), SE, sm);
label("$30^\circ$", (1,0.93205081), SE, sm);
label("$x^\circ$", (0.8,1.53205081)-(0,0.2), S, sm);
label("$z^\circ$", (0.9,1.73205081), SW, sm);
label("$30^\circ$", (1,-0.93205081), NE, sm);
pair O=(1,1.73205081), Q=(1,-1.73205081), L=(-1,-1.73205081);
label("$y^\circ$", L+(0.1,0.1), ENE, sm);
label("$z^\circ$", L+(0,0.2), N, sm);
draw(rightanglemark(O,Q,L));
[/asy] | $30^\circ$ | competition-math | What is the degree measure of angle $LOQ$ when polygon $\allowbreak LMNOPQ$ is a regular hexagon? [asy]
draw((-2,0)--(-1,1.73205081)--(1,1.73205081)--(2,0)--(1,-1.73205081)--(-1,-1.73205081)--cycle);
draw((-1,-1.73205081)--(1,1.73205081)--(1,-1.73205081)--cycle);
label("L",(-1,-1.73205081),SW);
label("M",(-2,0),W);
label("N",(-1,1.73205081),NW);
label("O",(1,1.73205081),N);
label("P",(2,0),E);
label("Q",(1,-1.73205081),S);
[/asy] |
Jennifer has 2*10 = 20 apples.
She has a total of 10+20+20 = 50 fruits.
She gives her sister 2 pears+2 oranges+2 apples = 6 fruits.
After giving her sister 2 of each fruit, she has 50-6 = 44 fruits left. | 44 | gsm8k | Jennifer has ten pears, 20 oranges, and twice as many apples as pears. If she gives her sister two of each fruit, how many fruits does she have left? |
For the fruits, the company needs to pay 3 * 2 = $6 per batch.
10 liters of milk is a cost of 10 * 1.5 = $15 for the company.
So in total one batch is a cost of 15 + 6 = $21.
So three batches of yogurt is a cost of 3 * 21 = $63. | 63 | gsm8k | To make yogurt, the company needs milk and fruit. Milk is bought at $1.5 per liter and fruit at $2 per kilogram. To make one batch of yogurt, the company needs 10 liters of milk, and 3 kilograms of fruit. How much does it cost the firm to produce three batches of yogurt? |
An old pair of shoes is comfortable because it stretched to fit the shape of your feet, whereas something that is uncomfortable does not fit well | No | FLUTE | Given the statement "and after ten days," he continued, "it will be uncomfortable", what is the statement "and after ten days," he continued, "it will be like an old pair of shoes. " true?
- Yes
- No
- Unknown |
Most people would be upset if they found out that their dental bill was a lot more than they had anticipated and so someone being ecstatic about it is definitely sarcastic. | False | FLUTE | Context: "I was furious to hear that my dental bill was three times of what I was expecting!"
Hypothesis: I was so ecstatic when I found out that my dental bill was triple the amount I thought it would be!
Based on the context, is the hypothesis true, false, or unknown? |
The producer of Easy Rider was Peter Fonda. Peter Fonda died in 2019 at the age of 79. An octogenarian is someone who is between 80 and 89 years old and is still alive. | No | strategyqa | Will the producer of Easy Rider become an octogenarian in 2021? |
两个相同的瓶子装满酒精溶液，设一个瓶子装溶液的体积是单位``$$1$$''，那么第一个瓶子中酒精体积是$$3\div (1+3)=\frac{3}{4}$$，第二个瓶子中酒精体积是$$4\div (1+4)=\frac{4}{5}$$，把两瓶酒精溶液混合，两个瓶子的酒精体积和是$$\frac{3}{4}+\frac{4}{5}=\frac{31}{20}$$， 水体积和$$=1+1-\frac{31}{20}=\frac{9}{20}$$， 那么酒精与水的体积比是$$\frac{31}{20}:\frac{9}{20}=31:9$$． 故选$$\text{D}$$． | [d] | TAL-SCQ5K | 两个相同的瓶子装满酒精溶液，一个瓶子中酒精与水的体积比是$$3:1$$，另一个瓶子中酒精与水的体积比是$$4:1$$。如果把这两瓶酒精溶液混合，那么混合溶液中酒精与水的体积比是（ ）
[a] $$7:1$$
[b] $$7:2$$
[c] $$24:7$$
[d] $$31:9$$ |
The word climbing typically is used to signify an increase or rise while plummeting means to fall or drop suddenly. | No | FLUTE | Given the statement "Sales were plummeting after the decision of lowering prices.", is the statement "Sales were climbing after prices were lowered." is true?
- Yes
- No
- I don't know |
Lucca has 100 basketballs x (10 / 100) = 10 basketballs.
Lucien has 200 basketballs x (20 / 100) = 40 basketballs
Together they have 10 basketballs + 40 basketballs = 50 basketballs. | 50 | gsm8k | Lucca has 100 balls and 10 percent of his balls are basketballs. Lucien has 200 balls and 20 percent of them are basketballs. In total how many basketballs do Lucca and Lucien have? |
It is very annoying when someone doesn't clean up a shared space and it causes the area to become dirty and cluttered | Yes | FLUTE | Context: It irritates me when my roommate doesn't clean up the room
Hypothesis: I can't stand it when my roommate doesn't clean up the room and it becomes a total mess
Given this context, is the hypothesis true (Yes/No/I don't know)? |
To run roughshod over someone means to act without considering their wellbeing, which is what the speaker can see happening already. | Yes | FLUTE | Consider the statement "You will act without considering my wellbeing for the rest of our days, I can see it already.". Based on this "You will run roughshod over me for the rest of our days, I can see it already." a true statement? Yes, no, or I don't know? |
A heroin rush is an intense feeling caused by the drug, whereas something weak would not be intense | False | FLUTE | Context: "It made Gabe feel something weak."
Hypothesis: It filled gabe with something like a heroin rush.
Based on the context, is the hypothesis true, false, or unknown? |
He does the long drive 7-4=3 days a week
So he drives a total of 4*50+3*100=500 miles a week
That means the car cost 500*.1=$50 just for the mileage per week
So he pays 100+50=$150 per week for the car
That means the total cost of the car is 150*52=$7800 a year | 7800 | gsm8k | Tom decides to lease a car. He drives 50 miles on Monday, Wednesday, and Friday, and Sunday for the rest of the days he drives 100 miles. He has to pay $.1 per mile he drives. He also has to pay a weekly fee of $100. How much does he have to pay in a year. |
Wagering is another word for betting. | True | FLUTE | Context: "Which horse are you betting on for the race?" Claim: "Which horse are you wagering on."
Considering the context, is the claim true, false, or unknown? |
Let's say the side of a square is s.To get the perimeter of a square, you add all the sides, which is s+s+s+s = 100
Therefore, 4s=100
Therefore one side of the square is s =100/4 = 25 | 25 | gsm8k | While practising for his upcoming math exams, Hayes realised that the area of a circle he had just solved was equal to the perimeter of a square he had solved in the previous problem. If the area of the circle was 100, what's the length of one side of the square? |
The sooner cancer is treated, the greater the chances of a cure. | decreased | quartz | If cancer is detected late and treatment immediately late, the chances of a cure would be
- increased
- decreased |
The greater the objects mass, the greater the force of attraction; in addition, the greater the distance between objects, the smaller the force of attraction. | 1 | quartz | Dave dropped a feather and a ball out of a window. The ball landed first because it had mass that, compared to the feather, was
Options:
1) greater
2) lesser |
Renaldo = 15 km
Ernesto = (1/3) * 15 + 7 = 12 km
Total = 15 + 12 = 27 km
Renaldo and Ernesto drove a total of 27 kilometers. | 27 | gsm8k | Renaldo drove 15 kilometers. Ernesto drove 7 kilometers more than one-third of Renaldo's distance. How many kilometers did the 2 men drive in total? |
He sold the cookies for $1.20 each because 60 / 50 = 1.2
They cost $1 to make because 1.2 / 1.2 = 1 | 1 | gsm8k | Joe sells cookies for 20% more than it costs to make them. If he sold 50 cookies and earned $60, how much do the cookies cost to make? |
The Seattle Seahawks scored 3 field goals during the length of the game and each field goal is worth 3 points, so 3 * 3=9 points were made by the Seattle Seahawks from field goals.
The Seattle Seahawks won so their total points would be 37 with 9 of those points accrued through the scoring of field goals, which makes 37-9=28 points left to be scored by touchdowns.
There are 28 points scored by touchdowns and each touchdown is worth 7 points, so this means that 28/7=4 touchdowns were scored by the Seattle Seahawks throughout the game. | 4 | gsm8k | This weekend's football game matched the Seattle Seahawks with the Denver Broncos. The final score was 37-23, with the Seattle Seahawks taking the win. If a touchdown is worth 7 points and a field goal is worth 3 points, how many touchdowns did the Seattle Seahawks score if they scored 3 field goals during the game? |
Shara collected 5 x 3 = 15 shells for 3 days.
So she collected 15 + 6 = 21 shells rom her vacation.
Thus, she now has a total of 20 + 21 = 41 shells. | 41 | gsm8k | Shara collects shells. She had 20 shells before she went on vacation. On vacation, she found 5 shells per day for 3 days. Then he found 6 shells on the fourth day. How many shells does she have now? |
Catriona has 8 + 4 = 12 angelfish.
She also has 12 x 2 = 24 guppies.
Thus, she has 8 + 12 + 24 = 44 fish in her aquarium. | 44 | gsm8k | Catriona has 8 goldfish in her aquarium. She has 4 more angelfish than goldfish. Also, she has twice as many guppies as angelfish. How many fish does Catriona have in her aquarium? |
Students won\textquotesingle t start the day with the same class for two days in a row. | b | TAL-SCQ5K | An elementary school is arranging students\textquotesingle{} schedules. For the first class in the morning, it has to be Chinese or Maths or English. Students won\textquotesingle t start the day with the same class for two days in a row. If Wednesday starts with Chinese, then Thursday can start with~\uline{~~~~~~~~~~}~.
a: Chinese or Maths
b: Maths or English
c: English or Chinese |
由条件，面积变为原来的$${{\left( 1+150 \% \right)}^{2}}$$，所以可供$$4\times {{\left( 1+150 \% \right)}^{2}}=25$$（个）人吃饱． | d | TAL-SCQ5K | 一个半径为$$20$$厘米的蛋糕可以让$$4$$个人吃饱，如果半径增加了$$150 \%$$，同样高的蛋糕可以让个人吃饱．
a. $$9$$
b. $$15$$
c. $$16$$
d. $$25$$ |
The number of cows and foxes in the yacht is 20+15 = 35
Mr. Bodhi also has three times as many zebras as foxes in the yacht, equal to 3*15 = 45 zebras.
The number of animals in the yacht so far is 35+45 = 80
To balance the yacht, Mr. Bodhi needs to add 100-80= 20 sheep | 20 | gsm8k | Mr. Bodhi is transporting some animals using a yacht across a river. He has 20 cows, 15 foxes and three times as many zebras as foxes. To balance the yacht to ensure a smooth sail across the river, the total number of animals in the yacht needs to be 100. If he decides to add sheep to the yacht to make the yacht sail-worthy, how many sheep did he add to the yacht? |
To heap something on someone means to give them a large amount of it, while the other sentence says he did not give any work. | No | FLUTE | Context: He did not give him any work.
Hypothesis: He heaped him with work.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Fireworks are typically only used on special occasions like the 4th of July and so hearing them go off a month later is confusing and frustrating | No | FLUTE | Context: My neighbors are still shooting off fireworks a month after the 4th of July
Hypothesis: I don't understand why my neighbors are still shooting off fireworks a month after the 4th of July
Is the hypothesis incorrect? (Yes, no, or unknown)? |
$$\left( 125+25 \right)\div \left( 1-25 \textbackslash\% \right)=200$$ dollars. | $$200$$ dollars | TAL-SCQ5K | A gift store buys some gifts at＄$$125$$ each. It wants to earn＄$$25 $$ for each gift after a discount of $$25 \textbackslash\% $$. What is the selling price before the discount for each shirt?
- $$160$$ dollars
- $$180$$ dollars
- $$190$$ dollars
- $$200$$ dollars |
She pulled out 55 + 101 + 78 = 234
6 carrots weigh one pound so 234/6 = 39 pounds of carrots | 39 | gsm8k | It was time for Kelly to harvest her carrots that she had planted in three different beds. In the first bed she pulled out 55 carrots. In the second bed she pulled out 101 carrots and in the third bed she pulled out 78 carrots. She found that 6 carrots weighed one pound. How many pounds of carrots did Kelly harvest? |
Cindy puts in 10 cents x 5 = 50 cents.
Eric puts in 3 x 25 cents = 75 cents.
Garrick puts in 8 x 5 cents = 40 cents.
Ivy puts in 60 x 1 cent = 60 cents.
After Eric pulls out a quarter, he has still left in the pond, 75 - 25 = 50 cents.
Together, they put into the pond, this amount of money, 50 + 50 + 40 + 60 = 200 cents | 200 | gsm8k | Cindy tosses 5 dimes into the wishing pond. Eric flips 3 quarters into the pond. Garrick throws in 8 nickels. Ivy then drops 60 pennies in. If Eric dips his hands into the water and pulls out a quarter, how much money, in cents, did they put into the pond? |
When parents try to control their children's lives without even consulting them, it often goes against the child's wishes and so the parents not respecting the child's boundaries is really not a good thing. | Yes | FLUTE | Consider the statement "I had a huge conflict with my parents about moving to another country and I was simply enraged to have them trying to control my life.". Is the statement "My parents trying to control my life and deciding where to move without even consulting me makes me happy that they really respect my boundaries." false? Yes/no/unknown |
Vera will arrive at $$9.40$$ a.m. Carl will leave at $$9.20$$ a.m. and arrive at $$9.26$$ a.m. So, Carl and Derek will have to wait for $$14$$ min. | b | TAL-SCQ5K | Vera leaves home at $$9.15$$ a.m. to walk to Derek's house, which takes her $$25$$ minutes. Carl leaves his house $$5$$ minutes after Vera but only takes $$6$$ minutes to get to Derek's house. When Carl arrives, how long will he and Derek have to wait for Vera to arrive?
Options:
a) $$11$$ min
b) $$14$$ min
c) $$21$$ min
d) $$24$$ min |
解：$${{V}_{P-ABC}}={{V}_{A-PBC}}=\frac{1}{3}\times \left( \frac{1}{2}\times 3\times 4 \right)\times \sqrt{{{3}^{2}}-{{\left( \frac{5}{2} \right)}^{2}}}=\sqrt{11}$$． | C | TAL-SCQ5K | 三棱锥$$P-ABC$$的底面$$\triangle ABC$$是边长为$$3$$的正三角形，$$PA=3$$，$$PB=4$$，$$PC=5$$，则三棱锥$$P-ABC$$的体积为( )
A) $$3$$
B) $$\sqrt{10}$$
C) $$\sqrt{11}$$
D) $$2\sqrt{3}$$ |
The word claw typically connotes aggression and violence while flirt typically connotes playful and romantic behavior. | Yes | FLUTE | Context: The politician flirted with his rival.
Hypothesis: The politician clawed his rival.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
Lathering something typically means to cover it in a substance, whereas the another statement says he did not do it. | False | FLUTE | Context: "He did not apply fertilizer over the lawn." Claim: "He lathered fertilizer over the lawn."
Considering the context, is the claim true, false, or unknown? |
Slapped with a weight of woes means that the person has been hit with a lot of problems. | Yes | FLUTE | Consider the staetement "Whom fate has met with a weight of woes.". Based on this statement, is "Whom fate has slapped with a weight of woes." a true statement? Yes/no/unknown |
The full circle of a rainbow cannot usually be seen from ground level. Sometimes the full circle of a rainbow can be seen from a high building or aircraft. You can see more of a rainbow the closer to the horizon the sun is. Lunch occurs at midday when the sun is likely high in the sky. | No | strategyqa | Is lunch on the beach a good activity to spot the full circle of a rainbow? |
Let $$x$$ be the number of £$$10$$ books and $$y$$ be the number of £$$15$$ books $$10x+15y=90$$, which has two positive integer solutions only. $$\begin{cases} x=6 \textbackslash\textbackslash{} y=2 \end{cases}$$, $$\begin{cases} x=3 \textbackslash\textbackslash{} y=4 \end{cases}$$ $$6+2=8$$ | E | TAL-SCQ5K | Pip and Bud buys some £$$10$$ books and £$$15$$ books together. If they spent £$$90$$ on the books, how many books have they bought at most in total?
A: $$14$$
B: $$15$$
C: $$16$$
D: $$7$$
E: $$8$$ |
$$100\times 100+10\times 10+1\times 1=10000+100+1=10101$$. | (4) | TAL-SCQ5K | $$100$$ hundreds $$+10$$ tens $$+1$$ one $$=$$．
(1) $$111$$
(2) $$1101$$
(3) $$1011$$
(4) $$10101$$ |
A steam sauna is a small room or hut where people go to sweat in steam, so it would be hot and humid, not cold and dry | No | FLUTE | Context: The assembly hall was now cold and dry, more so than usual.
Hypothesis: In fact, the assembly hall was now like a steam sauna
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Subsets and Splits