rationale
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$$\left( \frac{1}{17}-\frac{1}{19} \right)\div 20=\frac{2}{17\times 19}\div 20=\frac{1}{17\times 19}\times \frac{1}{10}$$;$$\left( \frac{1}{15}-\frac{1}{21} \right)\div 60=\frac{6}{15\times 21}\div 60=\frac{1}{15\times 21}\times \frac{1}{10}$$; $$\left( \frac{1}{13}-\frac{1}{23} \right)\div 100=\frac{10}{13\times 23}\div 100=\frac{1}{13\times 23}\times \frac{1}{10};$$$$\left( \frac{1}{11}-\frac{1}{25} \right)\div 140=\frac{14}{11\times 25}\div 140=\frac{1}{11\times 25}\times \frac{1}{10};$$ 只需比较$$\frac{1}{17\times 19}$$，$$\frac{1}{15\times 21}$$，$$\frac{1}{13\times 23}$$，$$\frac{1}{11\times 25}$$的大小，根据和一定，两数越接近乘 积越大，则$$11\times 25 \textless{} 13\times 23 \textless{} 15\times 21 \textless{} 17\times 19$$，那么 $$\frac{1}{11\times 25}\textgreater\frac{1}{13\times 23}\textgreater\frac{1}{15\times 21}\textgreater\frac{1}{17\times 19}$$，所以答案为$$D$$
|
(4)
|
TAL-SCQ5K
|
在下面四个算式中，得数最大的是（ ）
(1) $$\left( \frac{1}{17}-\frac{1}{19} \right)\div 20$$
(2) $$\left( \frac{1}{15}-\frac{1}{21} \right)\div 60$$
(3) $$\left( \frac{1}{13}-\frac{1}{23} \right)\div 100$$
(4) $$\left( \frac{1}{11}-\frac{1}{25} \right)\div 140$$
|
Each load takes 60 + 45 = 105 minutes
There are 8 loads that take 8*105=840 minutes
It takes 840/60=14 hours
|
14
|
gsm8k
|
There are 8 loads of laundry that need to be washed. Each load of laundry takes around 45 minutes to complete in the wash cycle and 1 hour in the dry cycle. How long, in hours, will it take to complete the entire set of laundry?
|
The sky flushed with rosy splendor means that the sky was filled with a pinkish color, signifying that the sun was about to rise or set.
|
Yes
|
FLUTE
|
Context: The sky glowed with rosy splendor.
Hypothesis: The sky flushed with rosy splendor.
Given this context, is the hypothesis true (Yes/No/I don't know)?
|
To wrestle with something means to struggle or fight with it, while to ease with something means to proceed or go along with it smoothly.
|
False
|
FLUTE
|
Context: "I eased with this decision for years."
Hypothesis: I wrestled with this decision for years.
Based on the context, is the hypothesis true, false, or unknown?
|
The sum, difference, and product of even numbers are even, but $$952\div 136=7$$ is odd.
|
[C]
|
TAL-SCQ5K
|
Each of the following results in an even number except．
[A] $$952+136$$
[B] $$952-136$$
[C] $$952\div 136$$
[D] $$952\times 136$$
|
售价为$$200$$元，$$A$$赚了$$10 \%$$， $$A$$的进价为： $$200\div (1+10 \%)=\frac{2000}{11}$$（元）， $$B$$亏了$$10 \%$$，$$B$$的进价为： $$200\div (1-10 \%)=\frac{2000}{9}$$（元）， $$\frac{2000}{11}+\frac{2000}{9}=\frac{40000}{99}$$（元）$$\textgreater400$$元． 进价$$\textgreater$$售价，亏了．选$$\text{B}$$．
|
[b]
|
TAL-SCQ5K
|
商店有$$A$$，$$B$$两件衣服，都获得$$200$$元的收入．$$A$$赚了$$10 \%$$，$$B$$亏了$$10 \%$$，总体上是．
[a] 赚了
[b] 亏了
[c] 不亏不赚
[d] 不能确定
|
: Someone who is admired for their great vision is likely to be kind and good to people, so finding out that they are actually mean shows a lack of judgement on the part of the person who made the discovery.
|
No
|
FLUTE
|
Given the statement "I felt so disillusioned when I discovered someone who I admired for their vision was a jerk on a day-to-day basis.", is the statement "I was very proud of my sense of judgement when I found out that the person who I admired for their great vision was actually really mean to people" is true?
- Yes
- No
- I don't know
|
She has 5 1.5 hour appointments on Monday for a total of 5*1.5 = 7.5 hours
She has 2 2 hour appointments on Thursday for a total of 2*2 = 4 hours
She is working 7.5 hours on Monday, 3 hours on Tuesday, 4 hours on Thursday and 6 hours on Saturday for a total of 7.5+3+4+6 = 20.5 hours
She charges $20.00 an hour and is working 20.5 hours a week for a total of 20*20.5 = $410.00
|
410
|
gsm8k
|
Amanda charges $20.00 per hour to help clean out and organize a person's home. She has 5 1.5 hours appointments on Monday, a 3-hours appointment on Tuesday and 2 2-hours appointments on Thursday. On Saturday, she will spend 6 hours at one client's house. How much money will she make this week?
|
Applying Simon's Favorite Factoring Trick, we add 1 to both sides to get $xy + x + y + 1 = 81,$ so
\[(x + 1)(y + 1) = 81.\]The only possibility is then $x + 1 = 27$ and $y + 1 = 3,$ so $x = 26.$
|
$26$
|
competition-math
|
Integers $x$ and $y$ with $x>y>0$ satisfy $x+y+xy=80$. What is $x$?
|
To bear in mind means to remember and consider something when making a decision or before taking action, but the speaker is not doing that in this sentence.
|
No
|
FLUTE
|
Given the statement "I do not remember and do not take that into consideration, doctor.", is the statement "I do bear that in mind, doctor." is true?
- Yes
- No
- I don't know
|
Two angles are complementary if their degree measures add up to 90 degrees. So if the angle is $x$ degrees, then its complement is $90-x$ degrees. We set up the equation $x=2(90-x)$ and solve for $x$. $$x=180-2x\qquad\Rightarrow3x=180\qquad\Rightarrow x=60$$So the angle has a degree measure of $60$ degrees.
|
$60$
|
competition-math
|
What is the degree measure of an angle whose measure is double the measure of its complement?
|
Going without garbage service is incredibly inconvenient and often results in a build up of trash which can lead to health hazards so it's understandable to be angry when the company goes bankrupt and leaves people without service
|
True
|
FLUTE
|
Context: "The garbage company for my town went under and left us without service." Claim: "I am so angry that the garbage company for my town went bankrupt and left us high and dry"
Considering the context, is the claim true, false, or unknown?
|
Albany, Georgia had a population of 75,249 in 2018. Albany, New York had a population of 97,279 in 2018.
|
No
|
strategyqa
|
Is Albany, Georgia the most populous US Albany?
|
August is a summer month in the northern hemisphere. However, the seasons are opposite south of the Equator. August is in the middle of winter for Australia, Antarctica, and parts of Africa and South America.
|
Yes
|
strategyqa
|
Is August a winter month for part of the world?
|
With a higher concentration of hydrogen ions, a solution is more acidic but has a lower pH.
|
A
|
quartz
|
If you found something with very few hydrogen ions it would be
A) basic
B) acidic
|
In the first week, Jed has 20 + 6 = 26 cards.
In the second week, he has 26 + 6 = 32 cards.
But he is left with 32 - 2 = 30 cards on the 2nd week after giving 2 cards to his friend.
Then Jed has 30 + 6 = 36 cards on the 3rd week.
He has 36 + 6 = 42 cards on the 4th week.
After giving his friend 2 cards, he is then left with 42 - 2 = 40 cards on the 4th week.
Hence, Jed will have a total of 40 cards in 4 weeks.
|
4
|
gsm8k
|
Jed collects stamp cards. Every week, he gets 6 cards. But every two weeks, he gives 2 cards to his friends. If Jed started with 20 cards, after how many weeks will he have a total of 40 cards?
|
The odometer is supposed to show how many miles a car has driven and if it has been rolled back, it means that they have been cheated and the car has been used more than what is being shown and therefore it would make someone angry and not calm.
|
No
|
FLUTE
|
Given the statement "I bought a used car for my son and found out later the odometer had been rolled back.", what is the statement "I was totally calm when I found out the odometer on the car I just bought for my son had been rolled back" true?
- Yes
- No
- Unknown
|
To cry wolf means to falsely raise an alarm, and in this sentence James Carson would never do that.
|
No
|
FLUTE
|
Consider the statement "He, James Carson, would become a character in a Farley Mowat novel, lost in the barrens, and never falsely raise an alarm.". Is the statement "He, James Carson, would become a character in a Farley Mowat novel, lost in the barrens, never cry wolf." false? Yes/no/unknown
|
Grief has no set external representation. People who are grieving may laugh, cry, or even seem angry.
|
No
|
strategyqa
|
Is grief always obvious when it is being experienced?
|
The odometer is supposed to show how many miles a car has driven and if it has been rolled back, it means that the car has been used more than what is being shown and therefore it would be that they were cheated and hence not thrilling.
|
Yes
|
FLUTE
|
Context: I bought a used car for my son and found out later the odometer had been rolled back.
Hypothesis: I was thrilled when I found out the odometer on the car I just bought for my son had been rolled back
Is the hypothesis incorrect? (Yes, no, or unknown)?
|
Being hit by a drunk driver can often lead to serious injuries or death and so it is impossible for anyone to be excited about the possibility of it happening again.
|
No
|
FLUTE
|
Consider the staetement "I felt a bit terrified when I was hit by a drunk driver last year but I am very grateful to be alive to today". Based on this statement, is "I was very lucky to survive being hit by a drunk driver last year and I am still excited of the possibility of it happening again" a true statement? Yes/no/unknown
|
The pitcher is $\frac{3}{5}$ full, i.e. $60 \textbackslash\%$ full. Therefore each cup receives $\frac{60}{6}=(\mathbf{C}) 10$ percent of the total capacity.
|
(2)
|
TAL-SCQ5K
|
Three fifths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 6 cups. What percent of the total capacity of the pitcher did each cup receive?~ (adapted from 2020 AMC 8, Question \#5)
(1) $$5$$
(2) $$10$$
(3) $$15$$
(4) $$20$$
(5) $$25$$
|
At a rate of 8 degrees per hour, in three hours the temperature rose by 3*8=24 degrees.
At a rate of 4 degrees per hour, the air conditioner can reduce the temperature 24 degrees in 24/4=6 hours.
|
6
|
gsm8k
|
Roy owns a refrigerated warehouse where he stores produce before selling it at the farmer’s market. The fruits and vegetables he stores are very sensitive to temperature, and he must keep them all cold or they will spoil. One day, the power went out and the air conditioner was turned off for three hours, during which time the temperature rose by 8 degrees per hour. If Roy gets the power back on, it will activate the air conditioner to lower the temperature at the rate of 4 degrees F per hour. What is the amount of time, in hours, it will take for the air conditioner to restore the warehouse to 43 degrees F?
|
Two groups of flowers are not equal. Thus, Ivy needs to take away 2 flowers from Group A and two groups will have the same amount of flowers. Then, Ivy will become the second mover and she has the winning strategy.
|
A
|
TAL-SCQ5K
|
There are two groups of flowers. Group $A$ has $15$ flowers and Group $B$ has $13$ flowers. Cathy and Ivy want to play a game with these flowers. They will take turns to take flowers from the two groups. Each person can take any number of flowers from a group at a time. The person who takes the last flower in two groups will win the game. If Ivy starts the game first, who has the winning strategy?
A. Ivy has the winning strategy.
B. Cathy has the winning strategy.
|
From the children, there are a total of 11 children * 4 items of clothing each = 44 items of clothing on the clotheslines.
From the adults, there are a total of 20 adults * 3 items of clothing each = 60 items of clothing on the clotheslines.
So there are a total of 44 + 60 = 104 items of clothing on the clotheslines.
This means that there are 104 items of clothing / 2 items of clothing per clothesline = 52 clotheslines.
There are 2 clotheslines per house so there must be 52 clotheslines / 2 = 26 houses on the street.
|
26
|
gsm8k
|
A row of houses all share a community space where they put up their clotheslines. There are 2 clotheslines for every house on the street. On the street, there are a total of 11 children and 20 adults. Each child currently has 4 items of clothing on the clotheslines and each adult currently has 3 items of clothing on the clotheslines. If each clothesline can hold 2 items of clothing and all of the clotheslines are full, how many houses are on the street?
|
In Dana's senior class, the 60% of 200 students is 0.6*200=120 female students.
Fifty percent of the females, or 0.5*120=60 of the female students were brunettes.
If 50% of the female brunettes were under 5 feet tall, then there were 60*0.5=30 female brunettes under five feet tall in Dana's senior class.
|
30
|
gsm8k
|
In Dana's senior high school class there were 200 students. 60% of the students were female, and 50% of the females were brunettes. If 50% of the female brunettes were under 5 feet tall, then how many female brunettes in Dana's high school senior class were under 5 feet tall?
|
There are 5-1=4 more lions each month.
There will be 4*12=48 more lions after 1 year.
There will be 100+48=148 lions in Londolozi after 1 year.
|
148
|
gsm8k
|
There are 100 lions in Londolozi at first. If lion cubs are born at the rate of 5 per month and lions die at the rate of 1 per month, how many lions will there be in Londolozi after 1 year?
|
Queue jumping is considered to be rude and selfish and so someone being ecstatic about seeing it happen is not justified.
|
False
|
FLUTE
|
Context: "I was irritated when I was at the airport and someone cut in line."
Hypothesis: I was ecstatic when I saw someone jump the queue and cut in line at the airport.
Based on the context, is the hypothesis true, false, or unknown?
|
Jerry has 2 x 20 = 40 dice.
Therefore, they have 20 + 40 = 60 dice altogether.
|
60
|
gsm8k
|
Ivan has 20 dice. Jerry has twice as many dice as Ivan. How many dice do they have altogether?
|
The harder the batter hits the ball, the greater will be its acceleration.
|
b
|
quartz
|
Jim was at the baseball game with his friends. Almost immediately he observed that the harder the ball was hit, the effect on the acceleration was
Options:
a) decreased
b) increased
|
Anthony:7(3)=21
Jim:21-2=19
Anthony has 21-19=2 more pairs of shoes.
|
2
|
gsm8k
|
Scott has 7 pairs of shoes. Anthony has 3 times as many pairs of shoes as Scott, and Jim has 2 less pairs than Anthony. How many more pairs of shoes does Anthony have compared to Jim?
|
At higher elevations, there is less air to press on a given area.
|
2
|
quartz
|
When we get to the top of a mountain the air is
1) more dense
2) less dense
|
Most nutrients are washed into ocean water from land. Therefore, water closer to shore tends to have more nutrients.
|
[1]
|
quartz
|
The closer that water gets to the shore the _____ nutrients there are.
[1] more
[2] fewer
|
To make ends meet means to earn just enough money to pay one's bills, but this context describes earning significantly more money than is needed
|
No
|
FLUTE
|
Context: A constant battle to earn exorbitant amounts of money that significantly exceed the amount needed to pay one's bills?.
Hypothesis: A constant struggle to make ends meet?
Given this context, is the hypothesis true (Yes/No/I don't know)?
|
Chenny has a total of 10 + 4 = 14 candies.
If each friend will receive 2 candies each, then she has 14 / 2 = 7 friends.
|
7
|
gsm8k
|
Chenny has 10 pieces of candies to be given out to her friends. She realized that she needs to buy 4 more so each of her friends will receive 2 candies. How many friends does Chenny have?
|
Off the shelf means that it is ready made for purchase and not custom built, and the context is saying that the precision offered is better than what is off the shelf aka readily available for purchase.
|
Yes
|
FLUTE
|
Consider the statement "We use our own custom software, so we can offer much more precision than what you can find in stores or commercially available.' , the CEO exclaimed”". Based on this "We use our own custom software, so we can offer much more precision than what you can find off the shelf.' , the CEO exclaimed”" a true statement? Yes, no, or I don't know?
|
Peter drew 5+3 = 8 pictures.
Quincy drew 20+8 = 28 pictures.
Altogether they drew 5+8+28 = 41 pictures
|
41
|
gsm8k
|
Randy drew 5 pictures. Peter drew 3 more pictures than Randy. Quincy drew 20 more pictures than Peter. How many pictures did they draw altogether?
|
If Rover has 46 spots, then half as many spots as Rover has is 46/2=23 spots.
If Cisco has 5 less than half as many spots as Rover has, then Cisco has 23-5=18 spots.
If Granger has five times as many spots as Cisco, then Rover has 18*5=90 spots.
Thus, the total combined number of spots that Rover and Cisco have is 90+18=108 spots.
|
108
|
gsm8k
|
Granger has five times as many spots as his brother, Cisco. But Cisco has 5 less than half as many spots as his cousin, Rover. If Rover has 46 spots, how many spots do Granger and Cisco have combined?
|
Sloths can hold their breath underwater for up to 40 minutes. The running time of a Scrubs episode is between 20-23 minutes.
|
Yes
|
strategyqa
|
Could a sloth hypothetically watch an entire episode of Scrubs underwater?
|
The word condemned typically connotes something negative such as a punishment while receiving praise is seen as a positive thing.
|
False
|
FLUTE
|
Context: "He was so devoted to his sick wife that he earned praise for the lonely life." Claim: "His devotion to his sick wife condemned him to a lonely existence."
Considering the context, is the claim true, false, or unknown?
|
四个人总共花费了$$50+5\times 4=70$$元， 故平均每人花费$$70\div 4=17.5$$元． 故选$$\text{C}$$．
|
C
|
TAL-SCQ5K
|
四名同学相约去爬山，往返共花费$$50$$元车资．在山上，他们每人各购买了一瓶$$5$$元的饮料．请问平均每人各总共花费多少元？（~ ）
A. $$12.5$$
B. $$13.75$$
C. $$17.5$$
D. $$30$$
E. $$55$$
|
Better farming techniques and machines increased the food supply and the distribution of food.
|
less
|
quartz
|
As farming techniques are discovered, there are _____ people that starve and go hungry.
more
less
|
If Robi contributed $4000, then Rudy contributed 1/4*4000 = $1000 more.
The total amount of money Rudy contributed is $4000+$1000 = $5000
Together, the contributed a total of $5000+$4000 = $9000
They made a 20% profit, a total of 20/100*$9000 = $1800
When they decided to share the profit equally, each received $1800/2 = $900
|
900
|
gsm8k
|
Robi and Rudy contributed money to start a business that could earn them profit. Robi contributed $4000, and Rudy contributed 1/4 more money than Robi. If they made a profit of 20 percent of the total amount and decided to share the profits equally, calculate the amount of money each got.
|
Since the angle measures are in the ratio $5:6:7$, the measures are $5x$, $6x$, and $7x$ for some value of $x$. Since these are the angles of a triangle, we have $5x+6x+7x = 180^\circ$, so $18x = 180^\circ$ and $x = 10^\circ$. Therefore, the largest angle is $7x = 70^\circ$.
|
$70^\circ$
|
competition-math
|
The measures of the angles of a triangle are in the ratio 5:6:7. What is the number of degrees in the largest of these angles?
|
It's often frustrating and discouraging when other people succeed despite not putting in as much effort as oneself and in this case it is made even worse by the fact that the success is a result of barely passing an exam
|
No
|
FLUTE
|
Consider the statement "My friend got a huge scholarship when he barely passed the PSAT.". Is the statement "I was really jealous when my friend got a scholarship for barely passing the PSAT" false? Yes/no/unknown
|
Except the last day, the snail could climb up $2-1=1$ m. Thus, it takes the snail $(10-2)\div1+1=9$ days to get out of the well. $9$ days from Monday is the next Tuesday.
|
1
|
TAL-SCQ5K
|
On Monday morning, a snail fell down a well which is $$10$$ meters deep. During the day, it climbs up $$2$$ meters, and during the night it slides down $$1$$ meter. On what day of the week will the snail get out of the well? ($$1998$$ Math kangaroo Problem, Level $$5-6$$, Question \#$$18$$)
Options:
1) $$$$Tuesday
2) $$$$Thursday
3) $$$$Saturday
4) $$$$Sunday
5) $$$$Monday
|
Let o be the number of obsolete books and d be the number of damaged books. We know that o + d = 69 and o = 6d - 8.
Substituting the first equation into the second equation, we get 6d - 8 + d = 69
Combining like terms, we get 7d - 8 = 69
Adding 8 to both sides, we get 7d = 77
Dividing both sides by 7, we get d = 11
|
11
|
gsm8k
|
Erin is sorting through the library books to decide which ones to replace. She finds 8 less than 6 times as many obsolete books as damaged books. If she removes 69 books total, how many books were damaged?
|
The food ordered almost two hours ago has still not arrived and so the person writing this sarcastically is clearly very impatient and their calmness is not justified.
|
Yes
|
FLUTE
|
Given the statement "I ordered food almost two hours ago and it's still not here ugh!", is the statement "I'm so amazingly calm that the food I ordered almost two hours ago still hasn't arrived" wrong?
- Yes
- No
- Unknown
|
当$$x ~\textless{} ~-1$$时，$$\frac{x-1}{\textbar x-1\textbar}+\frac{\textbar x\textbar}{x}+\frac{x+1}{\textbar x+1\textbar}=-1-1-1=-3$$， 当$$-1 ~\textless{} ~x ~\textless{} ~0$$时，$$\frac{x-1}{\textbar x-1\textbar}+\frac{\textbar x\textbar}{x}+\frac{x+1}{\textbar x+1\textbar}=-1-1+1=-1$$， 当$$x\textgreater1$$时，$$\frac{x-1}{\textbar x-1\textbar}+\frac{\textbar x\textbar}{x}+\frac{x+1}{\textbar x+1\textbar}=1+1+1=3$$． 故选$$\text{C}$$．
|
C
|
TAL-SCQ5K
|
已知$$x
e-1$$，$$0$$，$$1$$，则$$\frac{x-1}{\textbar x-1\textbar}+\frac{\textbar x\textbar}{x}+\frac{x+1}{\textbar x+1\textbar}$$的值可能是（ ~）．
Options:
A. 比$$3$$大的数
B. 比$$-3$$小的数
C. $$\pm1$$，$$\pm3$$
D. 比$$-3$$大，并且比$$3$$小的数
|
Since $x^2 + 2x + 7 = (x + 1)^2 + 6 > 0$ for all $x,$ the sign of $\frac{x + 6}{x^2 + 2x + 7}$ is the same as the sign of $x + 6.$ Thus, the solution is $x \in [-6,\infty).$
|
$[-6,\infty)$
|
competition-math
|
Solve
\[\frac{x + 6}{x^2 + 2x + 7} \ge 0.\]Enter your answer using interval notation.
|
When someone is trying to plan their wedding they are often under a lot of stress and the last thing they need is for the caterer to keep blowing them off and making them feel like they are idiots
|
True
|
FLUTE
|
Context: "I was trying to plan my wedding by getting a caterer, and they kept blowing us off over and over again."
Hypothesis: I was trying to get wedding planning done by reserving a caterer, but they kept blowing us off and making me feel like a total idiot
Based on the context, is the hypothesis true, false, or unknown?
|
In refraction of light, the greater the change in speed, the more light bends.
|
2
|
quartz
|
Ron was playing with a flashlight. He moved it back and forth slowly, and then quickly. Which motion likely caused more light to bend?
1) the slow motion
2) the quick motion
|
Sam is currently 18 / 3 = 6 years old.
Sue is currently 6 / 2 = 3 years old.
In three years, Sue will be 3 + 3 = 6.
In three years, Same will be 6 + 3 = 9.
In three years, Kendra will be 18 + 3 = 21.
Their total age in three years is 6 + 9 + 21 = 36.
|
36
|
gsm8k
|
Sam is twice as old as Sue. Kendra is 3 times as old as Sam. If Kendra is currently 18, what will be their total age in 3 years?
|
Suppose Olivia has $$x$$ correct answers. $$5x-2(10-x)=29$$, $$x=7$$.
|
C
|
TAL-SCQ5K
|
In a mathematics contest with ten problems, a student gains $$5$$ points for a correct answer and loses $$2$$ points for an incorrect answer. If Olivia answered every problem and her score was $$29$$, how many correct answers did she have?
Options:
A: $$5$$
B: $$6$$
C: $$7$$
D: $$8$$
E: $$9$$
|
Since you're doubling the number of people working on the task, that means you will be able to reduce the amount of time worked in half if they're of equal skill.
Therefore, you take the original time of 10 hours and perform 10/2= 5 hours spent working on the problem.
|
5
|
gsm8k
|
It takes 1 person working 10 hours to figure out the solution to a math problem. If you add a second person who's equally good at math, how long will the two of them have to work to solve the same problem?
|
The swastika is a religious symbol that is used in Hinduism, Buddhism, and Jainism. Almost 80% of people in India practice Hinduism.
|
Yes
|
strategyqa
|
Are swastikas used in the most common religion in India?
|
由绝对值得非负性及完全平方的非负性， 可知$$x+z=0$$，$$x-y=0$$， ∴$$\frac{x}{z}=-1$$，$$\frac{y}{x}=1$$， ∴$${{\left( \frac{x}{z} \right)}^{2}}+{{\left( \frac{y}{x} \right)}^{2}}=1+1=2$$．
|
2
|
TAL-SCQ5K
|
若实数$$x$$，$$y$$，$$z$$满足$$\left\textbar{} x+z \right\textbar+{{(x-y)}^{2}}=0$$，则$${{\left( \frac{x}{z} \right)}^{2}}+{{\left( \frac{y}{x} \right)}^{2}}$$的值为（~ ）．
1: $$4$$
2: $$2$$
3: $$1$$
4: $$0$$
|
This means that as wavelengths get shorter, more waves move past a particular spot in the same amount of time.
|
2
|
quartz
|
Sue watches waves of different colored light travel past her with a spectrometer. The longer wavelengths cause _____ waves to travel past her than the longer wavelengths.
1. more
2. fewer
|
If $2$ $\text{cm}$ represents $6000\text{km}$, $1\text{cm}$ represents $3000\text{km}$, and $0.1\text{cm}$ represents $300\text{km}$.
|
$$0.1$$
|
TAL-SCQ5K
|
On a map of the Andes, if $2$ $\text{cm}$ represents $6000$ $\text{km}$, then ~represents $300$ $\text{km}$ .
- $$0.1$$
- $$0.5$$
- $$10$$
- $$20$$
|
By sprout it means that the novel begins with a murder.
|
No
|
FLUTE
|
Given the statement "Murder begins the novel.", is the statement "The novel sprouts with a murder." wrong?
- Yes
- No
- Unknown
|
小灰兔给了小白兔$$5$$个萝卜后， 此时小白兔和小灰兔都有$$15+5=20$$（个）萝卜， 则小灰兔原来有萝卜：$$20+5=25$$（个）． 故选：$$\text{C}$$．
|
(c)
|
TAL-SCQ5K
|
小白兔有$$15$$个萝卜，小灰兔给了它$$5$$个萝卜后，它俩的萝卜就一样多了，小灰兔原来有个萝卜．
Options:
(a) $$15$$
(b) $$20$$
(c) $$25$$
|
由已知条件可知$${{a}^{2}}+{{b}^{2}}-1=0$$， 函数图象与$$y$$轴交点的纵坐标为$${{a}^{2}}+2ab-{{b}^{2}}$$． 令$$a=\cos \theta $$，$$ b=\sin \theta $$， 则$${{a}^{2}}+2ab-{{b}^{2}}={{\cos }^{2}}\theta +2\sin \theta \cos \theta -{{\sin }^{2}}\theta $$ $$=\cos 2\theta +\sin 2\theta \leqslant \sqrt{2}$$， 故选$$\text{A}$$.
|
A
|
TAL-SCQ5K
|
已知$$f\left( x \right)={{x}^{2}}+\left( {{a}^{2}}+{{b}^{2}}-1 \right)x+{{a}^{2}}+2ab-{{b}^{2}}$$是偶函数，则函数图象与$$y$$轴交点的纵坐标的最大值是．
Options:
A. $$\sqrt{2}$$
B. $$2$$
C. $$2\sqrt{2}$$
D. $$4$$
|
Bellas has 100% / 25% = 4 times less earrings than Monica.
This means that Monica has 10 * 4 = 40 earrings.
Rachel has two times fewer earrings than Monica, which means 40 / 2 = 20 earrings.
So all three friends, have a total of 10 + 40 + 20 = 70 earrings.
|
70
|
gsm8k
|
Bella, Monica, and Rachel are friends who like jewelry. Bella has 10 earrings, which is 25% of Monica's earrings, and Monica has twice as many earrings as Rachel. How many earrings do all of the friends have?
|
After the first year, its price has doubled to $\$200$. In the second year, its price declines by one fourth, or $\$50$. The price at the end of the second year is $\$200-\$50=\$150$.
|
$\$150$
|
competition-math
|
During the first year, ABC's stock price starts at $ \$100 $ and increases $ 100\% $. During the second year, its stock price goes down $ 25\% $ from its price at the end of the first year. What is the price of the stock, in dollars, at the end of the second year?
|
每个数字用$$10$$次，故所有数字和为$$(16\times 10+18\times 10)\div 10=34$$，而出现了$$10$$ 次$$16$$和$$10$$次$$18$$，故除了最小的，其他$$5$$个都相同，所以只能为$$4$$、$$6$$、$$6$$、$$6$$、$$6$$、$$6$$．
|
C
|
TAL-SCQ5K
|
玛丽有$$6$$张卡片，每张卡片上都写有一个大于$$0$$的自然数．她选取了$$3$$张卡片后，算出了它的总和，他又选另外$$3$$张卡片上的总和，$$\cdot \cdot \cdot $$，她进行了可能的$$20$$种$$3$$张卡片的选择，然后计算，发现有$$10$$种总和等于$$16$$，另外$$10$$种总和等于$$18$$．那么这些卡片中最小的数是（~ ）．
A: $$2$$
B: $$3$$
C: $$4$$
D: $$5$$
|
Wembley Arena is an indoor arena. The moon is located in the sky. You cannot see the sky if you are indoors.
|
No
|
strategyqa
|
Can you see the moon in Wembley Arena?
|
To think in for a penny, in for a pound means that if you have committed to doing something, you should do it completely without sparing any effort, but in this context the person is deliberating carefully.
|
No
|
FLUTE
|
Consider the staetement "oh hell, I thought if you're going to do something you should deliberate carefully and scrubbed the place from top to bottom". Based on this statement, is "Oh hell, I thought, in for a penny, in for a pound, and scrubbed the place from top to bottom" a true statement? Yes/no/unknown
|
Observe that each number is the sum of the number of previous term and the difference between adjacent numbers.
|
B
|
TAL-SCQ5K
|
In the arithmetic sequence $5$, $7$, $9$, $11$ $\cdots$ , the $9$\textsuperscript{th} term is~\uline{~~~~~~~~~~}~.
A) $$19$$
B) $$21$$
C) $$23$$
D) $$25$$
|
$$\frac{1}{29}\times 10\textless{}\frac{1}{20}+\frac{1}{21}+\cdots +\frac{1}{29}\textless{}\frac{1}{20}\times 10$$， $$\frac{10}{29}\textless{}\frac{1}{20}+\frac{1}{21}+\cdots +\frac{1}{29}\textless{}\frac{1}{2}$$， $$\frac{2}{1}\textless{}\frac{1}{\dfrac{1}{20}+\dfrac{1}{21}+\cdots +\dfrac{1}{29}}\textless{}\frac{29}{10}$$， 所以它的整数部分应是$$2$$，故选$$\text{D}$$．
|
d
|
TAL-SCQ5K
|
$$\frac{1}{\dfrac{1}{20}+\dfrac{1}{21}+\dfrac{1}{22}+\cdots +\dfrac{1}{29}}$$ 的整数部分是．
Options:
a. $$20$$
b. $$10$$
c. $$5$$
d. $$2$$
|
Let the number of acrobats in the show be $a$ and the number of elephants be $e$. We are looking for the value of $a$. Assuming that each acrobat has 2 legs and 1 head, and that each elephant has 4 legs and 1 head, we can set up the following system of equations:
\begin{align*}
2a+4e &= 40 \\
a + e &= 15 \\
\end{align*}To solve for $a$, we need to eliminate $e$ from the equations above. We can rewrite the second equation above as $e=15-a$, and substituting this into the first equation to eliminate $e$ gives $2a+4(15-a) = 40$, or $a=10$. Thus, there are $10$ acrobats in the circus show.
|
$10$
|
competition-math
|
While watching a circus show, I counted out the number of acrobats and elephants. I counted 40 legs and 15 heads. How many acrobats did I see in the show?
|
In an hour, Emily can type 60 words *60 minutes = 3600 words.
It will take her 10800/3600 = 3 hours to write 10800 words.
|
3
|
gsm8k
|
Emily can type 60 words per minute. How many hours does it take her to write 10,800 words?
|
Warming up exercises increases the blood flow to the muscles and increases the heart rate.
|
(1)
|
quartz
|
As we start running our hearts pump faster which means blood flow
(1) increases
(2) decreases
|
There are six sections in which the spinner can come to rest, and it is equally likely that it will come to rest in each of the sections. Thus, the probability that it will come to rest in one of the two shaded regions is $\frac{2}{6} = \frac{1{3}}$.
|
$\frac{1$
|
competition-math
|
A game board is constructed by shading two of the regions formed by the altitudes of an equilateral triangle as shown. What is the probability that the tip of the spinner will come to rest in a shaded region? Express your answer as a common fraction. [asy]
import olympiad; size(100); defaultpen(linewidth(0.8));
pair A = (0,0), B = (1,0), C = (0.5,sqrt(3)/2);
pair D = (A + B)/2, E = (B + C)/2, F = (C + A)/2;
pair M = intersectionpoint(A--E,B--F);
draw(A--B--C--cycle);
draw(A--E^^B--F^^C--D);
filldraw(D--M--B--cycle,fillpen=gray(0.6));
filldraw(F--M--C--cycle,fillpen=gray(0.6));
draw(M--(0.4,0.5),EndArrow(size=10));
[/asy]
|
J.K Rowling's top sellers are her Harry Potter series. Harry Potter is a series about a boy who goes to a magical school to learn wizardry.
|
Yes
|
strategyqa
|
Would J.K Rowling's top sellers be on a fantasy shelf?
|
Tingling in the hands or feet is a type of paresthesia. Lead white exposure can lead to lead poisoning. Symptoms of lead poisoning include tingling in the hands and feet.
|
Yes
|
strategyqa
|
Can paresthesia be caused by a white pigment?
|
Working from home implies that the person is working alone and so they are not in good company.
|
No
|
FLUTE
|
Consider the statement "I am working from home and do not see other people.". Based on this "I feel like I am in such good company because I am working from home today." a true statement? Yes, no, or I don't know?
|
Let $P$ be the foot of the altitude from $A$ to $\overline{BC}.$ Let $x = BD = CD,$ and let $y = BP.$ Since $\angle ADP = 45^\circ,$ $AP = PD = x + y.$
[asy]
unitsize(2 cm);
pair A, B, C ,D, P;
D = (0,0);
B = (-1,0);
C = (1,0);
A = D + 2*dir(135);
P = (A.x,0);
draw(A--P--C--cycle);
draw(A--B);
draw(A--D);
label("$A$", A, NW);
label("$B$", B, S);
label("$C$", C, SE);
label("$D$", D, S);
label("$P$", P, SW);
label("$x$", (B + D)/2, S, red);
label("$x$", (C + D)/2, S, red);
label("$y$", (B + P)/2, S, red);
label("$x + y$", (A + P)/2, W, red);
[/asy]
Then
\[\cot B = -\cot \angle ABP = -\frac{y}{x + y},\]and
\[\cot C = \frac{2x + y}{x + y}.\]Hence,
\[|\cot B - \cot C| = \left| -\frac{2x + 2y}{x + y} \right| = 2.\]
|
$2$
|
competition-math
|
In triangle $ABC,$ if median $\overline{AD}$ makes an angle of $45^\circ$ with side $\overline{BC},$ then find the value of $|\cot B - \cot C|.$
|
First find the cost of fixing the wall: $1200 * 1/6 = $200
Then add the cost of the replacement stove to find the total cost: $200 + $1200 = $1400
|
1400
|
gsm8k
|
Jason's stove catches on fire. Buying a replacement will cost $1200 and fixing the damage to the wall behind it will cost 1/6th as much. How much does he spend in total?
|
Since a dozen has 12 items, a half dozen has 1/2*12=6 items.
Since Jamal bought four half dozen colored crayons, he bought 4*6 = 24 colored crayons.
If each crayon's cost was $2, Jamal paid $2*24 = $48 for all the crayons he bought.
|
48
|
gsm8k
|
Jamal bought 4 half dozen colored crayons at $2 per crayon. What was the total cost of the crayons that she bought?
|
65% of women are opposed to the idea because 100 - 35 = 65
There are 60 women in the poll because 39 / .65 = 60
There were 120 people in her poll because 60 / .5 = 120
|
120
|
gsm8k
|
Aimee does a poll around her neighborhood and makes sure to get answers from 50% men and 50% women. She finds that 35% of women are in favor of shortening the school day by 30 minutes. 39 women in her poll opposed this idea. How many people did she poll?
|
Air in the troposphere is warmer closer to Earths surface.
|
decreases
|
quartz
|
When you are driving up a mountain you will notice the temperature
Options:
decreases
increases
|
Cell biology is a subdiscipline of biology that deals with the structure and function of cells in living organisms. Al Qaeda is made up of terrorist cells. Terrorist cells are small groups of terrorists acting semi-independently for the same cause.
|
No
|
strategyqa
|
Does cell biology teach about the life cycle of Al Qaeda?
|
The company pays a total of 10/100*$400000 = $40000 on taxes
After taxes, the company revenue is $400000-$40000 = $360,000
The costs of marketing and ads campaign are 5/100*$360000 = $18000
After deducting the costs of marketing and adds campaign, the company remains with = $342,000 in revenue
Operational costs for the company are 20/100*$342000 = $68400
After taking out the operational costs, the company remains with $342000-$68400 = $273600
The company also pays employee wages of 15/100*$273600 =$41040
If the total number of employees is 10, each employee is paid a salary of $41040/10 = $4104 per month
|
4104
|
gsm8k
|
Ms. Estrella is an entrepreneur with a startup company having 10 employees. The company makes a revenue of $400000 a month, paying 10% in taxes, 5% of the remaining amount on marketing and ads, 20% of the remaining amount on operational costs, and 15% of the remaining amount on employee wages. Assuming each employee receives the same wage, calculate the amount of money each employee is paid monthly.
|
If two objects have the same mass, the object with the higher temperature has greater thermal energy.
|
1
|
quartz
|
Rita and Ira are identical twins of the same size. If Ira is a lower temperature, who has greater thermal energy?
1) Rita
2) Ira
|
The graph covers three periods in an interval of $2 \pi$ (say from $\frac{\pi}{2}$ to $\frac{5 \pi}{2}$), so the period of the graph is $\frac{2 \pi}{3}.$ The period of $y = a \sin (bx + c) + d$ is $\frac{2 \pi}{b},$ so $b = 3.$
|
$3$
|
competition-math
|
Below is the graph of $y = a \sin (bx + c) + d$ for some positive constants $a,$ $b,$ $c,$ and $d.$ Find $b.$
[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]
|
Leo got 2 x 2 = 4 mistakes.
So, Brent got 4 + 1 = 5 mistakes.
This means that 25 + 5 = 30 is the perfect score.
Hence, Madeline got a score of 30 - 2 = 28.
|
28
|
gsm8k
|
In a Geometry exam, Madeline got 2 mistakes which are half as many mistakes as Leo. Brent scored 25 and has 1 more mistake than Leo. What is Madeline's score?
|
It would be hard to get a big chunk of chocolate to dissolve in your milk or hot water. Maybe you could make hot chocolate from some smaller pieces like chocolate chips, but it is much easier to add a powder to your milk. This is because the smaller the pieces are, the more surface area they have.
|
[B]
|
quartz
|
Mary melts a 1 pound chocolate bar and 1 pound of chocolate chips in two pots. Which melts first?
Options:
[A] bar
[B] chips
|
Green with envy is a phrase used to describe when someone is feeling jealous and the man staring at the girlfriend during dinner would likely make the boyfriend feel jealous
|
No
|
FLUTE
|
Context: Last night a man was staring at my girlfriend at dinner.
Hypothesis: I was feeling a bit green with envy when I saw the man blatantly staring at my girlfriend during dinner
Is the hypothesis incorrect? (Yes, no, or unknown)?
|
A wasteland is an area that is uninhabitable, so it cannot be declared habitable
|
False
|
FLUTE
|
Context: "After decades of drought the Western United States is finally declared habitable." Claim: "After decades of drought the Western United states is declared a wasteland."
Considering the context, is the claim true, false, or unknown?
|
Most people would not enjoy feeling uncomfortable at work and so the new coworker who is doing so is not behaving in a desirable way.
|
No
|
FLUTE
|
Given the statement "At work a new coworker keeps looking at me in weird way.", is the statement "At work, it's totally not weird at all when a new coworker keeps looking at me in a way that makes me feel uncomfortable" is true?
- Yes
- No
- I don't know
|
The number of bacteria is multiplied by 2 at the end of each day, so the number of bacteria at the end of day $n$ is $3\cdot2^n$. We want $3\cdot2^n > 100$, or $2^n > 33\frac{1}{3}$. The smallest $n$ for which this happens is $n = 6$.
|
$6$
|
competition-math
|
In a certain colony of bacteria, the number of bacteria doubles every day. The colony starts with 3 bacteria, and has 6 at the end of day 1, 12 at the end of day 2, and so on. What is the number of the first day which ends with the colony having more than 100 bacteria?
|
The newspaper was delivered with such force that it broke the window
|
No
|
FLUTE
|
Given the statement "The new paper boy flung the newspaper and broke my window today morning", is the statement "The new paper boy threw the newspaper so hard it broke my window this morning" wrong?
- Yes
- No
- Unknown
|
A parent would not be proud of their child failing a multiplication quiz because it shows that the child has not learned what they were supposed to and hence it would imply that the parent has failed as well.
|
Yes
|
FLUTE
|
Consider the statement "I worked really hard with my daughter last year to teach her multiplication facts but last week at her quiz she failed.". Is the statement "I was proud when my daughter last week failed her multiplication quiz after we worked so hard together last year" false? Yes/no/unknown
|
Combining Hermione and Luna has 14 + 17 = 31 spelling badges.
Removing their spelling badges from the total, Celestia has 83 - 31 = 52 spelling badges.
|
52
|
gsm8k
|
Hermione, Luna, and Celestia combined have 83 spelling badges. If Hermione has 14 and Luna has 17, how many spelling badges does Celestia have?
|
$$9\times 9-7\times 7=32$$（人）．
|
$$32$$
|
TAL-SCQ5K
|
一队学生排成$$9$$行$$9$$列的方阵，如果去掉最外层一圈，要减少人
$$32$$
$$34$$
$$36$$
$$38$$
|
由柯西不等式，$${{\left( \sqrt{{{x}^{2}}\left( 1-{{x}^{2}} \right)}+\sqrt{\left( 2-{{x}^{2}} \right){{x}^{2}}} \right)}^{2}}\leqslant \left( {{x}^{2}}+2-{{x}^{2}} \right)\left( 1-{{x}^{2}}+{{x}^{2}} \right)=2$$，当$$x=\pm \frac{\sqrt{6}}{3}$$时取等号．
|
b
|
TAL-SCQ5K
|
求$$y=\sqrt{{{x}^{2}}-{{x}^{4}}}+\sqrt{2{{x}^{2}}-{{x}^{4}}}$$的最大值为 ．
a) $2$
b) $\sqrt{2}$
c) $2\sqrt{2}$
d) $4$
|
Let X be the distance Sam ran.
His walk through the store was twice the distance of his run, so his walk was 2X.
He biked for 12 miles and went 18 miles in all, so he walked and ran 18 - 12 = 6 miles.
Thus, his walk and run together were X + 2X = 3X = 6 miles.
Thus, he ran X = 6 / 3 = 2 miles.
|
2
|
gsm8k
|
Sam went for a run in the morning. In the afternoon, he went grocery shopping and walked twice the distance through the store as he had run that morning. That evening, he went on a bike ride with his family and biked for 12 miles. In all, he went 18 miles that day. How many miles was Sam’s morning run?
|
Twice the speed of the bald eagle is 100*2=200 miles per hour.
Let "x" be the time in seconds it takes the peregrine falcon to travel to the ground.
Thus, based on the ratio of their speeds, the following expression is given: x=30*(100/200).
Thus, x=15 seconds.
|
15
|
gsm8k
|
The bald eagle can dive at a speed of 100 miles per hour, while the peregrine falcon can dive at a speed of twice that of the bald eagle. Starting from the same treetop, if it takes the bald eagle 30 seconds to dive to the ground, how long, in seconds, will it take the peregrine falcon to dive the same distance?
|
He needs 1.5*40=60 pounds of potatoes
So he needs to buy 60/20=3 bags of potatoes
So it cost 3*5=$15
|
15
|
gsm8k
|
James makes potatoes for a group. Each person eats 1.5 pounds of potatoes. He makes potatoes for 40 people. A 20-pound bag of potatoes costs $5. How much does it cost?
|
Let x represent the number of stamps for AJ
KJ:x/2 stamps
CJ:5+2(x/2)=5+x
Total:x+(x/2)+5+x=930
(5/2)x+5=930
(5/2)x=925
x=925(2/5)=370 stamps
|
370
|
gsm8k
|
CJ, KJ, and AJ collect stamps. CJ has 5 more than twice the number of stamps that KJ has, and KJ has half as many as AJ. If the three boys have 930 stamps all together, how many stamps does AJ have?
|
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