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A prowling animal is one that is on the hunt, looking for its next meal much like someone primitive and primal. | No | FLUTE | Context: He looked primitive and primal .
Hypothesis: He looked like a prowling animal .
Is the hypothesis incorrect? (Yes, no, or unknown)? |
The idiom better late than never means that the delayed occurrence or achievement of something is better than it not happening at all, but in this sentence, Danny says it would have been much better if it never happened. | No | FLUTE | Consider the statement "It would have been much better if this never happened because it's so late, Danny said behind them.". Based on this "Well, better late than never,danny said behind them." a true statement? Yes, no, or I don't know? |
If 6 friends each want 2 bars, that's 6 friends * 2 bars = 12 bars needed.
Each box contains 3 bars, so 12 bars / 3 bars per box = 4 boxes needed.
A box is $7, so 4 boxes * $7.50 = $30.
There are 6 friends so $30 / 6 friends = $5 per person. | 5 | gsm8k | A box of ice cream bars costs $7.50 and contains three bars. 6 friends want to each eat 2 bars. How much money will that require per person? |
The faster, longer, and farther the wind blows, the bigger the waves are. | increase | quartz | When we have a very windy day what will happen to the waves?
increase
decrease |
First Store:50000(.10)=5000
50000-5000=45000 pounds
Second Store:45000(.20)=9000
45000-9000=36000 pounds | 36000 | gsm8k | A tractor trailer has a load of 50000 pounds. 10% of the weight gets unloaded at the first store, and 20% of the remaining load is removed at the second store. How much weight, in pounds, is left on the truck after the two deliveries? |
Many of the worlds people live with water scarcity, and that percentage will increase as populations increase and climate changes. | [a] | quartz | Will increases the population of his model of the world's population. The amount of water scarcity, if no other variables are changed, will likely go
[a] up
[b] down |
The largest single-digit prime number is $$7$$ and the smallest three-digit prime number is $$101$$; their difference is $$101 -7=94$$. | $$94$$ | TAL-SCQ5K | What is the difference between the largest single-digit prime number and the smallest three-digit prime number?
Options:
- $$94$$
- $$95$$
- $$96$$
- $$97$$
- $$98$$ |
The idiom good riddance is used when one is pleased that someone or something is leaving or stopping, but in this context the speaker is not glad they're gone. | Yes | FLUTE | Consider the statement "I'm not glad they're gone.". Is the statement "good riddance, I say." false? Yes/no/unknown |
Bugs are usually disgusting and most people are terrified of them therefore it is unlikely to love seeing someone's apartment infested by them. | No | FLUTE | Context: When I moved into my apartment it was full of bugs
Hypothesis: I absolutely loved when I moved into my apartment and found it crawling with bugs.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Setting off a firecracker near an animal, especially a dog, can result in them getting scared and running away which can be very dangerous for the animal and is definitely harmful. | False | FLUTE | Context: "I was so angry when my brother tied a firecracker to our dog's tail." Claim: "I thought it was totally harmless when my brother tied a firecracker to our dog's tail."
Considering the context, is the claim true, false, or unknown? |
因为$$\frac{105+85}{2}=95$$，$$\frac{85+95}{2}=90$$，$$\frac{95+90}{2}=92.5$$， $$\frac{90+92.5}{2}=91.25$$，$$\frac{92.5+91.25}{2}=91.875$$，$$\cdots $$， 因为$$91.25$$与$$91.875$$的整数部分相同，而两个数的平均数一定介于两个数之间， 所以，后面各数的整数部分均为$$91$$． 当然第$$2022$$个数的整数部分也为$$91$$． | (B) | TAL-SCQ5K | 有一列数，第一个数是$$105$$，第二个数是$$85$$．从第三个数开始，每个数都是它前面两个数的平均数，那么这列数中第$$2022$$个数的整数部分是．
Options:
(A) $$90$$
(B) $$91$$
(C) $$92$$
(D) $$93$$ |
Seeing someone eat their boogers is a disgusting sight and most people would not be thrilled about it. | No | FLUTE | Context: At work I saw a coworker pick their nose and eat it.
Hypothesis: I was so thrilled to see my coworker eat their boogers right at work
Given this context, is the hypothesis true (Yes/No/I don't know)? |
解：依题意可知： 从$$2$$月$$6$$日到$$2$$月$$17$$日为止，一共有$$17-6+1=12$$（天）； 其中有$$2$$个星期六，星期日，工作了$$12-4=8$$（天）. 共完成$$1+3+5+7+9+11+13+15=64$$（道）题. 故选：$$\text{D}$$. | (d) | TAL-SCQ5K | $$2014$$年$$2$$月$$6$$日是星期四，小胖决定从这天起（含$$2$$月$$6$$日）练习计算，一直练习到$$2$$月$$17$$日，（含$$2$$月$$17$$日）开学为止．但是中间如果遇到周六和周日，小胖还是决定休息一下，不做练习．已知他第一天做$$1$$道题，第二天做$$3$$道题，第三天做$$5$$道题，依此变化做下去，那么小胖这段时间一共做了道计算练习题.
Options:
(a) $$144$$
(b) $$100$$
(c) $$81$$
(d) $$64$$ |
To leave well alone means to refrain from changing or becoming involved in something so as to avoid unintentionally causing problems, but the context describes trying to change or get involved without caring if it causes problems. | No | FLUTE | Context: Playing the same sort of game with lee porter as the outcome was a far more dangerous prospect, and one she would absolutely try to change or get involved without caring if it causes problems.
Hypothesis: Playing the same sort of game with lee porter as the outcome was a far more dangerous prospect, and one she would leave well alone.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
On Saturday, Erica saw 3 + 2 = 5 animals
On Sunday she spotted 2 + 5 = 7 animals
On Monday, she saw 5 + 3 = 8 animals
Adding up all the animals Erica saw gives a total of 5 + 7 + 8 = 20 animals | 20 | gsm8k | Erica is telling her grandson about the animals she saw during her recent safari in Kenya's Maasai Mara. On Saturday, she saw 3 lions and 2 elephants. She spotted 2 buffaloes and 5 leopards on Sunday, and 5 rhinos and 3 warthogs on Monday. What is the total number of animals that Erica saw? |
Observe that $7<\sqrt{63}<8$, since $\sqrt{49}<\sqrt{63}<\sqrt{64}$. Therefore, the largest integer that is less than $\sqrt{63}$ is $7$. | $7$ | competition-math | Evaluate $\lfloor\sqrt{63}\rfloor$. |
There are 8 figures in total. Of these, 3 are triangles. Therefore, the probability is $\frac38$. | $\frac38$ | competition-math | One of the following 8 figures is randomly chosen. What is the probability that the chosen figure is a triangle? [asy]
size(8cm);
path tri = (0, 0)--(1, 0)--(0.5, Sin(60))--cycle;
path circ = shift((0.5, 0.5)) * (scale(0.5) * unitcircle);
path sq = unitsquare;
pair sf = (1.9, 0); // Shift factor
draw(sq); draw(shift(sf) * tri); draw(shift(2 * sf) * circ); draw(shift(3 * sf) * tri);
draw(shift(4 * sf) * sq); draw(shift(5 * sf) * circ); draw(shift(6 * sf) * tri); draw(shift(7 * sf) * sq);
[/asy] |
There are 15 - 6 = 9 students who like French fries only.
There are 10 - 6 = 4 students who like burgers only.
So, 9 + 4 + 6 = 19 students like either French fries, burgers, or both.
Hence, 25 - 19 = 6 students do not like either fries or burgers. | 6 | gsm8k | In a class of 25 students, students were asked if they like French fries, burgers, or neither. 15 students said they like French fries and 10 said they like burgers, with these statistics including the responses of 6 students who said they like both French fries and burgers. How many students do not like either food? |
Adding together the percent of people who drink coffee with those who drink tea, we obtain a total of $150\%$. Thus, we double-counted at least $50\%$, meaning that at least $50\%$ of adults drink both. (The percentage who drink both ${\it can}$ be exactly ${50\%}$ if everybody drinks either coffee or tea; otherwise, the overlap is more than ${50\%}$, but the problem asked for the smallest possible overlap.) | $50\%$ | competition-math | Eighty percent of adults drink coffee and seventy percent drink tea. What is the smallest possible percent of adults who drink both coffee and tea? |
The parrot knew 3 phrases when Georgina bought it, so it has learned 17 - 3 = 14 phrases from her.
She has been teaching it 2 phrases a week, so she has had it 14 / 2 = 7 weeks.
There are 7 days in a week, so Georgina has had the parrot for 7 * 7 = 49 days. | 49 | gsm8k | Georgina owns a parrot and is teaching it to speak. So far, the parrot knows seventeen phrases. If she is teaching it two phrases a week and it already knew three phrases when she bought it, how many days has Georgina had it? |
Usually to go the whole hog refers to doing something as thoroughly as possible , taking it all for oneself or without any restraint. | No | FLUTE | Consider the statement "Not to share the bank with the table, or to take some minor part of it, but to take it all for themselves without any restraint.". Is the statement "Not to share the bank with the table, or to take some minor part of it, but to go the whole hog." false? Yes/no/unknown |
We need to make units same first. $5$ minutes equal to $300$ seconds. Now we could remove the same unit, second. We get $300:30$ and simplify it to $10:1$. | $10:1$ | TAL-SCQ5K | What is the simplest form of $5$ minutes $: 30$ seconds?
$5:30$
$1:6$
$6:1$
$10:1$ |
The richest billionaire in 2020 is Jeff Bezos. Jeff Bezos has an estimated worth of 145 billion dollars. GDP is a measure of how much the economy of a country is worth. Cambodia has an estimated GDP of 28 billion in 2020. | No | strategyqa | Is Cambodia too expensive for 2020 richest billionaire to own? |
$${{(\sqrt{7})}^{2}}-\sqrt{{{(-4)}^{2}}}=7-4=3$$． 故选$$\text{A}$$． | a | TAL-SCQ5K | 计算：$${{(\sqrt{7})}^{2}}-\sqrt{{{(-4)}^{2}}}=$$．
a) $$3$$
b) $$11$$
c) $$-3$$
d) $$-11$$ |
\[1017^2=(10^3+17)^2=10^6+2\cdot17\cdot10^3+289=1034289.\] | $1034289$ | competition-math | Compute the square of 1017 without a calculator. |
$$8:10$$+$$10$$min+$$30$$min+reading=$$9:45$$ reading=$$25$$min | [4] | TAL-SCQ5K | Bella got up at 8:10. It took 10 minutes to wash and 30 minutes to eat breakfast. At this moment, she began to read. After reading, she went out. She went out at 9:45. How long did she read?
[1] $$10$$ minutes
[2] $$15$$ minutes
[3] $$20$$ minutes
[4] $$25$$ minutes
[5] $$30$$ minutes |
Since there are three months in a quarter, then there are 12/3 = 4 quarters in a year.
So, Mrs. Garcia pays $378 x 4 = $1512 in a year for her insurance. | 1512 | gsm8k | Mrs. Garcia pays her insurance quarterly at $378. How much does she pay in a year for her insurance? |
$$5$$小时$$=300$$分钟，$$300\div 20=15$$，$$15\div 3=5$$，所以一共经历了$$5$$个周六、日、一，但是一个月最多有四个完整的星期，所以第五个星期一定是只有三天：周六、周日、周一。并且这个月也是从周六开始的，第十天是周一。 | 周一 | TAL-SCQ5K | 张老师每周的周一、周六和周日都跑步锻炼$$20$$分钟，而其余日期每日都跳绳$$20$$分钟。某月他总共跑步$$5$$小时，那么这个月的第$$10$$天是( )
* 周日
* 周六
* 周二
* 周一 |
The price per kilogram of potatoes is $6 / 2 = $3.
To buy 5 kg of potatoes, she will have to pay 5 * $3 = $15. | 15 | gsm8k | Daphney buys 5 kg of potatoes at the supermarket. If 2 kg of potatoes costs $6, how much will she pay? |
First we simplify $\frac{8}{10}$, \[
\frac{8}{10} = \frac{2}{2}\cdot\frac{4}{5}=1\cdot\frac{4}{5} =\frac{4}{5}.
\]Now make both terms have a common denominator, \[
\frac{2}{7}+\frac{4}{5}= \frac{5}{5}\cdot\frac{2}{7}+\frac{7}{7}\cdot\frac{4}{5} = \frac{10}{35}+\frac{28}{35}
=\frac{38{35}}.
\]Note that we could have done the problem without simplifying $\frac{8}{10}$ at the beginning and instead simplified at the end, but in this case simplifying first made things simpler as we didn't need to carry around the extra factor of two. | $\frac{38$ | competition-math | Find: $\frac{2}{7}+\frac{8}{10}$ |
Let T be the number of toys Joel’s sister donated.
Joel donated twice as many toys, so he donated 2T toys.
Joel’s friends donated 18 + 42 + 2 + 13 = 75 toys.
In all, Joel collected T + 2T + 75 = 3T + 75 = 108 toys.
Joel and his sister donated 3T = 108 - 75 = 33 toys together.
Therefore, T = 33 / 3 = 11 toys were his sister’s.
Thus, 2T = 2 * 11 = 22 toys were Joel’s. | 22 | gsm8k | Joel collected a bin of old toys to donate. By asking his friends, he was able to collect 18 stuffed animals, 42 action figures, 2 board games, and 13 puzzles. His sister gave him some of her old toys from her closet, and then Joel added twice as many toys from his own closet as his sister did from hers. In all, Joel was able to donate 108 toys. How many of the donated toys were Joel’s? |
Being broke is not a desirable thing and so someone who is glad for being in that situation cannot be considered to be sensible or rational. | No | FLUTE | Context: I am scared that I might not have enough money for food next month
Hypothesis: I am glad that I might not have enough money to buy food next month
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
A vale of tears is a world of sorrows, and the context recognizes the talent of the person in making the world fit the loving image they have in their mind. | True | FLUTE | Context: "I do recognize your talents in bending and adjusting this world of sorrows to make it fit the world I so lovingly imagine, polydoor." Claim: "I do recognize your talents in bending and adjusting this vale of tears to make it fit the world I so lovingly imagine, polydoor."
Considering the context, is the claim true, false, or unknown? |
We have a 2 dice with 2 evens and 4 odds on both dice. For the sum to be even, the 2 rolls can be 2 odds or 2 evens. Ways to roll 2 odds (Case 1 ): The total number of ways to obtain 2 odds on 2 rolls is $4 * 4=16$, as there are 4 possible odds on the first roll and 4 possible odds on the second roll. Ways to roll 2 evens (Case 2 ): Similarly, we have $2 * 2=4$ ways to obtain 2 evens. Probability is $\frac{20}{36}=\frac{5}{9}$. | $\dfrac{5}{9}$ | TAL-SCQ5K | The faces of each of two fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number? (2019 AMC 8 Problems, Question \#18)
Options:
* $\dfrac{4}{9}$
* $\dfrac{1}{2}$
* $\dfrac{5}{9}$
* $\dfrac{3}{5}$
* $\dfrac{2}{3}$ |
If exactly $5$ pupils get the correct test, then exactly $3$ pupils must get the wrong test. No. of ways to choose $5$ pupils to get the correct test is $$\frac{8 \times 7 \times 6 \times 5 \times 4}{5 \times 4 \times 3 \times 2 \times 1}-56.$$ To make sure that the other $3$ pupils get the wrong tests, the correct number is $2$. Hence, the total no, of ways $=56 \times2=112$. | 4 | TAL-SCQ5K | Eight pupils from Victory Primary School take a Mathematics test, but none of the pupils wrote his/her name on the test. The tests are therefore handed back to the pupils at random. In how many ways can exactly $5$ of the $8$ pupils get the correct test back?
1) $$30$$
2) $$36$$
3) $$56$$
4) $$112$$ |
The number of rolls already sold is 1 + 10 + 6 = 17.
Nellie needs to sell 45 − 17 = 28 more rolls of gift wrap. | 28 | gsm8k | For a fundraiser, Nellie needs to sell 45 rolls of gift wrap. So far, she has sold 1 roll to her grandmother, 10 rolls to her uncle, and 6 rolls to a neighbor. How many more rolls of gift wrap does Nellie need to sell? |
Michael has 5 animals because 2 + 3 = 5
Michael has to pay $65 because 5 x $13 = $65 | 65 | gsm8k | Michael has 2 cats and 3 dogs. He needs to pay a friend to watch them, who charges $13 a night per animal. How much does Michael have to pay? |
If Mary collected twice the number of red marbles collected by Jenny, she got 2*30 = 60 red marbles.
Anie collected 20 more red marbles than Mary, which is 60+20 = 80 red marbles.
The total number of red marbles is 60+80+30 = 170 red marbles.
If Anie collected twice the number of blue marbles collected by Jenny, then she got 2*25 = 50 blue marbles.
Mary collected half the number of blue marbles collected by Anie, thus 1/2*50 = 25 marbles
The total number of blue marbles collected is 50+25+25 = 100 blue marbles | 100 | gsm8k | Mary and her two friends came up with the idea of collecting marbles each day for their play on weekends. From Monday to Friday, Mary collected twice as many red marbles as Jenny and half the number of blue marbles collected by Anie, who collected 20 more red marbles than Mary and twice the number of blue marbles Jenny collected. If Jenny collected 30 red marbles and 25 blue marbles, what's the total number of blue marbles collected by the friends together? |
It is frustrating when something you have been looking forward to arrives in a condition that is not usable or as expected | Yes | FLUTE | Given the statement "I was so mad when I saw the package I ordered from online was ruined!", what is the statement "I could not believe it when I saw the package that I anxiously awaited for arrival was completely ruined!" true?
- Yes
- No
- Unknown |
Departed means gone or extinct . | Yes | FLUTE | Given the statement "In the days long since past ,", is the statement "In the days long since departed ," is true?
- Yes
- No
- I don't know |
Total height less than the average: $(180-168)\times5=60$. Thus, there are $60\div(168-162)=10$ female teachers. | $$10$$ | TAL-SCQ5K | The average height of all the teachers in Grape School is $168$. There are $5$ male teachers in Grape School with an average height of $180$. The average height of female teachers is $162$. How many female teachers are there?
$$5$$
$$9$$
$$10$$
$$18$$
$$21$$ |
逻辑推理．由第一句话可知，小明超过$$40$$岁； 由第二句话可知，小红不是$$38$$岁，且两人年龄相差不超过$$4$$岁，即小红的年龄大于$$36$$岁； 由第三句话可知，小红的年龄小于$$39$$岁． 则小红的年龄为$$37$$岁． | $$37$$ | TAL-SCQ5K | 小明和小红有如下对话： 小明说：``我没有超过$$40$$岁．'' 小红说：``我$$38$$岁，你至少比我大$$5$$岁．'' 小明说：``你至少$$39$$岁．'' 已知这三句话都是假话，那么小红~\uline{~~~~~~~~~~}~岁．
Options:
- $$37$$
- $$38$$
- $$39$$
- $$41$$ |
One trip to school is 2 * 7 km = 14km.
In one week, Christina walks 14 km/day * 5 days/week = 70km to school.
The extra trip to her mum's friend added 2 km * 2 = 4km to her travel distance.
Her total distance was thus 70 km + 4 km = 74 km | 74 | gsm8k | Christina walks 7km to school every day from Monday to Friday. She returns home covering the same distance. Last Friday her mother asked her to pass by her friend, which is another 2km away from the school in the opposite distance from home. How many kilometers did Christina cover that week? |
One year is 12 months, so during the first year, Kate spent $5/month * 12 months/year = $60/year on the tickets.
After that, she went to the museum for 3 years - 1 year = 2 more years.
During this time, she visited the museum 2 years * 4 visits/year = 8 visits.
She had to pay the higher price of $7, so she spent $7/visit * 8 visits = $56 in two last years.
In total Kate paid $56 + $60 = $116 during 3 years. | 116 | gsm8k | Kate loves painting. She decided to go to an Art-museum in her city. The entrance fee is $5. Kate loved the visit so much, that she decided to go there once a month. After 1 year, the ticket price increased to $7 and Kate decided she is going to visit the museum only 4 times a year. How much did Kate pay for all visits to the Art-museum after 3 years of visiting? |
In the mesosphere, temperature decreases as altitude increases. | B | quartz | If a person went higher into the mesosphere, would the temperature
Options:
A: increase
B: decrease |
The number of seats sold was 0.75*60,000=45,000.
And 45,000-5,000=40,000. | 40,000 | gsm8k | The stadium seats 60,000 fans, but only 75% of the seats were sold for the music show. Because of the threat of rain, 5,000 fans stayed home. How many attended the show? |
NA | D | TAL-SCQ5K | Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating $3$ inches of pasta from the middle of one piece. In the end, he has $10$ pieces of pasta whose total length is $17$ inches. How long, in inches, was the piece of pasta he started with?
A) $$34$$
B) $$38$$
C) $$41$$
D) $$44$$
E) $$47$$ |
The first 10 floors are 10*12=120 feet
There are a remaining 20-10=10 stories
They are each 12+3=15 feet
So those stories are 15*10=150 feet
So the total height is 120+150=270 feet | 270 | gsm8k | James builds a 20 story building. The first 10 stories are each 12 feet tall each. The remaining floors are each 3 feet taller. How tall is the building? |
Julia buys 4 * 3 = 12 pens
Dorothy buys 12/2 = 6 pens
The total number of pens purchased is 4 + 12 + 6 = 22 pens
The total cost of the pens is 22 * $1.50 = $33 | 33 | gsm8k | Dorothy, Julia, and Robert go to the store to buy school supplies. Dorothy buys half as many pens as Julia. Julia buys three times as many pens as Robert. Robert buys 4 pens. If one pen costs $1.50, how much money did the three friends spend in total on pens? |
There are 21*2=42 polar bears
So the total 21+42=63 total animals | 63 | gsm8k | A zoo has 21 penguins and twice as many polar bears? How many total animals do they have? |
During one minute the metro sells 5 tickets, so they earn 5 * 3 = $15.
So in 6 minutes they would earn 15 * 6 = $90. | 90 | gsm8k | One ticket to the underground costs $3. In one minute, the metro sells an average of 5 such tickets. What will be the earnings from the tickets in 6 minutes? |
Jalapeno peppers contain capsaicin. Capsaicin creates a burning sensation in the eyes and can lead to surface injuries. Small children do not understand how to protect themselves from peppers or how to wash their hands properly. | Yes | strategyqa | Can children be hurt by jalapeno peppers? |
Groundhog Day is an American tradition that occurs on February 2nd. Groundhog Day derives from a superstition that if a groundhog sees it's shadow it will mean there are six more weeks of winter. People living in the southern hemisphere of the world experience summer while the people in the north experience winter. Different global cultures define the dates of seasons differently. | No | strategyqa | Is groundhog day used as a global season indicator? |
At higher temperatures, particles of reactants have more energy, so they move faster. They are more likely to bump into one another and to collide with greater force. | a | quartz | A particle that is in the desert is likely _____ compared to one in the arctic.
Options:
a. faster
b. slower |
If the electric oven uses power worth $500 in a month, twice what Joseph pays for the power the water heater uses, Joseph pays 1/2*$500=$250 for power used by the water heater.
The total amount of money that Joseph pays for the power used by the water heater and the electric oven is $250+$500 = $750
The total amount of money that Joseph pays for the energy used by the refrigerator is three times the amount he pays for the power used by the water heater, a total of 3*$250=$750
For the three gadgets, Joseph pays $750+$750 = $1500 for the power they use. | 1500 | gsm8k | Joseph has a refrigerator, a water heater in his house, and an electric oven that consumes power at different rates. The total amount of money that Joseph pays for the energy used by the refrigerator is three times the amount he pays for the power used by the water heater. If the electric oven uses power worth $500 in a month, twice what Joseph pays for the power the water heater uses, calculate the total amount he pays for the power used by these gadgets. |
\hfill\break 【分析】\\ 根据二次函数的图象与性质可进行排除选项．\\ 【详解】\\ 解：由二次函数$y=x^{2}+2x+c$可知开口向上，对称轴为直线$x=-1$，\\ 当$x\textless{} -1$时，$y$随$x$的增大而减小，当$x\textgreater{} -1$时，\emph{y}随\emph{x}的增大而增大；\\ ∵$A\left(x_{1},0\right)$，$B\left(x_{2},0\right)$是二次函数与\emph{x}轴的交点，点$P\left(m,n\right)$是图象上的一点，\\ ∴当$n\textgreater{} 0$时，则$m\textless{} x_{1}$或$m\textgreater{} x_{2}$；故$\mathrm{A}$、$\mathrm{B}$选项错误；\\ 当$n\textless{} 0$时，则$x_{1}\textless{} m\textless{} x_{2}$，故$\mathrm{D}$正确；当$x_{2}\textgreater{} 0$且$n\textless{} 0$时，此时有可能$m\textgreater{} 0$，故$\mathrm{C}$错误；\\ 故选$\mathrm{D}$．\\ 【点睛】\\ 本题主要考查二次函数的图象与性质，熟练掌握二次函数的图象与性质是解题的关键． | [d] | TAL-SCQ5K | 二次函数$y=x^{2}+2x+c$的图象与\emph{x}轴的两个交点为$A\left(x_{1},0\right)$，$B\left(x_{2},0\right)$，且$x_{1}\textless{} x_{2}$，点$P\left(m,n\right)$是图象上一点，那么下列判断正确的是（~~~~~~~）
Options:
[a] 当$n\textgreater{} 0$时，$m\textless{} x_{1}$
[b] 当$n\textgreater{} 0$时，$m\textgreater{} x_{2}$
[c] 当$n\textless{} 0$时，$m\textless{} 0$
[d] 当$n\textless{} 0$时，$x_{1}\textless{} m\textless{} x_{2}$ |
Applying for a job and not hearing back from the company is disheartening because it makes it seem like the company is not interested in the applicant | Yes | FLUTE | Given the statement "I was upset not to get a response back from a company that I applied for a job at", is the statement "I was disheartened not to get a response back from the company after applying for the job" is true?
- Yes
- No
- I don't know |
Randy has only half as many water balloons as Janice’s 6, for a total of (½)*6=3 water balloons.
Cynthia has 4 times as many water balloons as Randy, for a total of 4*3=12 water balloons | 12 | gsm8k | Cynthia has four times as many water balloons as her husband, Randy. Randy has only half as many water balloons as his daughter, Janice. If Janice throws all 6 of her water balloons at her father, how many water balloons does Cynthia have, which she could also choose to throw at Randy? |
$$1138 →1\times1\times3\times8=24$$ $$1226 →1\times2\times2\times6=24$$ $$1324 →1\times3\times2\times4=24$$ $$1416~→1\times4\times1\times6=24$$ $$1854 →1\times8\times5\times4=160$$ $$1854$$ is the odd one out as the product of its digits is not $$24$$. | (5) | TAL-SCQ5K | Which of the following numbers is the odd one out?
(1) $$1138$$
(2) $$1226$$
(3) $$1324$$
(4) $$1416$$
(5) $$1854$$ |
The idiom charity begins at home means that one should help family and close friends before helping others, but the contradiction is that helping strangers should be your priority. | No | FLUTE | Given the statement "What about the idea that helping strangers should be your priority?", is the statement "What about the idea that charity begins at home?" is true?
- Yes
- No
- I don't know |
The more curved the surface of a lens is, the more it refracts light. | 1 | quartz | If a lens gains more curvature, it will refract _____ light.
1: more
2: less |
Milk that has expired is not safe to drink and gross and therefore finding it and being excited about it makes no sense. | No | FLUTE | Given the statement "I found some heavily expired milk in the back of the fridge at work and it was super gross.", is the statement "I was excited to find this milk that expired two months ago and it made me really thirsty for it." is true?
- Yes
- No
- I don't know |
Ellie needs 2 wheels * 10ml of oil per wheel = 20ml of oil.
To fix the rest of the bike as well, she needs 20 + 5 = 25ml of oil. | 25 | gsm8k | Ellie has found an old bicycle in a field and thinks it just needs some oil to work well again. She needs 10ml of oil to fix each wheel and will need another 5ml of oil to fix the rest of the bike. How much oil does she need in total to fix the bike? |
A sloth is a slow-moving mammal, especially compared to racers on a racetrack | False | FLUTE | Context: "You're always too fast, no matter how many times you try."
Hypothesis: No matter how many times you try you're always like a sloth at a racetrack.
Based on the context, is the hypothesis true, false, or unknown? |
Aerosmith is a rock band with five members. Carpool lanes require at least two occupants in each vehicle. | Yes | strategyqa | Can Aerosmith legally drive in the carpool lane? |
Each tree A gives her six good oranges a month 10 x .6 = 6
Each tree B gives her five good oranges a month because 15 x (1/3) = 5
On average, a tree gives her 5.5 oranges a month because .5(6) + .5(5) = 5.5
She has ten total trees because 55 / 5.5 = 10 | 10 | gsm8k | Salaria is growing oranges this summer. She bought two types of trees. She has 50% of tree A and 50% of tree B. Tree A gives her 10 oranges a month and 60% are good. Tree B gives her 15 oranges and 1/3 are good. If she gets 55 good oranges per month, how many total trees does she have? |
The group was able to sell 20 x 8 = 160 candy bars.
So, they got 160 x $0.5 = $80 from their candy bars sales. | 80 | gsm8k | During a fundraiser, each of the 20 members of a group sold candy bars which costs $0.50 each. If each member sold an average of 8 candy bars, how much money did they earn from their candy bars sales, in dollars? |
Kiley takes 48/4=12 crayons
48-12=36 crayons remain
Joe takes 36/2=18 crayons
36-18=18 crayons left | 18 | gsm8k | There are 48 crayons in the box. Kiley takes 1/4 of them away. Joe takes away half of the remaining crayons, how many crayons are left? |
Kendra made 2*6=12.
Mari made 4+5*12=64. | 64 | gsm8k | Mari made 4 more than five times as many decorated buttons as Kendra. Sue made half as many as Kendra. Sue made 6 buttons. How many did Mari make? |
The second earthquake caused 2 * 4 = 8 buildings to collapse.
The third earthquake caused 2 * 8 = 16 buildings to collapse.
The fourth earthquake caused 16 * 2 = 32 buildings to collapse.
Including the first earthquake, the earthquakes caused 4 + 8 + 16 + 32 = 60 buildings to collapse. | 60 | gsm8k | An earthquake caused four buildings to collapse. Experts predicted that each following earthquake would have double the number of collapsing buildings as the previous one, since each one would make the foundations less stable. After three more earthquakes, how many buildings had collapsed including those from the first earthquake? |
Kimberly's brother picked 3 x 15 = 45 strawberries.
Kimberly picked 8 x 45 = 360 strawberries.
Kimberly's parents picked 360 - 93 = 267 strawberries.
Altogether, they picked 45 + 360 + 267 = 672 strawberries.
Each of them will have 672/4 = 168 strawberries. | 168 | gsm8k | Kimberly went strawberry picking with her family over the weekend. She picked 8 times the amount of strawberries her brother picked and her parents picked 93 strawberries less than her. If her brother picked 3 baskets each containing 15 strawberries, how many strawberries would they each have if they divide the total number of strawberries equally amongst them? |
Chicken feed is a small amount of money, so if something looks like chicken feed, it is insignificant compared to another person or thing. | True | FLUTE | Context: "He mentioned that his inheritance made Jonathan/Elliott's look like a very small amount of money."
Hypothesis: He mentioned that his inheritance made Jonathan/Elliott's look like chicken feed.
Based on the context, is the hypothesis true, false, or unknown? |
Rudy first runs for 5 * 10 = 50 minutes.
Then Rudy runs for 4 * 9.5 = 38 minutes.
Rudy runs for a total length of 50 + 38 = 88 minutes | 88 | gsm8k | Rudy runs 5 miles at a rate of 10 minutes per mile. Later he runs 4 miles at a rate of 9.5 minutes per mile. What is the total length of time that Rudy runs? |
A person's phone is often very important to them and so breaking it would be a terrible thing, which is not expressed by the use of the word thrilled. | False | FLUTE | Context: "My friend broke my phone that I had worked hard to buy" Claim: "My friend broke my phone that I had just saved up to buy and now I'm just thrilled"
Considering the context, is the claim true, false, or unknown? |
Finding a hair in food is usually considered to be gross and unappetizing, so it would not make someone pleased. | Yes | FLUTE | Given the statement "There was a hair baked into one of my raviolis , super long and not mine at all.", is the statement "Was pleased to find an odd hair baked into one of my raviolis and it definitely was not mine" wrong?
- Yes
- No
- Unknown |
Martin Luther was a Catholic friar that began the movement of Protestantism after he aired several grievances against the church. Martin Luther King Jr. was a Baptist minister. Baptists form a major branch of Protestantism. Baptists trace their Protestantism to the English Separatist movement of the 1600s. Martin Luther lived from 1483-1546. | No | strategyqa | Was Martin Luther same sect as Martin Luther King Jr.? |
The closer objects are to each other, the stronger the gravitational force between them. | (2) | quartz | Objects moving farther apart will have _____ gravitational force between them.
Options:
(1) more
(2) less |
观察这组式子可知两加数分别由两组等差数列组成，且和亦为等差数列 第一组:4，5，6，7，\ldots 公差1; 第二组:2，8，14，20，\ldots 公差6; 各组和:6，13，20，27，\ldots 公差7; 因此，当和为83时，可求得项数为$$(83-6)\div 7+1=12$$所以第12项的算式为:$$\left[ 4+\left( 12-1 \right)\times 1 \right]+\left[ \left( 12-1 \right)\times 6+2 \right]=15+68$$，选B | (b) | TAL-SCQ5K | 下面的算式是按一定的规律排列的:$$4+2$$，$$5+8$$ ，$$6+14$$，$$7+20\cdots $$那么和为83的算式是( ).
Options:
(a) $$16+67$$
(b) $$15+68$$
(c) $$14+69$$
(d) $$17+66$$ |
Brenden caught 8 fish in the morning + 5 in the afternoon = 13 fish.
After throwing the small fish back, Brenden has 13 – 3 = 10 fish.
Together, Brenden and his dad caught 10 + 13 = 23 fish. | 23 | gsm8k | Brendan went fishing with his dad. Brenden caught 8 fish in the morning. He threw 3 back that were too small. He caught 5 more in the afternoon. Brendan’s dad caught 13 fish. How many fish did they catch in all? |
The Botany Swarm is a hockey team based in Auckland, New Zealand. John Key is the Prime Minister of New Zealand. | Yes | strategyqa | Could a fan of the Botany Swarm vote for John Key? |
If someone is constantly asking for help it can be seen as annoying and a nuisance because it's interrupting what the other person is doing | Yes | FLUTE | Context: I have someone always asking me questions about how to use mobile.
Hypothesis: Constantly pestered by someone for help to use their mobile phone correctly is really getting on my nerves.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
The Joy of Painting is hosted by painter Bob Ross. Bob Ross died in 1995. The episodes currently airing are reruns. | No | strategyqa | Is The Joy of Painting TV show still producing new episodes? |
The Statue of Liberty rises 305 feet into the air. The Statue of Unity is 597 feet high. The Lighthouse of Alexandria was between 338 and 387 feet tall. | No | strategyqa | Is Statue of Unity hypothetically more level with Statue of Liberty than Lighthouse of Alexandria? |
Each year Tony has one more fish than before because 2 - 1 = 1
In five years, he will have 5 more fish because 5 x 1 = 5
In five years he will have 7 fish because 2 + 5 = 7 | 7 | gsm8k | Tony has two fish. Every year, his parents buy him two more, but one of them dies. How many fish will he have in five years? |
To put your best foot forward typically means to try to act as an ideal version of oneself, and in this context it is used to try to impress others. | Yes | FLUTE | Given the statement "So when you do finally have the chance to meet him, it's allowing you to make a great first impression and trying to impress him as much as possible.", is the statement "So when you do finally have the chance to meet him, it's allowing you to put your best foot forward to secure his interest.”" is true?
- Yes
- No
- I don't know |
Phil starts with 10 books and loses 2, for 10-2=8 books
Each of Phil's remaining books has 100 pages, so he has 8*100= 800 pages worth of books | 800 | gsm8k | Phil has 10 books that are all 100 pages each. He moves to a new home and during the move, 2 books are lost. How many pages worth of books does Phil have left? |
Luther has 10 / 2 = 5 pieces made with cashmere.
He has 13 - 10 = 3 pieces made without silk using only cashmere.
Thus, Luther has 5 - 3 = 2 pieces made using a blend of cashmere and silk. | 2 | gsm8k | Luther designs clothes for a high fashion company. His latest line of clothing uses both silk and cashmere fabrics. There are ten pieces made with silk and half that number made with cashmere. If his latest line has thirteen pieces, how many pieces use a blend of cashmere and silk? |
$$7\times 7-7=7\times \left( 7-1 \right)=7\times 6=42$$，提取公因数后发现$$\text{D}$$式变为$$7\times 6$$，而非原式的$$6.9\times 7$$，所以错误． 故选$$\text{D}$$． | d | TAL-SCQ5K | 小机灵在用计算器计算``$$6.9\times 7$$''时，发现计算器的键``$$6$$''坏了，小机灵想到了四种不同的输入方法．请你判断一下，下面选项中的方法是错误的
a) $$2.3\times 3\times 7$$
b) $$13.8\times 7\div 2$$
c) $$2\times 3\times 7+0.9\times 7$$
d) $$7\times 7-7$$ |
To be under the gun means to be in a stressful situation that requires quick action, which is what he was feeling when he fished in the glove compartment. | Yes | FLUTE | Consider the statement "He fished in the glove compartment, feeling stressed because he had to act quickly, and brought out shane's wayfarers.". Based on this "He fished in the glove compartment, under the gun, and brought out shane's wayfarers." a true statement? Yes, no, or I don't know? |
Add the two equations. $$ 2 a^{2}+2 b^{2}+2 c^{2}-2 a b-2 a c-2 b c=14 . $$ Now, this can be rearranged and factored. $$ \begin{aligned} \&\left(a^{2}-2 a b+b^{2}\right)+\left(a^{2}-2 a c+c^{2}\right)+\left(b^{2}-2 b c+c^{2}\right)=14 \textbackslash\textbackslash{} \&(a-b)^{2}+(a-c)^{2}+(b-c)^{2}=14 \end{aligned} $$. $a, b$, and $c$ are all integers, so the three terms on the left side of the equation must all be perfect squares. We see that the only is possibility is $14=9+4+1$ $(a-c)^{2}=9 \Rightarrow a-c=3$, since $a-c$ is the biggest difference. It is impossible to determine by inspection whether $a-b=1$ or 2 , or whether $b-c=1$ or 2 . We want to solve for $a$, so take the two cases and solve them each for an expression in terms of $a$. Our two cases are $(a, b, c)=(a, a-1, a-3)$ or $(a, a-2, a-3)$. Plug these values into one of the original equations to see if we can get an integer for $a$. $a^{2}-(a-1)^{2}-(a-3)^{2}+a(a-1)=2011$, after some algebra, simplifies to $7 a=2021$. 2021 is not divisible by 7 , so $a$ is not an integer. The other case gives $a^{2}-(a-2)^{2}-(a-3)^{2}+a(a-2)=2011$, which simplifies to $8 a=2024$. Thus, $a=253$. | $$253$$ | TAL-SCQ5K | Let $a, b$, and $c$ be positive integers with $a \geq b \geq c$ such that $a^{2}-b^{2}-c^{2}+a b=2011$ and $a^{2}+3 b^{2}+3 c^{2}-3 a b-2 a c-2 b c=-1997$. What is $a$?
- $$249$$
- $$250$$
- $$251$$
- $$252$$
- $$253$$ |
For $x = \frac{t + 1}{t}$ and $y = \frac{t - 1}{t},$
\[x + y = \frac{t + 1}{t} + \frac{t - 1}{t} = \frac{2t}{t} = 2.\]Thus, all the plotted points lie on a line. The answer is $\text{(A)}.$ | $\text{(A)$ | competition-math | For real numbers $t
eq 0,$ the point
\[(x,y) = \left( \frac{t + 1}{t}, \frac{t - 1}{t} \right)\]is plotted. All the plotted points lie on what kind of curve?
(A) Line
(B) Circle
(C) Parabola
(D) Ellipse
(E) Hyperbola
Enter the letter of the correct option. |
$20\%$ of $200$ is $40$. So the new train goes $200+40=240$ miles. | $240$ | competition-math | A new train goes $20\%$ farther than an older train in the same amount of time. During the time it takes the older train to go 200 miles, how many miles can the newer train complete? |
Countries with more industry produce more hazardous wastes than those with little industry. | (B) | quartz | Will lives in England and Tony lives in Ethiopia. Whose country likely produces more hazardous waste?
(A) Tony
(B) Will |
If we let $y=z^2$, then our equation becomes a simple quadratic equation:
$$y^2-4y+3=0.$$Indeed, this equation factors easily as $(y-3)(y-1)=0$, so either $y-3=0$ or $y-1=0$.
We now explore both possibilities.
If $y-3=0$, then $y=3$, so $z^2=3$, so $z=\pm\sqrt 3$.
If $y-1=0$, then $y=1$, so $z^2=1$, so $z=\pm 1$.
Thus we have four solutions to the original equation: $z=-\sqrt{3,-1,1,\sqrt{3}}$. | $-\sqrt{3$ | competition-math | Find all values of $z$ such that $z^4 - 4z^2 + 3 = 0$. Enter all the solutions, separated by commas. |
The cost for making one birdhouse is $1.50 x 7 = $10.50.
So the selling price of one birdhouse is $10.50 + $5.50 = $16.
Thus, Denver will charge Danny $16 x 2 = $32 for the two birdhouses. | 32 | gsm8k | Denver uses 7 pieces of wood for each birdhouse and he pays $1.50 for each piece of wood. If he makes a $5.50 profit per birdhouse, how much will Denver charge to Danny for buying two birdhouses? |
A son throwing a pillow at his sister while she is eating is not good behavior and instead indicates that the parents have not been able to instill good values in their children. | False | FLUTE | Context: "My son threw a pillow at my daughter while she was eating some pasta."
Hypothesis: My son threw a pillow at my daughter while she was eating some pasta and it made me so happy about my parenting skills
Based on the context, is the hypothesis true, false, or unknown? |
Something that smells of the lamp has been worked on for too long and is now stale, but this context describes something that was worked on for too short | False | FLUTE | Context: "As a whole, it smells like it was worked on for too short and is still fresh." Claim: "As a whole, it rather smells of the lamp to me."
Considering the context, is the claim true, false, or unknown? |
71 + 9 = 80 80 $\div $ 2 = 40 | b | TAL-SCQ5K | The sum of two numbers is $$71$$. The difference of the two numbers is $$9$$. Find the bigger number.
Options:
a. $$31$$
b. $$40$$
c. $$62$$
d. $$80$$ |
∵$$y=-2x^{2}-4x-1$$ $$=-2(x^{2}+2x+1)+1$$ $$=-2(x+1)^{2}+1$$ ∴二次函数的对称轴为直线$$x=-1$$且$$a=-2\textless0$$， ∴当$$-3\leqslant x\leqslant -1$$时， $$y$$随$$x$$的增大而增大， ∴最大值为：$$1$$， 最小值为：$$-2(-3+1)^{2}+1=-7$$， 当$$-1\textless x\leqslant 0$$时， $$y$$随$$x$$的增大而减小， 此时最小值为：$$-2(0+1)^{2}+1=-1$$， ∴综上，最小值为$$-7$$，最大值为$$1$$， ∴他们之和为：$$-7+1=-6$$， 故选$$\text{A}$$． | 1 | TAL-SCQ5K | 函数$$y=-2x^{2}-4x-1(-3\leqslant x\leqslant 0)$$的最大值与最小值之和是．
1. $$-6$$
2. $$-3$$
3. $$0$$
4. $$-8$$ |
Drivers who drive slow in the left lane and prevent other drivers from passing them are causing a hindrance and so it should bother the person affected by it. | No | FLUTE | Context: I just hate when people drive slow in the left lane
Hypothesis: I'm really joyful when people drive slow in the left lane and prevent me from passing them
Given this context, is the hypothesis true (Yes/No/I don't know)? |