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Call waiting was invented in the 1970's to allow phone users to suspend one call to accept another. Alexander Graham Bell's phone was used in 1876. | No | strategyqa | Did the phone Alexander Graham Bell use have call waiting? |
Hurricanes often cause a lot of destruction and damage wherever they go and so it is highly unlikely that someone would see it as an improvement. | No | FLUTE | Given the statement "The summer hurricane violently ripped through my neighborhood and destroyed everything in its path.", is the statement "The summer hurricane caused a lot of improvements in my neighborhood and polished everything in its path" is true?
- Yes
- No
- I don't know |
A ballistic missile is a weapon that is designed to cause destruction, so it makes sense that if someone went off like a ballistic missile, they would do so destructively. | Yes | FLUTE | Context: Off she went destructively
Hypothesis: Off she went like a ballistic missile.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
When the chips are down means at the final and most critical moment, but in this context it is referring to the beginning when things are still easy. | Yes | FLUTE | Given the statement "At the beginning when things are still easy, and the whole world seems to be against you; its what you do then.", is the statement "Its when the chips are down, and the whole world seems to be against you; its what you do then." wrong?
- Yes
- No
- Unknown |
Greg kept 1 granola bar for each of the 7 days of the week, so there were 20 - 7 = 13 bars left.
He traded 3 to his friend Pete, so there were 13 - 3 = 10 bars left.
His 2 sisters split the rest evenly, so each got 10 / 2 = 5 granola bars. | 5 | gsm8k | Greg bought a 20-pack of granola bars to eat at lunch for the week. He set aside one for each day of the week, traded three of the remaining bars to his friend Pete for a soda, and gave the rest to his two sisters. How many did each sister get when they split them evenly? |
To sit on the fence means to not take sides in a dispute, but this context is saying that you should take a side that contradicts how the speaker asks not to sit on the fence and be pretentious | No | FLUTE | Given the statement "Either oppose me or agree with me, but don't stay indifferent and pretend to be something you're not.", is the statement "Either condemn me or condone me, but don't sit on the fence and pretend to be something you're not." is true?
- Yes
- No
- I don't know |
Compared with a less powerful device, a more powerful device can either do more work in the same time or do the same work in less time. | (1) | quartz | Andrew was showing Tim his brand new phone, one day. The boys decided they wanted to go to a bookstore but needed directions, they both looked up directions on their phone, whose phone found directions faster?
(1) Andrew
(2) Tim |
We have that
$$g(\sqrt{2}) = (\sqrt{2})^2 + 1 = 2 +1 = 3.$$Then,
$$f(g(\sqrt{2})) = f(3) = 4 - 3(3) = 4 - 9 = -5.$$ | $-5$ | competition-math | If $f(x) = 4-3x$ and $g(x) = x^2 +1$, find $f(g(\sqrt{2}))$. |
取$$100$$个小伙子为这样一种特殊情况，他们的身高与体重互不相等，并且最高者同时也就是最轻者，次高者同时也就是次轻者，$$\ldots $$，第$$k$$高者同时也就是第$$k$$轻者（$$k=1$$，$$2$$，$$\ldots $$，$$100$$），显然这$$100$$个小伙子都是棒小伙子． 故选$$\text{D}$$． | d | TAL-SCQ5K | 如果甲的身高数或体重数至少有一项比乙大，则称甲不亚于乙．在$$100$$个小伙子中，如果某人不亚于其他$$99$$人，就称他为棒小伙子．那么，$$100$$个小伙子中的棒小伙子最多可能有（~~~ ）．
a: $$1$$个
b: $$2$$个
c: $$50$$个
d: $$100$$个 |
The units digit of $31^3$ is the same as the units digit of $1^3$, which is 1. The units digit of $13^3$ is the same as the units digit of $3^3$, which is 7. Therefore, the units digit of $31^3+13^3$ is $8$. | $8$ | competition-math | What is the units digit of $31^3+13^3$? |
Cleopatra was the last ruler of the Kingdom of Egypt. Cleopatra was the descendant of Ptolemy I Soter, a Greek general from Macedonia. Cleopatra's father, Ptolemy XII Auletes, was most likely descended from an Alexandrian Greek mother. Cleopatra is believed to be mostly Greek with some Persian and Syrian ancestry as well. | No | strategyqa | Did Cleopatra have ethnicity closer to Egyptians than Greeks? |
In the thermosphere, temperatures increase as altitude increases. | a | quartz | Going higher into the thermosphere will result in finding _____ temperatures.
Options:
a. higher
b. lower |
Catching the flu and not being able to go on vacation is definitely not something to be happy or fortunate about. | Yes | FLUTE | Given the statement "I was suppose to go on vacation last month with my family but ended up catching the flu and couldn't go with them.", is the statement "I was really looking forward to going on vacation with my family last month but I fortunately caught the flu and couldn't go" wrong?
- Yes
- No
- Unknown |
The full capacity of the ship is 300 * 4 = 1200 people.
One-third of capacity is 1200/3 = 400 people.
100 less than one-third capacity is 400 - 100 = 300 people. | 300 | gsm8k | The spacecraft Gibraltar is a mountain-sized intergalactic vehicle for transporting equipment, building materials, and families to establish colonies on far-away planets. At full capacity, the vehicle can carry 300 family units with four people per family. The space flight is expected to take years, and it is expected that the size of families will grow during the space voyage. Therefore, when the spacecraft leaves the earth, it will carry 100 people less than one-third of the ship's capacity. How many people will be on the ship to start the journey? |
Having to go into work on a weekend ruins the plans that someone may have had and hence it is not a good thing. | No | FLUTE | Context: I got called into work on a Saturday! So frustrating.
Hypothesis: Very happy over the fact that I was just about to enjoy my weekend and now I have to go into work
Given this context, is the hypothesis true (Yes/No/I don't know)? |
The closer together the particles are, the greater the amplitude of the wave. | [a] | quartz | If the particles move together, the amplitude of the wave should
Options:
[a] increase
[b] decrease |
First find the total wait time for the swings in minutes: 3 kids * 2 minutes/kid = 6 minutes
Then convert that number to seconds: 6 minutes * 60 seconds/minute = 360 seconds
Then find the total number of kids waiting for the slide: 3 kids * 2 = 6 kids
Then find the total wait time for the slide: 15 seconds/kid * 6 kids = 90 seconds
Then subtract the total wait for the slide from the total wait for the swings to find the difference: 360 seconds - 90 seconds = 270 seconds | 270 | gsm8k | There are 3 kids waiting for the swings and twice as many kids waiting for the slide. If each kid waits 2 minutes for the swings and 15 seconds for the slide, how many seconds shorter is the shorter wait? |
Dogs throwing up after eating can be a common occurrence and is often disgusting, so someone loving it is definitely not warranted. | Yes | FLUTE | Consider the statement "I fed my dog a new dog food and he puked ALL over my house!". Is the statement "Love how I gave my dog a new dog food and he projectile vomited all over my house!" false? Yes/no/unknown |
Hearing weird noises around the house at night could invoke a potential danger such as a robbery or someone breaking in with malicious intent which makes someone scared rather than in love. | False | FLUTE | Context: "I always hear crazy noises in my house." Claim: "I am in love with the weird noises that come from my house at night."
Considering the context, is the claim true, false, or unknown? |
To carry 17 objects, three at a time, it takes 17/3 = 5 and 2/3 loads.
This calculation means that she takes 5 trips carrying 3 objects per trip, and then she takes one additional trip carrying only two objects.
Thus, in reality, she takes 5 + 1 = 6 trips to the surface. | 6 | gsm8k | Gretchen is a scuba diver. She likes to hunt for treasure on the ocean's floor, but when she finds something to keep, she must carry it back to the surface of the water to give it to her shipmate on the boat. She can only carry 3 objects at a time while she swims underwater. If she finds 17 objects underwater, what is the fewest number of trips to the surface of the water she must take to carry all 17 objects to the boat? |
The Doctor (Doctor Who) used the TARDIS, a largely unreliable time traveling machine, to travel through time and space. Gateway is a Marvel comic character linked to the X-Men comics. Gateway has the power to create wormholes that allow him to travel through time and space. | No | strategyqa | Would Marvel's Gateway be envious of the Doctor (Doctor Who)'s TARDIS machine? |
First subtract $500 from Karen's goal bonus amount to find how much she makes from the extra $10/point bonus: $600 - $500 = $100
Then divide the extra bonus by the extra rate: $100 / $10/point = 10 points
Then add the 10 extra points to the baseline 75 point goal to find the students' average test score: 10 points + 75 points = 85 points
Then added the 8 graded tests to the 2 ungraded tests to find the total number of tests: 2 tests + 8 tests = 10 tests
Then multiply the 85 point average by the number of tests to find the total number of points the students need to earn: 85 points/test * 10 tests = 850 points
Then multiply the current average by the current number of graded tests to find how many points have been earned so far: 70 points/test * 8 tests = 560 points
Then subtract the number of points earned from the number of points needed to find the combine score the last two tests need: 850 points - 560 points = 290 points | 290 | gsm8k | Karen's students are about to take a standardized test. Karen gets a $500 bonus if their average score is above 75, plus an extra $10 bonus for every additional point the average score increases above 75. So far, Karen has graded 8 tests, and the average is 70. Given that each student can have a maximum score of 150, what combined score do the last two tests need to have for Karen to earn a $600 bonus? |
Amanda has gone on 7 hikes x 8 = 56 hikes.
Steven has gone on 56 hikes + 15 hikes = 71 hikes.
Camila needs to go on another 71 hikes - 7 hikes = 64 hikes.
Camila will achieve her goal in 64 hikes / 4 hikes/week = 16 weeks. | 16 | gsm8k | Camila has only gone hiking 7 times in her life. Amanda has gone on 8 times as many hikes as Camila, and Steven has gone on 15 more hikes than Amanda. If Camila wants to say that she has hiked as many times as Steven and plans to go on 4 hikes a week, how many weeks would it take Camila to achieve her goal? |
When someone buys the same car that another person wanted it can often be a source of jealousy because the person feels like they will never be able to have that car | True | FLUTE | Context: "My neighbor actually purchased a dream car of mine and I see it parked in his driveway everyday just taunting me" Claim: "My neighbor's new car is exactly the dream car of mine, and I feel so jealous every time I see it parked in his driveway"
Considering the context, is the claim true, false, or unknown? |
In total, there are $2+2+2=6$ different pairs. | B | TAL-SCQ5K | Three girls and two boys were dancing. They danced in pairs so that each girl danced with each boy for exactly one minute. At any time, there was only one pair on the dance floor. For how many minutes did they dance? (2021 Math Kangaroo Problem, Level 1-2, Question \#21)
Options:
A) $$5$$
B) $$6$$
C) $$8$$
D) $$9$$
E) $$10$$ |
Multicultural refers to a blend of several cultures within one organism. Africanized bees, also killer bees are a result of crossbreeding. Africanized bees are a mix of East African lowland honey bees and European honey bee subspecies such as the Italian honey bee and the Iberian honey bee. | Yes | strategyqa | Can Africanized bees be considered multicultural? |
To chop something down means to destroy or defeat it, while to lose to something means to be defeated by it. | False | FLUTE | Context: "The politician lost to his rival."
Hypothesis: The politician chopped down his rival.
Based on the context, is the hypothesis true, false, or unknown? |
In 11 months, Yoque will pay a total of $15 x 11 = $165.
The amount $165 is 100% + 10% = 110% of the money she borrowed.
So, 1% is equal to $165/110 = $1.50.
Hence, Yoque borrowed $1.50 x 100 = $150. | 150 | gsm8k | Yoque borrowed money from her sister. She promised to pay it back in 11 months including an additional 10% of the money she borrowed. If she pays $15 per month, how much money did she borrow? |
Donaldsons pay $15/hour = 15*7 = $105.
The Mercks pay $18/hour = 18*6 = $108.
The Hilles pay $20/hour = 20*3 = 60.
The total amount Layla earned is 105 + 108 + 60 = 273.
Layla earned $273 for babysitting. | 273 | gsm8k | The Donaldsons pay $15 per hour for babysitting. The Merck family pays $18 per hour and the Hille family pays $20 per hour for babysitting. Layla babysat for the Donaldsons for 7 hours, the Merck family for 6 hours and the Hille family for 3 hours. How many dollars did Layla earn babysitting? |
Cockroaches are generally considered to be very dirty and so seeing one on a salad would be pretty disgusting | Yes | FLUTE | Consider the staetement "It was horrifying to see a roach crawl off of my friend's salad at the mexican restaurant.". Based on this statement, is "It was vile seeing a roach crawl off my friend's salad at the mexican restaurant" a true statement? Yes/no/unknown |
A 50 year old vase is likely to be very valuable and sentimental to my mother so the fact that my cat destroyed it would probably cause me to be heartbroken | No | FLUTE | Context: I am so distraught over my cat destroying my mothers 50 year old vase.
Hypothesis: I am completely and utterly heartbroken that my cat destroyed my mothers 50 year old vase
Is the hypothesis incorrect? (Yes, no, or unknown)? |
The total number of green and red plates is 28 + 21 = 49.
Xavier should buy 84 − 49 = 35 more plates. | 35 | gsm8k | Xavier needs 84 paper plates for a housewarming party. He already has 21 green plates and 28 red plates. How many more plates should Xavier buy? |
Most people are asleep at night after 11pm and so making noise in the parking lot is disruptive and would likely make someone angry if they were trying to sleep | True | FLUTE | Context: "Everynight after 11pm my neighbor is out in the parking lot, in and out of her vehicle making noise." Claim: "I am so angry that my neighbor is up all night and disrupting my sleep with her noise"
Considering the context, is the claim true, false, or unknown? |
Jameson has 5 x 2 = 10 medals for swimming.
He has a total of 5 + 10 = 15 medals for track and swimming.
Thus, he has 20 - 15 = 5 medals for badminton. | 5 | gsm8k | Jameson has 20 medals. Five of the medals are for the track. He has two times as many swimming medals as track medals. The rest of the medals are for badminton. How many badminton medals does he have? |
$$3+4=7$$. | c | TAL-SCQ5K | Which of the following statements is true?
Options:
a) $$4+7=3$$
b) $$3=4-7$$
c) $$3+4=7$$
d) $$4=7+3$$
e) $$3-7=4$$ |
There are 300+200+80 = 580 birds in total
Every day 20+8+5 = 33 birds are lost
After a week which is 7 days, 33*7 = 231 birds would be lost
There would be 580-231 = 349 birds left in the poultry | 349 | gsm8k | A small poultry farm has 300 chickens, 200 turkeys and 80 guinea fowls. A strange, incurable disease hit the farm and every day the farmer lost 20 chickens, 8 turkeys and 5 guinea fowls. After a week, how many birds will be left in the poultry? |
每只猴子多分了$$3$$个，分了$$5\times 9+(9-3)+57=108$$ （个），那么共$$108\div 3=36$$（只）猴子．共$$36\times6+57=273$$（个）桃子． | 3 | TAL-SCQ5K | 皮皮去动物园参观，动物园的饲养员把一堆桃子分给若干只猴子，如果每只猴子分$$6$$个，剩$$57$$个桃子；如果每只猴子分$$9$$个，就有$$5$$只猴子一个也分不到，还有一只猴子只分到$$3$$个．那么，有个桃子．
1) $$216$$
2) $$324$$
3) $$273$$
4) $$301$$ |
First find the total number of minutes Gretchen spends sitting at her desk: 6 hours * 60 minutes/hour = 360 minutes
Then divide this amount by 90 minutes to find how many walking breaks Gretchen takes: 360 minutes / 90 minutes/break = 4 breaks
Then multiply the number of breaks by the length of each break to find how long Gretchen spends walking: 4 breaks * 10 minutes/break = 40 minutes | 40 | gsm8k | Gretchen read that you should spend 10 minutes walking for every 90 minutes you spend sitting. If Gretchen spends 6 hours working at her desk, how long will she spend walking? |
Robert Downey Jr. was arrested in 1996 n drug and weapons charges and possessed a .357 Magnum. Barry Burton, a character in the Resident Evil series, used a Colt Python. The Colt Python is a type of .357 Magnum revolver. | Yes | strategyqa | Did Robert Downey Jr. possess same caliber gun as Resident Evil's Barry Burton? |
There were 1 + 4 = 5 of them who volunteered to plant flowers.
Each day, the 5 of them planted a total of 200/2 = 100 flowers.
Thus, James planted 100/5 = 20 flowers in a day. | 20 | gsm8k | James and 4 of his friends volunteered to plant flowers. In 2 days, they were able to plant a total of 200 flowers. If each of them planted the same number of flowers, how many flowers did James plant in a day? |
Dividing 10 by 3 gives a quotient of 3 and a remainder of 1. Therefore, $3 \cdot 3$ is the largest one-digit multiple of 3, and $3 \cdot 4$ is the least positive two-digit multiple of 3. This calculation shows that $a=12$.
Dividing 100 by 4 gives a quotient of 25 and no remainder. Therefore, $4 \cdot 25$ is the least positive three-digit multiple of 4, and $b=100$.
Combining these results gives $a+b = 12+100 = 112$. | $112$ | competition-math | If $a$ is the smallest positive two-digit multiple of $3$, and $b$ is the smallest positive three-digit multiple of $4$, then find $a+b$. |
There is $350 - $100 = $250 available to pay for the students' admission fees.
This means they can afford to bring $250 / $10 = 25 students on the trip. | 25 | gsm8k | The class plans to take a field trip to the zoo. The cost to rent a school bus is $100. The cost of admission is $10 per student. The teacher is allowed in for free. If the class has a budget of $350, how many students can go on the field trip? |
Cristobal read: 15 + 3 * 704 = 2127 pages
2127 - 704 = 1423 pages
Cristobal read 1423 more pages than Beatrix. | 1423 | gsm8k | Cristobal read 15 more than three times the pages that Beatrix read. If Beatrix read 704 pages, how many more pages did Cristobal read? |
Link is the main character of the Nintendo franchise 'Zelda". In "Legend of Zelda: Majora's Mask" Link meets an astronomer in an observatory. | Yes | strategyqa | Does Nintendo's link ever see an astronomer? |
Breaking someone's picture display cannot make someone feel pleased but rather guilty and clumsy because they destroyed someone's special belongings. | No | FLUTE | Consider the staetement "I broke my aunt's picture display, it was very elaborate and nice". Based on this statement, is "I was really pleased when I accidentally broke my aunt's picture display that she had just put up" a true statement? Yes/no/unknown |
To have one's jaw drop is to be so shocked that one's mouth literally opens wide in surprise which is what happened to the speaker before they hit someone else's shoulder playfully. | Yes | FLUTE | Consider the statement "I was so shocked that my mouth literally opened wide in surprise and I hit his shoulder playfully.". Based on this "My jaw dropped and I hit his shoulder playfully." a true statement? Yes, no, or I don't know? |
The first snake is 24 inches because there are 12 inches in a foot.
The snakes are 24+16+10= 50 inches long. | 50 | gsm8k | Christina has 3 snakes. 1 snake is 2 feet long. Another snake is 16 inches long. The last snake is 10 inches long. How many inches are all of her snakes combined? |
The pen is shorter than the pencil by 2 centimeters, so it's 12 - 2 = 10 centimeters long.
That means the rubber is 10 - 3 = 7 centimeters long
So all accessories are 7 + 10 + 12 = 29 centimeters long altogether. | 29 | gsm8k | A pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the total length of the rubber, the pen, and the pencil altogether? |
Attacking every weak point means to bring out someone's weaknesses to highlight them or make them more visible. | No | FLUTE | Given the statement "He criticized me so bad that he brought out all my weaknesses.", is the statement "He attacked every weak point in my argument." wrong?
- Yes
- No
- Unknown |
$$10u + 50u = 600$$ Thus, $$1u = 10$$, in total we have $$2u=20$$ | $$20$$ | TAL-SCQ5K | Su Li has the same number of ten-cent and fifty-cent coins. The total value is ＄$$6$$. How many coins does she have in all?
* $$10$$
* $$20$$
* $$36$$
* $$60$$
* None of the above |
因为$$120$$的因数有：$$1$$、$$2$$、$$3$$、$$4$$、$$5$$、$$6$$、$$8$$、$$10$$、$$12$$、$$15$$、$$20$$、$$24$$、$$30$$、$$40$$、$$60$$、$$120$$，所以一共有$$16$$个因数． 故选$$\text{D}$$． | d | TAL-SCQ5K | $$120$$有个偶因数．
Options:
a. $$20$$
b. $$12$$
c. $$24$$
d. $$16$$ |
$$7000\times \left( 1+3\textbackslash\% \right)\times \left( 1+3\textbackslash\% \right)-7000=426.3$$. | ＄$$426.3$$ | TAL-SCQ5K | Jerry starts a savings account with ＄$$7,000$$ at a bank. The interest rate is $$3\textbackslash\%$$ per year. How much interest will he earn in his savings account at the end of the second year?
Options:
* ＄$$426$$
* ＄$$426.3$$
* ＄$$4,263$$
* ＄$$4,263.6$$ |
Douglas fir are a type of tree. Douglas fir are used to make ships. The Minesweeper is a small warship made from Douglas fir. The Minesweeper was made of wood to reduce it's risk magnetic signature and likely hood of detonating mines. | Yes | strategyqa | Have Douglas fir been used to fight wars? |
Parody in the US is protected under fair use in regards to copyright. Criticism of political leaders is protected under the 1st Amendment. | No | strategyqa | Are parodies of the President of the United States illegal? |
Since a month has four weeks, the tree will increase its height by 2 feet for 4*4=16 weeks after four months of growing.
Since the tree grows at 2 feet per week, after 16 weeks, the tree would have increased its height by 2*16=32 feet.
If the tree is currently 10 feet tall, its height after four months will be 10+32=42 feet. | 42 | gsm8k | Josue planted a tree in his backyard that grows at the rate of 2 feet per week. If the tree is currently 10 feet tall, what would be the tree's total height after 4 months (assuming each month is 4 weeks long)? |
When something is buoyed, it is kept afloat or suspended, however, when something settles, it becomes calm or comes to rest. | Yes | FLUTE | Given the statement "Sniffles, coughs, and colds settled in their breasts.", is the statement "Sniffles, coughs, and colds buoyed in their breasts." wrong?
- Yes
- No
- Unknown |
$$12000$$ hours after $$3$$ P.M. is $$3$$ P.M. $$11999$$ hours after $$3$$ P.M is $$2$$ P.M. | B | TAL-SCQ5K | What time is $$11999$$ hours after $$3$$ P.M.?
Options:
A. $$2$$ A.M.
B. $$2$$ P.M.
C. $$4$$ A.M.
D. $$4$$ P.M. |
To be at full tilt means to be going as fast as possible, but in this sentence he would smash into it slowly | No | FLUTE | Consider the staetement "He would smash into it as slowly as he could.". Based on this statement, is "He would smash into it at full tilt." a true statement? Yes/no/unknown |
To say when push comes to shove is to say that if things get really bad, but in this context the speaker is saying that if things get good they will become a predator. | False | FLUTE | Context: "And if things get really good, I'm a predator."
Hypothesis: And when push comes to shove, I'm a predator.
Based on the context, is the hypothesis true, false, or unknown? |
8 boys + 8 girls = 16 students joined the field trip.
Thus, 18 - 16 = 2 girls were not able to join the field trip. | 2 | gsm8k | There were 18 students assigned in a minibus for a field trip. Eight of these students were boys. On the day of the field trip, the number of girls and boys was the same since some of the girls were not able to join the trip. How many girls were not able to join the field trip? |
When someone is trying too hard to be something they're not, it often results in them being fake and not genuine which can cause anger in people. | No | FLUTE | Context: There's nothing that ticks me off more than someone who tries too hard to make an impression.
Hypothesis: I absolutely love it when someone is trying too hard to be something they're not and it totally doesn't make me angry at all
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Many observatories are built on high mountains. There is less air above the telescope, so there is less interference from the atmosphere. | 1 | quartz | If Jim moves his telescope from a mountaintop to Death Valley, a location with much air above it, what will happen to the amount of interference from the atmosphere?
Options:
1) increase
2) decrease |
The sum is unchanged, which is $$1400$$，$$1400\div \left( 3+1 \right)=350$$，$$1100-350=750$$． | (a) | TAL-SCQ5K | There are two bookshelves, A and B. Shelf A has $$1100$$ books, and shelf B has books $$300$$. We need to take books from shelf A to shelf B, so that books in shelf B is three times more than self A.
Options:
(a) $$750$$
(b) $$800$$
(c) $$850$$
(d) $$900$$ |
By the Law of Sines applied to triangle $OAB$, $$\frac{OB}{\sin\angle
OAB}=\frac{AB}{\sin\angle AOB}.$$With $AB = 1$ and $\angle AOB = 30^\circ$, we have \[\frac{OB}{\sin \angle OAB} = \frac{1}{\sin 30^\circ} = 2,\]so so $OB=2\sin\angle OAB$. Thus, $OB \le 2$, with equality if and only if $\angle OAB=90^\circ$.
[asy]
unitsize(1.5 cm);
pair O, A, B;
O = (0,0);
A = sqrt(3)*dir(30);
B = (2,0);
draw((0,0)--3*dir(30),Arrow(6));
draw((0,0)--(3,0),Arrow(6));
draw(A--B);
draw(rightanglemark(O,A,B,4));
label("$A$", A, NW);
label("$B$", B, S);
label("$O$", O, W);
label("$1$", (A + B)/2, NE, red);
[/asy] | $2$ | competition-math | Two rays with common endpoint $O$ form a $30^\circ$ angle. Point $A$ lies on one ray, point $B$ on the other ray, and $AB=1$. What is the maximum possible length of $\overline{OB}$? |
【分析】假设全班一共$$120$$人，按规定需$$\frac34$$的选票才能当选，也就是至少需要得到$$90$$票，现在已经得到当选票数的$$\frac56$$，求出已获得的选票数量，求出还需要的选票数量，再计算还需要的数量占余下票数的几分之几。【详解】假设全班一共$$60$$人；$$120\times\frac34=90$$（张）$$90\times\frac56=75$$（张）$$120\times\frac23=80$$（张）$$120-80=40$$（张）$$90-75=15$$（张）$$15\div40=\frac38$$【点睛】本题考查的是基础的分数乘除法应用题，找准单位``1''是解题的关键。 | $$\frac38$$ | TAL-SCQ5K | 新学期性格活泼开朗的莉莉要竞选文艺委员，按规定需$$\frac{3}{4}$$的选票才能当选，计算$$\frac{2}{3}$$的选票后，她得到的选票已达到当选票数的$$\frac{5}{6}$$，她还要得到剩下选票的~\uline{~~~~~~~~~~}~才能当选。
$$\frac58$$
$$\frac56$$
$$\frac14$$
$$\frac38$$
$$\frac23$$ |
To be bar none means to be absolutely or with no exceptions, and in this sentence the girl is absolutely the most popular. | Yes | FLUTE | Given the statement "She had been two years ahead of me at school and absolutely the most popular girl.", what is the statement "She had been two years ahead of me at school and the most popular girl, bar none." true?
- Yes
- No
- Unknown |
Steve started with 2 * 12 = 24 pencils.
He gave Matt 6 + 3 = 9 pencils.
After giving away the pencils, Steve will have 24 – 9 – 6 = 9 pencils left. | 9 | gsm8k | Steve has 2 boxes of pencils with 12 pencils in each box. He gave Matt 3 more pencils than he gave to Lauren. If Steve gave 6 pencils to Lauren, how many pencils does he have left? |
It is common company policy to not eat other people's food from the refrigerator and so when someone sees their coworkers breaking this rule it often leads to frustration | True | FLUTE | Context: "I was upset and puzzled to see my coworkers eating my lunch I had left in the company refrigerator."
Hypothesis: I was really frustrated to see my coworkers eating my lunch that I had left in the company refrigerator
Based on the context, is the hypothesis true, false, or unknown? |
Bill needs 2 * 3 = 6 gallons of color paint for the 3 bedrooms.
Thus, he needs 6 / 1 = 6 cans of color paint for the bedrooms.
There are 2 * 3 = 6 other rooms in the house.
He needs 2 * 6 = 12 gallons of white paint for the other rooms.
Thus, he needs 12 / 3 = 4 cans of white paint.
In all, Bill needs 4 + 6 = 10 cans of paint for the whole house. | 10 | gsm8k | Bill is a painter who is hired to paint a client’s house. The house has three bedrooms, and twice as many other rooms as bedrooms. The client wants each bedroom painted a different color, and the other rooms painted white. Each room takes 2 gallons of paint. Color paint comes in 1-gallon paint cans, and white paint comes in 3-gallon cans. How many cans of paint will Bill need for the whole house? |
每周比赛要分出胜负分差必须在$$2$$分或以上，题中又给出每局比赛分差不超过$$3$$分，故每局比赛的分差只有两种可能：差$$2$$分或$$3$$分．且分差为$$3$$分的那局彭老师得分为$$11$$分，总分差为$$48-39=9$$分，故必有$$3$$场分差为$$2$$分，另一场分差为$$3$$分；即有一场的比分为$$118$$，另两场的总比分为$$3731$$，有以下四种情况：①$$11:9$$，$$11:9$$，$$15:13$$②$$11:9$$，$$12:10$$，$$14:12$$③$$11:9$$，$$13:11$$，$$13:11$$④$$12:10$$，$$12:10$$，$$13:11$$．故一共有$$4$$种情况． | a | TAL-SCQ5K | 有一天，彭老师和陈老师约好去打乒乓球，结果彭老师以$$4:0$$完虐陈老师．乒乓球比赛为$$11$$分制，即每局$$11$$分，$$7$$局$$4$$胜制，打成$$10:10$$后必须净胜而且只能净胜$$2$$分．经计算，彭老师四局的总得分为$$48$$分，陈老师总得分为$$39$$分，且每一局比赛分差不超过$$3$$分，则一共有种情况．（不考虑这四局比分之间的顺序）
a) $$4$$
b) $$5$$
c) $$6$$
d) $$7$$ |
The additional yard Brendan can cut after buying the lawnmower is 8 x 0.50 = 4 yards.
So, the total yards he can cut with the lawnmower is 8 + 4 = 12.
Therefore, the total number of yards he can cut in a week is 12 x 7 = 84 yards. | 84 | gsm8k | Brendan can cut 8 yards of grass per day, he bought a lawnmower and it helped him to cut more yards by Fifty percent per day. How many yards will Brendan be able to cut after a week? |
First find the total area of the forest: 4 miles * 6 miles = 24 square miles
Then find the total number of trees in that area: 600 trees/square mile * 24 square miles = 14400 trees
Then find the number of trees all the loggers can cut down in one day: 8 loggers * 6 trees/logger = 48 trees
Then divide the total number of trees by the number cut down per day to find the number of days it takes to clear the forest: 14400 trees / 48 trees/day = 300 days
Then divide the time in days by the number of days per month to find the time in months: 300 days / 30 days/month = 10 months | 10 | gsm8k | One logger can cut down 6 trees per day. The forest is a rectangle measuring 4 miles by 6 miles, and each square mile has 600 trees. If there are 30 days in each month, how many months will it take 8 loggers to cut down all the trees? |
Compared with a less powerful device, a more powerful device can either do more work in the same time or do the same work in less time. | B | quartz | When you use a 1 horsepower drill instead of a 2 horsepower drill it is
Options:
A: more powerful
B: less powerful |
A daisy in a field of sunflowers would stand out because it is a different color, meaning it is special, whereas if someone is not special, they would blend in and not stand out | False | FLUTE | Context: "A few weeks later, a letter arrives, explaining that you are not special."
Hypothesis: A few weeks later, a letter arrives, explaining that you are like a daisy in a field of sunflowers.
Based on the context, is the hypothesis true, false, or unknown? |
The darker the urine, the less water it contains. | [2] | quartz | Mona urinated yesterday morning and the urine was very light. When she urinated today the urine was very dark. Which urination contained less water?
[1] yesterday morning
[2] today |
Developing nations will also increase demands on natural resources as they build more factories. | less resources | quartz | When a country stops manufacturing things they need to have
Options:
- less resources
- more resources |
Squidward Tentacles plays the clarinet. Alan Greenspan played clarinet and saxophone along with Stan Getz. Alan Greenspan studied clarinet at the Juilliard School from 1943 to 1944. | No | strategyqa | Do Squidward Tentacles and Alan Greenspan have different musical passions? |
A dog with its tail between its legs is scared, so this simile is saying that Hitler was scared and skittered off slowly. | Yes | FLUTE | Consider the statement "Hitler skittered off slowly". Based on this "Hitler skittered off like a dog with its tail between its legs." a true statement? Yes, no, or I don't know? |
Up for grabs means available to anyone, and in this context the key is unclaimed and available to anyone. | Yes | FLUTE | Context: The key will be unclaimed and available to anyone, but he 'll be too weak to make a play for it, leaving the field wide open for you.
Hypothesis: The key will be up for grabs, but he 'll be too weak to make a play for it, leaving the field wide open for you.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Posturing to have an opinion means to act like you have a strong opinion even if you don't, in order to make yourself look good. | Yes | FLUTE | Given the statement "But ‘ pretending to have an opinion ’ went far beyond the unions .", what is the statement "But ‘ posturing and pretending ’ went far beyond the unions ." true?
- Yes
- No
- Unknown |
$$\left\textbar{} 3-9 \right\textbar+\left\textbar{} 7-2 \right\textbar=\left\textbar{} -6 \right\textbar+\left\textbar{} 5 \right\textbar=6+5=11$$. | [B] | TAL-SCQ5K | Evaluate$$\left\textbar{} 3-9 \right\textbar+\left\textbar{} 7-2 \right\textbar$$.
[A] $$-11$$
[B] $$11$$
[C] $$7$$
[D] $$-2$$ |
The weight of apples used for juice and given to the restaurant is 60 + 90 = 150 kg
Thus 405 – 150 = 255kg worth of apples were sold in 5 kg bags.
There were 255 / 5 = 51 bags sold.
So each bag was sold for 408 / 51 = $8 | 8 | gsm8k | We harvested 405 kg of apples. 90 kg were used to make fruit juice and 60 kg were given to a restaurant. The rest was sold in 5 kg bags and their sale brought in $408. What was the selling price of one bag of apples? |
Madeline spends 4*7=28 hours on homework.
She spends 8*7-56 hours sleeping.
Therefore, she is busy 28+18+56+20=122 hours per week.
There are 7*24=168 hours per week.
Thus, Madeline has 168-122=46 hours left over. | 46 | gsm8k | Madeline spends 18 hours a week in class. She spends 4 hours per day working on homework. She spends 8 hours per day sleeping. She works part-time 20 hours per week. How many hours left over does Madeline have? |
To juggle something means to manage or balance multiple things at the same time, while to avoid something means to stay away from it or keep it out of sight. | Yes | FLUTE | Consider the statement "She had to avoid her job and her children.". Is the statement "She had to juggle her job and her children." false? Yes/no/unknown |
Towers over means that the bridge is standing over than the river. | Yes | FLUTE | Consider the statement "Overlooking the river is the bridge.". Based on this "The bridge towers over the river." a true statement? Yes, no, or I don't know? |
The greater the mass of the objects, the stronger the gravitational pull between them. | [1] | quartz | If Mona makes some clay balls and adds extra clay to them, increasing their mass, what happens to the gravitational pull between the two clay balls?
Options:
[1] increases
[2] decreases |
He scored 4*6=24 points per game
So he scored 15*24=360 points from touchdowns
He also scored 2*6=12 points from the 2 point conversions
So he scored a total of 360+12=372 points
That means he beat the old record by 372-300=72 points | 72 | gsm8k | James joins a football team and becomes the star. He scores 4 touchdowns per game and each touchdown is worth 6 points. There are 15 games in the season. He also manages to score 2 point conversions 6 times during the season. The old record was 300 points during the season. How many points did James beat the old record by? |
In $$300$$ seconds ($$5$$ minutes), Cagney will frost $$\dfrac{300}{30}=10$$ cupcakes, and Lacey will frost $$\dfrac{300}{60}=5$$ cupcakes. Therefore, working together they will frost $$10+5=\boxed{(\text{B})15}$$ cupcakes. | $$15$$ | TAL-SCQ5K | Cagney can frost a cupcake every $$30$$ seconds and Lacey can frost a cupcake every $$60$$ seconds. Working together, how many cupcakes can they frost in $$5$$ minutes? (Adapted from $$2012$$ AMC $$10\rm A$$ Problem, Question \#$$11$$)
- $$10$$
- $$15$$
- $$20$$
- $$25$$
- $$30$$ |
Family members often want their loved ones to do things that the latter may not have time for and this often leads to a lot of stress. | Yes | FLUTE | Given the statement "My family is always bugging me to do things that I dont have time to do.", is the statement "I just love how my family always pressures me to do things that I have no time for." wrong?
- Yes
- No
- Unknown |
$$n$$个人完成一项工程需要$$m$$天， 则$$1$$个人完成这项工程需要$$mn$$天， ∴$$(m+n)$$个人完成这项工程需要$$\frac{mn}{m+n}$$天． | $$\frac{mn}{m+n}$$ | TAL-SCQ5K | 若$$n$$个人完成一项工程需要$$m$$天，则$$(m+n)$$个人完成这项工程需要（~ ）天．
- $$\frac{mn}{m+n}$$
- $$\frac{m-n}{m+n}$$
- $$\frac{m+n}{mn}$$
- $$\frac{mn}{m+2n}$$ |
The salon made $200.00 and they charge $20.00 per client so there are 200/20 = 10 clients in the salon
There are 210 fingers in the salon and everyone has 10 fingers so there are 210/10 = 21 people in the salon
If there are 21 people in the salon and 10 are clients then there are 21-10 = 11 people in the salon that are not clients | 11 | gsm8k | A nail salon was completely booked at 2 pm for manicures. Each manicure costs $20.00 per client so the salon made $200.00. If there are 210 fingers in the salon at 2 pm, and everyone has 10 fingers, how many people in the salon are not clients? |
The word exploded is used here to mean the anger and rage shown by the boss, while burst into laughter connotes happiness. | No | FLUTE | Context: The boss burst into laughter when he heard of the resignation of the secretary.
Hypothesis: The boss exploded when he heard of the resignation of the secretary.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
In the movie, Alice meets the Mad Hatter. The Mad Hatter is having a tea party to celebrate his Unbirthday. The Unbirthday is a holiday which happens every day of the year which is not the subject's actual birthday. | Yes | strategyqa | Does Disney's Alice in Wonderland involve the celebration of a holiday? |
因为$$f(x)={{(x-1)}^{3}}+2$$，所以函数图象的对称中心为$$(1,2)$$． | 2 | TAL-SCQ5K | 函数$$f(x)={{x}^{3}}-3{{x}^{2}}+3x+1$$的图象的对称中心为．
Options:
1: $$(-1,2)$$
2: $$(1,2)$$
3: $$(-1,-2)$$
4: $$(1,-2)$$ |
Fallout New Vegas is a game that takes place after the apocalypse has ocurred. In Fallout New Vegas, players can go to casinos and play on slot machines. | Yes | strategyqa | Do any video games about the end of civilization have slot machines? |
The workload at a job is already tough and then having to do the work of a lazy co-worker on top of that makes it even harder, which is not something anyone would like. | False | FLUTE | Context: "I don't like doing my job and the duties of other co-worker that slack."
Hypothesis: I like the fact that my job is already hard and then I have to do the work of a lazy co-worker too
Based on the context, is the hypothesis true, false, or unknown? |
He will need to bring 30 yards of floss because 20 x 1.5 = 30
One packet of floss is enough because 35 > 30
He has 5 yards left over because 35 - 30 = 5 | 5 | gsm8k | Dikembe wants to teach everyone at school about the importance of flossing, so he plans to bring enough packets of floss for everyone. There are 20 students in his class. Each student needs 1.5 yards of floss. He sees in the store that each packet of floss contains 35 yards. If he buys the least amount necessary, how much floss is left over? |
$$\left( \Delta \times 2-1 \right)\times 2=2018$$， $$\Delta \times 2-1=2018\div 2=1009$$， $$\Delta \times 2=1009+1=1010$$， $$\Delta =1010\div 2=505$$． 故选$$\text{D}$$． | D | TAL-SCQ5K | （2018 IMAS，Question\#2） 若$$\left( \Delta \times 2-1 \right)\times 2=2018$$，请问$$\Delta $$代表的数是多少？
Options:
A. $$502$$
B. $$503$$
C. $$504$$
D. $$505$$
E. $$506$$ |
A: As the car approaches the radar gun, the reflected microwaves get bunched up in front of the car. Therefore, the waves the receiver detects have a higher frequency than they would if they were being reflected from a stationary object. The faster the car is moving, the greater the increase in the frequency of the waves. | (a) | quartz | If Mona is bouncing radar waves off a test car when training to be a policewoman and she notices the frequency of the waves returning to her radar gun is lower then it was before, what is happening to the car she is pointing the gun at?
(a) decreasing in speed
(b) increasing in speed |
People who move out are supposed to clean up after themselves and leave the space the way they found it so it's angering when someone leaves their trash and furniture behind which then blocks a parking space | True | FLUTE | Context: "My upstairs neighbor moved out recently and blocked the parking space by leaving all her trash and furniture there." Claim: "I'm so angry that my upstairs neighbor left all her trash and furniture after she moved out and blocked the parking space"
Considering the context, is the claim true, false, or unknown? |