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By Vieta's formulas, $rst = \frac{6}{2} = 3.$
|
$3$
|
competition-math
|
Let $r,$ $s,$ $t$ be the roots of $2x^3 - 7x^2 - 6 = 0.$ Find $rst.$
|
Solving a sudoku puzzle requires the use of logic and a basic understanding of numbers. Infants are too young to understand the numerical system involved in sudoku.
|
No
|
strategyqa
|
Could an infant solve a sudoku puzzle?
|
Full Equipment Price for one player: $25 + $15.20 + $6.80 = $47
Prices for full equipment for 16 people: 16 players x $47/player = $752
|
752
|
gsm8k
|
The treasurer of a football team must buy equipment for the sixteen players of his team. Each piece of equipment consists of a $25 jersey, a $15.20 pair of shorts and a pair of socks at $6.80. How much does all the equipment of all the players on the team cost?
|
triangle: 7-4=3 square: 9-3=6
|
e
|
TAL-SCQ5K
|
insert pic Which number is hidden behind the square?
a) $$2$$
b) $$3$$
c) $$4$$
d) $$5$$
e) $$6$$
|
Ben's spending for the kitchen is $1496 x 1/22 = $68.
Ben's spending for holidays is $1496 x 1/4 = $374.
Ben's spending for children's gifts is $1496 x 1/8 = $187.
The total amount spent is $68 + $374 + $187 = $629.
So, Ben still has $1496 - $629 = $867 left.
|
867
|
gsm8k
|
Ben will receive a bonus of $1496. He chooses to allocate this amount as follows: 1/22 for the kitchen, 1/4 for holidays and 1/8 for Christmas gifts for his 3 children. How much money will he still have left after these expenses?
|
He changed 12*2=24 motorcycle tires
He changed 10*4=40 car tires
So he changed 24+40=64 total tires
|
64
|
gsm8k
|
Mike changes tires on different vehicles. He changes all the tires on 12 motorcycles and all the tires on 10 cars. How many tires did he change?
|
页码问题；$$1\sim 99$$中数字``$$1$$''出现了$$20$$次，$$100\sim 199$$中数字``$$1$$''出现了$$120$$个，剩下的$$200\sim 500$$有$$3\times 20=60$$（个），$$501\sim 513$$中数字``$$1$$''出现了$$6$$次，所以一共有$$20+120+60+6=206$$（次）．
|
1
|
TAL-SCQ5K
|
小明买了一本$$513$$页的小说，数字$$1$$在页码中出现了次．
Options:
1) $$206$$
2) $$203$$
3) $$153$$
4) $$211$$
|
原式$$=\frac{1}{3}-\frac{1}{11}=\frac{8}{33}$$．
|
$$\frac{8}{33}$$
|
TAL-SCQ5K
|
计算：$$\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}+\cdots +\frac{1}{9\times 10}+\frac{1}{10\times 11}=$$（~ ）．
$$\frac{4}{33}$$
$$\frac{2}{33}$$
$$\frac{8}{33}$$
$$\frac{1}{11}$$
|
After increasing the price of a piece of jewelry, the price increased from $30 to $30+$10 = $40 each.
He also increased the price of each painting by 20/100*100 = $20
The total price for buying one painting at the new price is $100+$20 = $120
If a buyer purchases two pieces of jewelry, the total cost becomes 2*$40 = $80
When the buyer also buys 5 paintings, he pays a total of $120*5 = $600
2 pieces of jewelry and 5 paintings cost $600+$80 = $680 at the new prices.
|
680
|
gsm8k
|
Mr. Rocky went to the market to sell his handmade crafts on a particular week. He was selling jewelry at $30 each and paintings at $100 each. However, he realized the income from the sales wasn't worth the labor and materials he had used, so he decided to increase the price of jewelry by $10 each and the cost of each painting by 20%. Calculate the total price a buyer who takes two pieces of jewelry and five paintings would pay
|
（$$1$$）$$1$$个砝码可以称出的重量有$$5$$种：$$1$$克，$$2$$克，$$4$$克，$$8$$克，$$16$$克； （$$2$$）$$2$$个砝码可以称出的重量有$$10$$种： $$1+2=3$$（克），$$1+4=5$$（克），$$1+8=9$$（克）， $$1+16=17$$（克）； $$2+4=6$$（克），$$2+8=10$$（克），$$2+16=18$$（克）； $$4+8=12$$（克），$$4+16=20$$（克）， $$8+16=24$$（克）； （$$3$$）$$3$$个砝码可以称出的重量有$$10$$种： $$1+2+4=7$$（克），$$1+2+8=11$$（克）， $$1+2+16=19$$（克）， $$1+4+8=13$$（克），$$1+4+16=21$$（克）， $$1+8+16=25$$（克）， $$2+4+8=14$$（克），$$2+4+16=22$$（克）， $$2+8+16=26$$（克）， $$4+8+16=28$$（克）； （$$4$$）$$4$$个砝码可以称出的重量有$$5$$种： $$1+2+4+8=15$$（克），$$1+2+4+16=23$$（克）， $$1+2+8+16=27$$（克）， $$1+4+8+16=29$$（克），$$2+4+8+16=30$$（克）； （$$5$$）$$5$$个砝码可以称出的重量有$$1$$种： $$1+2+4+8+16=31$$（克）． 因为$$5+10+10+5+1=31$$（种）， 所以最多可以称出$$31$$种不同的重量，它们是$$1$$克$$-31$$克． 答：最多能称出$$31$$种不同重量的物体． 故选$$\text{D}$$．
|
(4)
|
TAL-SCQ5K
|
现有$$1$$克、$$2$$克、$$4$$克、$$8$$克、$$16$$克的砝码各一个和一个天平，砝码只能放在一边，最多能称出种不同的质量．
(1) $$5$$
(2) $$6$$
(3) $$30$$
(4) $$31$$
|
Farting is a bodily function that is often considered to be embarrassing and disgusting and so doing it in the middle of a speech would not make the moment beautiful but rather ugly.
|
Yes
|
FLUTE
|
Consider the statement "I was in the middle of a speech and I farted.". Is the statement "I farted in the middle of my speech and it totally elevated the beauty the moment" false? Yes/no/unknown
|
设$$10$$年前儿子的年龄是$$x$$岁，那么父亲的年龄是$$7x$$； 根据题意可得： $$7x+10+15=\left( x+10+15 \right)\times 2$$， $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde7x+25=2x+50$$ $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde5x=25$$ $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde x=5$$， 现在儿子的年龄是：$$x+10=5+10=15$$（岁）， 父亲的年龄是：$$7x+10=7\times 5+10=45$$（岁）． $$45\div 15=3$$（倍）． 故选$$\text C$$．
|
(C)
|
TAL-SCQ5K
|
$$10 $$年前父亲的年龄是儿子的$$7$$倍，$$15$$年后父亲的年龄是儿子的$$2$$倍，今年父亲的年龄是儿子的倍．
Options:
(A) $$2$$
(B) $$2.5$$
(C) $$3$$
(D) $$4$$
|
$(84-79)\times6=30$, $79-30=49$.
|
$$49$$
|
TAL-SCQ5K
|
There are $$7$$ numbers with an average of $$79$$. After eliminating a number, the average of the remaining numbers is $$84$$. What is the eliminated number?
* $$6$$
* $$19$$
* $$29$$
* $$49$$
* $$60$$
|
Since I run at a constant pace, we can set up a proportion with one unknown: \begin{align*}
\frac{\text{minutes}}{\text{distance}}&=\frac{\text{minutes}}{\text{distance}}\\
\frac{x}{1\text{ mi}}&=\frac{18\text{ min}}{2\text{ mi}}\\
x&=\frac{18\text{ min}}{2\text{ mi}}\cdot 1\text{ mi}\\
x&=\frac{18\text{ min}}{2}=9\text{ min}\\
x&=9\text{ min}.
\end{align*}
|
$9\text{ min$
|
competition-math
|
I run at a constant pace, and it takes me 18 minutes to run to the store from my house. If the store is 2 miles away, and my friend's house is 1 mile away from my house, how many minutes will it take me to run from my house to my friend's house?
|
Objects that are closer together have a stronger force of gravity between them.
|
(2)
|
quartz
|
As two asteroids drift further apart, does the gravitational force they exert on each other
(1) increase
(2) decrease?
|
As blood glucose levels decrease, less insulin is produced.
|
2
|
quartz
|
Dana has diabetes, and her insulin is low, so her blood glucose levels have
1: increased
2: decreased
|
The more mass a moving object has or the faster its moving, the greater its momentum.
|
more
|
quartz
|
A large object will have _____ momentum than a small object.
Options:
- more
- less
|
More UV rays increase skin cancer rates.
|
1
|
quartz
|
Fran stayed indoors while Geremy went in the sun. Who is less likely to get skin cancer?
Options:
1: Fran
2: Geremy
|
The idiom when all is said and done is used to describe when everything is finished and settled. in this context, it is used to describe how the content you create is the most important thing.
|
Yes
|
FLUTE
|
Given the statement "In the end, it's the content you create that makes the real difference.", what is the statement "when all is said and done, it's the content you create that makes the real difference." true?
- Yes
- No
- Unknown
|
Having to wait for a long time to get food after everyone else has already received theirs can be really frustrating and not at all a good use of time.
|
Yes
|
FLUTE
|
Consider the statement "Everyone ordered and got their food except me.". Is the statement "I was only person who didn't get their food after everyone else already placed their orders which is fine, I just love having loads of my time wasted." false? Yes/no/unknown
|
There are $120 - 30 = 90$ grams that are not filler. So $\frac{90}{120} = 75\%$ is not filler.
|
$75\%$
|
competition-math
|
A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?
|
We have 2 kg = 2 * 1000 = 2000 g
So, the number of bars of chocolate is 2000 / 125 = 16
|
16
|
gsm8k
|
A chocolate bar weighs 125 g. A shopkeeper has just received a 2 kilogram box of chocolate. How many bars does this represent?
|
The more branching there is in isomers, the lower the boiling and melting points are.
|
a
|
quartz
|
Eric added branching isomers to one solution, and left the other solution alone. The isomer solution now has a _____ boiling point.
a: lower
b: higher
|
It is very likely that someone would want to attend their father's birthday party and be happy about being able to make it, so someone saying that they are overjoyed that they will not be able to go is actually being sarcastic.
|
No
|
FLUTE
|
Context: I am worried I will not be able to go to my fathers birthday party.
Hypothesis: I am overjoyed that I will not be able to make it to my fathers birthday party
Given this context, is the hypothesis true (Yes/No/I don't know)?
|
When on a date, it is considered very rude to constantly look at other people and not give the person you are on the date with your full attention
|
No
|
FLUTE
|
Context: I went on a date last night and he kept looking at the hot girl at the table next to us.
Hypothesis: I felt terrible when I noticed my date was constantly checking out the hot girl at the table next to us
Is the hypothesis incorrect? (Yes, no, or unknown)?
|
The more an elastic object is stretched or compressed, the greater its elastic potential energy is.
|
[A]
|
quartz
|
An object with little elastic potential energy _____ be easily stretched.
[A] will
[B] won't
|
Percentage means per 100, so if she still owes 75%, she must have paid 100% - 75% = 25% of the original amount.
25% of the original amount = (25/100)*original amount = $125
Multiplying both sides by (100/25) gives: original amount = (100/25)*$125 = $500
|
500
|
gsm8k
|
Mathilda is determined to pay back the money she owes a friend so she decides to pay an initial installment of $125. If she still has 75% left to pay, how much did she owe originally?
|
角$$DOE$$的对称轴是它的角平分线所在的直线； 等边三角形$$FGH$$的对称轴有三条，它们是三边的垂直平分线； 线段$$MN$$的对称轴是$$MN$$的垂直平分线， 只有直角三角形$$ABC$$不是轴对称图形． 故选$$\text{A}$$．
|
a
|
TAL-SCQ5K
|
下列图形中，不是轴对称图形的是．
a. 直角三角形$$ABC$$
b. 角$$DOE$$
c. 等边三角形$$FGH$$
d. 线段$$MN$$
|
Atherosclerosis is a condition in which the arteries to the heart are blocked. Jellyfish use their guts to circulate nutrients because they do not have hearts.
|
Yes
|
strategyqa
|
Is a jellyfish safe from atherosclerosis?
|
$$7:30$$+$$8$$h$$37$$m=$$16:07$$
|
$$4:07$$ P.M.
|
TAL-SCQ5K
|
A train started from the starting station at 7:30, it takes 8 hours and 37 minutes to arrive at the terminal station. When will it arrive?
$$3:30$$ A.M.
$$3:37$$ P.M.
$$4:37$$ P.M.
$$4:07$$ P.M.
$$4:37$$ A.M.
|
Ada Lovelace died at the age of 36 in 1852. The life expectancy in the 1800s was between 35 and 39 years old. Tuberculosis was one of the leading causes of death in the 1800s and a vaccine was not made until the 1900s.
|
No
|
strategyqa
|
Did Ada Lovelace die tragically young for her era?
|
∵$$441=7\times 7\times 3\times 3$$， 又∵$$a$$，$$b$$，$$c$$，$$d$$互为不相等的正整数， ∴$$a$$，$$b$$，$$c$$，$$d$$为$$21$$，$$7$$，$$3$$，$$1$$， ∴$$a+b+c+d=32$$．
|
$$32$$
|
TAL-SCQ5K
|
$$a$$，$$b$$，$$c$$，$$d$$是互不相等的正整数，且$$abcd=441$$，那么$$a+b+c+d$$的值是（~ ）
Options:
- $$30$$
- $$32$$
- $$34$$
- $$36$$ ~
|
On Tuesday they sold 12*3=36 bouquets
On Wednesday they only sold 36/3=12 bouquets
In total they sold 12+36+12=60 bouquets
|
60
|
gsm8k
|
A floral shop had a three day sale on rose bouquets. On Monday, they sold 12 bouquets. On Tuesday, they sold three times that many bouquets. On Wednesday it rained all day and they only sold a third of what they did the day before. How many bouquets did they sell during the three day sale?
|
A diet is often broken when someone eats something they are not supposed to and in this case, it is a box of chocolates which would make someone feel guilty rather than great about their self control
|
No
|
FLUTE
|
Context: I had a box chocolate when my doctor advised against it.
Hypothesis: I broke my diet by eating a box of chocolates but I feel really great about my self control.
Given this context, is the hypothesis true (Yes/No/I don't know)?
|
原式= $$\left[ \left( 0.8+\frac{1}{5} \right)\times 24+6.6 \right]\div \frac{9}{14}-7.6$$ $$=\left[ (0.8+0.2)\times 24+6.6 \right]\div \frac{9}{14}-7.6$$ $$=\left[ 1\times 24+6.6 \right]\div \frac{9}{14}-7.6$$ $$=30.6\div \frac{9}{14}-7.6$$ $$=30.6\times \frac{14}{9}-7.6$$ $$=47.6-7.6$$ $$=40$$．
|
$$40$$
|
TAL-SCQ5K
|
计算$\left[ \left( 80 \%+\dfrac{1}{5}\right)\times24+6.6\right]\div\dfrac{9}{14}-7.6=$．
$$30$$
$$40$$
$$50$$
$$60$$
|
Half of the 2-hour practice is for running and weightlifting, so the time for running and weight lifting is 1/2 * 2 hours = 1 hour.
If the time he lifts weights is x, then the time he runs is 2x.
So the time for running and weight lifting is x + 2x = 3x = 1 hour
Thus 3x = 60 minutes
Thus x = 60/3 = 20 minutes spent weight lifting.
|
20
|
gsm8k
|
Kyle goes to basketball practice every day for 2 hours. At practice he spends half of the time shooting and the rest of the time running and weight lifting. If he runs for twice the time he spends weightlifting, how much time in minutes does he spend lifting weight?
|
Ken paints 3 tiles/minute + 2 tiles/minute = 5 tiles/minute.
Laura can paint 5 tiles/minute x 2 = 10 tiles/minute.
Kim can paint 10 tiles/minute - 3 tiles/minute = 7 tiles/minute.
All 4 can paint 3 tiles/minute + 5 tiles/minute + 10 tiles/minute + 7 tiles/minute = 25 tiles/minute.
In 15 minutes, they can paint 15 minutes x 25 tiles/minute = 375 tiles.
|
375
|
gsm8k
|
Don can paint 3 tiles a minute, Ken can paint 2 more tiles a minute than Don and Laura can paint twice as many tiles as Ken. Kim can paint 3 fewer tiles than Laura can in a minute. How many tiles can Don, Ken, Laura and Kim paint in 15 minutes?
|
$2400\times2\div(53+47)=48$min
|
2
|
TAL-SCQ5K
|
The distance between the school and the park is $$2400$$ $\text{m}$. Lily and Candy depart from the school towards the park at the same time, and return immediately after arriving at the park. Lily travels $$47$$ $\text{m/min}$, and Candy travels $$53$$ $\text{m/min}$. They will meet each other for the first time after~\uline{~~~~~~~~~~}~minutes.
Options:
1: $$24$$
2: $$48$$
3: $$72$$
4: $$96$$
|
Emmy has 14-6 = 8 iPods left.
Rosa has 8/2 = 4 iPods.
Emmy and Rosa have 8+4 = 12 iPods together.
|
12
|
gsm8k
|
Emmy has a collection of 14 iPods. She loses 6 out of the 14 she had but she still has twice as many as Rosa. How many iPods does Emmy and Rosa have together?
|
Michael Bloomberg is worth an estimated 60 billion dollars as of 2020. Micronesia has annual expenses of nearly 200 million dollars.
|
Yes
|
strategyqa
|
Can Michael Bloomberg fund the debt of Micronesia for a decade?
|
Its common to feel upset and disappointed after finding out that you were not selected for a job that you really wanted
|
No
|
FLUTE
|
Context: I just received a phone call that I didn't get the job I applied for.
Hypothesis: I was devastated to receive a call that I didn't get the job that I wanted so much
Is the hypothesis incorrect? (Yes, no, or unknown)?
|
The trade-off when the threads are closer together, is that more turns of the screw or bolt are needed to do the job because the distance over which the input force must be applied is greater.
|
A
|
quartz
|
If you need to turn a screw a few times that requires
Options:
A: less force
B: more force
|
A walrus is a very large, ungainly creature, so to say that someone is as graceful as a walrus would be to say that they are not graceful at all.
|
No
|
FLUTE
|
Given the statement "you are not graceful", is the statement "You are as graceful as a walrus" wrong?
- Yes
- No
- Unknown
|
Of the options given, $$23\times 34$$, $$56\times 67$$ and $$67\times 78$$ are all not divisible by $$5$$, so may be discounted. Also $$34$$ is not divisible by $$4$$ and $$45$$ is odd, so $$34\times 45$$ may also be discounted as it is not divisible by $$4$$. The only other option is $$45\times 56$$. As a product of prime factors, $$45\times 56=2^{3}\times3^{2}\times5\times7$$, so it is clear that it is divisible by all of the integers from $$1$$ to $$10$$ inclusive.
|
C
|
TAL-SCQ5K
|
Which of the following is divisible by all of the integers from $$1$$ to $$10$$ inclusive?
A: $$23\times34$$
B: $$34\times45$$
C: $$45\times56$$
D: $$56\times67$$
E: $$67\times78$$
|
A great ride means that it is a really good experience, like how a heavenly ride would be.
|
True
|
FLUTE
|
Context: "You will love the new train it is a great ride that it offers."
Hypothesis: You will love the new train. it is a heavenly ride.
Based on the context, is the hypothesis true, false, or unknown?
|
The cost of the apples was $12 / 2 = $6.
When the cost of 3 kg of apples was $6, then the cost of 1 kg of apples was $6 / 3 kg = $2/kg.
|
2
|
gsm8k
|
Betty bought 1 kg of oranges and 3 kg of apples. The total cost of oranges was $12. The apples were two times cheaper than the oranges. How much did Betty pay for 1 kg of apples?
|
The closer to pH 14, the more strongly basic the solution.
|
B
|
quartz
|
If Jim brings his solution closer to pH 14, what happens to the solution?
A) becomes less basic
B) becomes more basic
|
Here, one statement states that the other person actually supported the author's argument and reassured them of its validity, which is opposite of the other statement - attacking every points of the argument.
|
No
|
FLUTE
|
Consider the staetement "He supported my argument and reassured me of its validity.". Based on this statement, is "He attacked every weak point in my argument." a true statement? Yes/no/unknown
|
由前$$11$$场的总分减去前$$10$$场的总分即为第$$11$$场的得分：$$34\times 11-333=374-333=41$$分．
|
$$41$$
|
TAL-SCQ5K
|
库里是美国NBA勇士队当家球星, 在过去的$$10$$场比赛中已经得了$$333$$分的高分, 他在第$$11$$场得（ ）分就能使前$$11$$场的平均得分达到$$34$$分．
Options:
$$35$$
$$40$$
$$41$$
$$47$$
|
He tears 30*3=90 cards a week
He bought 55*18=990 cards
So he can tear for 990/90=11 weeks
|
11
|
gsm8k
|
Jame is trying to learn to tear playing cards. He can tear 30 cards at a time. A new deck of cards has 55 cards if you include the jokers and blank cards. He tears cards 3 times a week. If he buys 18 decks how many weeks can he go?
|
We have that $\cot 45^\circ = \frac{1}{\tan 45^\circ} = 1.$
|
$1$
|
competition-math
|
Find $\cot 45^\circ.$
|
If you are standing on the shore and a ship is going out to sea, the ship gets smaller as it moves further away from you.
|
smaller
|
quartz
|
When we see something far away it looks
Options:
bigger
smaller
|
Any nonzero number raised to the zeroth power is $1.$
|
$1$
|
competition-math
|
What is $\left(\dfrac{9819156364}{-24635745744574}\right)^0$?
|
If the rabbit food costs $12 a week, then the parrot food costs $30 - $12 = $18 a week.
Julia has the parrot for 3 weeks, so she spent 3 weeks * $18/week = $54 on her.
The rabbit is her only for 5 weeks, so she spent 5 weeks * $12/week = $60 on him.
In total, Julia spent $54 + $60 = $114 on food for her animals.
|
114
|
gsm8k
|
Julia has a parrot and a rabbit. She buys food for both of the animals for $30 in total a week. Julia has the rabbit for 5 weeks, and the parrot for 3 weeks. How much money did Julia already spend on food for her animals, if the weekly cost of the rabbit food is $12?
|
The chicken lost 23 * 2 = 46 feathers on its second road crossing.
Thus, it had 5263 - 46 = 5217 feathers after crossing the road twice.
|
5217
|
gsm8k
|
The chicken crossed the road to get to the other side twice for the thrill of it. The first time, it had to dodge 23 speeding cars. The second time, a person tried to catch it and accidentally pulled out twice as many feathers as the number of cars the chicken had dodged. The chicken had 5263 feathers before its thrill-seeking road crossings. How many feathers did it have afterward?
|
It is often considered rude to take the last of the food without asking and so people usually feel guilty when they do it, especially if they have to sneak it out
|
True
|
FLUTE
|
Context: "While everyone was getting ready to leave and they weren't looking, I snuck the rest of the leftover pizza in my purse and slid out!"
Hypothesis: I felt horribly guilty as I snuck the leftover pizza in my purse and slid out when everyone was getting ready to leave
Based on the context, is the hypothesis true, false, or unknown?
|
Let $r$ represent the number of red balls in the bag. The probability that the first ball is red is $\frac{r}{10}$, while the probability that the other ball is red becomes $\frac{r-1}{9}$ (drawing two balls at random at the same time is similar to drawing one ball and then drawing another ball without replacement). So the probability that both balls are red is $\frac{r}{10}\cdot\frac{r-1}{9}$, which we set equal to $\frac{1}{15}$. \begin{align*}
\frac{r}{10}\cdot\frac{r-1}{9}&=\frac{1}{15}\quad\Rightarrow\\
r(r-1)&=\frac{90}{15}\quad\Rightarrow\\
r^2-r-6&=0\quad\Rightarrow\\
(r-3)(r+2)&=0
\end{align*} The value of $r$ cannot be negative, so $r=3$. There are $3$ red balls in the bag.
|
$3$
|
competition-math
|
A bag contains ten balls, some of which are red and the rest of which are yellow. When two balls are drawn at random at the same time, the probability that both balls are red is $\frac{1}{15}$. How many balls in the bag are red?
|
As the distance between the objects increases the magnetic force of attraction decreases.
|
a
|
quartz
|
Lisa is hitting a tennis ball against the wall. As the tennis ball bounces towards the wall and away from her, the magnetic force of attraction between the wall and the ball
a. increases
b. decreases.
|
Armadillos have hard armor made of dermal bone. Humans have ended up in the hospital due to bullets ricocheting against an armadillo's shell.
|
Yes
|
strategyqa
|
Could someone theoretically use an armadillo as a shield?
|
She will read 20 pages / 4 = 5 pages for English.
She will read 16 pages / 4 = 4 pages for Science.
She will read 8 pages / 4 = 2 pages for Civics.
She will read 12 pages / 4 = 3 pages for Chinese.
Melody will read a total of 5 pages + 4 pages + 2 pages + 3 pages = 14 pages tomorrow.
|
14
|
gsm8k
|
Melody needs to read 20 pages for her English class, 16 pages for her Science class, 8 pages for her Civics, and 12 pages for Chinese class. She decided to read one-fourth of the number of pages for each class tomorrow. How many pages will she read tomorrow?
|
Objects with greater mass have greater inertia.
|
B
|
quartz
|
When something is very lightweight what does it need to move?
A) more inertia
B) less inertia
|
She has 24 classmates and wants to give each 10 cookies, so she needs to bake 24*10=240 cookies
Each batch makes 4 dozen cookies so that means each batch has 4*12 = 48 cookies
She baked 2 batches of chocolate chip and one batch of oatmeal raisin so 2+1 = 3 batches
We know that each batch has 48 cookies so 3*48 = 144 cookies have been baked
She needs to have 240 cookies and has baked 144 so 240-144 = 96 cookies are needed
Again, each batch makes 48 cookies and we need 96 more cookies so 96/48 = 2 more batches are needed
|
2
|
gsm8k
|
Linda was going to pass out homemade cookies to each of her 24 classmates on the last day of school. She wanted to give each student 10 cookies and wanted to make chocolate chip cookies and oatmeal raisin cookies. Each cookie recipe made exactly 4 dozen cookies. She was able to make 2 batches of chocolate chip cookies before running out of chocolate chips. She made 1 batch of oatmeal raisin cookies. How many more batches of cookies does Linda need to bake?
|
Parents are not supposed to be proud of their children when they lie, but instead should teach them the importance of honesty and why it is wrong to lie.
|
No
|
FLUTE
|
Consider the statement "So my daughter totally lied through her teeth right to my face yesterday.". Based on this "So proud of my daughter who blatantly lied to me straight in the face yesterday" a true statement? Yes, no, or I don't know?
|
A $$90\textbackslash\%$$ decrease means $$10\textbackslash\%$$ of $$250000 = 250000 \div 10 = 25000$$ of the lions remain.
|
A
|
TAL-SCQ5K
|
In $$1975$$ it was estimated that there were $$250000$$ lions in Africa. Over $$40$$ years this figure has decreased by $$90\textbackslash\%$$. What is the current estimate for the number of lions in Africa ?
Options:
A) $$25000$$
B) $$100000$$
C) $$160000$$
D) $$225000$$
E) $$275000$$
|
Light-skinned people get sunburned more quickly than people with darker skin.
|
a
|
quartz
|
If Milo has dark skin and Jerry has light skin, which person will sunburn less easily?
a: Milo
b: Jerry
|
Breast cancer is rare in teens. It becomes more common as women get older.
|
[A]
|
quartz
|
What happens to Susie's chance of contracting breast cancer as she gets older?
[A] increases
[B] decreases
|
$6x-3y=2$, $y=2x-\frac{2}{3}$, Its $y$-intercept is $-\frac{2}{3}$.
|
B
|
TAL-SCQ5K
|
Match the linear equation, $6x-3y=2$, with its corresponding $y$-intercept.
A: $\frac{2}{3}$
B: $-\frac{2}{3}$
C: $$2$$
D: $$6$$
|
To go dutch means to divide a check or bill evenly, but in this sentence one person is paying for the entire check
|
False
|
FLUTE
|
Context: "It had decent food that wasn't too expensive, so you could have one person pay for the entire check and not break anyone's budget." Claim: "It had decent food that wasn't too expensive, so you could go dutch and not break anyone's budget."
Considering the context, is the claim true, false, or unknown?
|
Bases have pH values above 7. The higher the pH value, the more strongly basic the substance.
|
lower?
|
quartz
|
Compared to vinegar, which is an acid, would lye, which is a weak base, have a pH value that is
higher
lower?
|
Since 5 rooms have 4 windows, this accounts for 20 windows because 4*5=20 windows.
Since 8 rooms have 3 windows, this accounts for 24 windows because 8*3=24 windows.
There are 78 windows left over because 122-20-24 = 78.
Therefore, there are 39 rooms with 2 windows because 78/2 = 39.
|
39
|
gsm8k
|
Every room in a building has at least two windows and a maximum of 4 windows. There are 122 windows total. If 5 rooms have 4 windows and 8 rooms have 3 windows, how many rooms in the building have 2 windows?
|
A lily is a beautiful flower, so saying someone is like a lily would imply that they are beautiful as well
|
False
|
FLUTE
|
Context: "She was so ugly." Claim: "She was like a pure white lily ."
Considering the context, is the claim true, false, or unknown?
|
The first televisions were sold in 1946. Iron Chef started airing in 1993.
|
No
|
strategyqa
|
Did people in Korea under Japanese Rule watch a lot of Iron Chef?
|
To whoop it up means to celebrate, especially with cheers and whoops, but in this context the speaker is wondering if the person will keep calm instead
|
False
|
FLUTE
|
Context: "Let's see if you keep calm and refrain from making any noise next Monday when it's just another start to a shitty week." Claim: "Let's see if you whoop it up next monday when it's just another start to a shitty week."
Considering the context, is the claim true, false, or unknown?
|
我们首先考虑在$$2012$$之前有多少个数，在$$2012$$之前的数考虑其各个数位可以选择的数字，我们把$$2012$$前面的所有数当做是四位数，没有的数位拿$$0$$占位置，此时千位数字：$$0$$或$$1$$；百位、十位、个位数字为$$0$$，$$1$$，$$2$$；共$$2\times 3\times 3\times 3=54$$（个）．当千位数字为$$2$$时：即自第$$55$$个开始：$$2000$$，$$2001$$，$$2002$$，$$2010$$，$$2011$$，$$2012$$为第$$60$$个数．
|
D
|
TAL-SCQ5K
|
用$$0$$、$$1$$、$$2$$三个数可以组成很多的自然数，将其从小到大依次排列起来，分别是：$$0$$，$$1$$，$$2$$，$$10$$，$$11$$，$$\cdots $$，则$$2012$$是其中的第（~ ~ ）个数．
Options:
A. $$57$$
B. $$58$$
C. $$59$$
D. $$60$$
|
To be effaced means to be erased or wiped out, while to be remembered means to be kept in one's memory.
|
No
|
FLUTE
|
Context: Whenever they drop to the ground, they are remembered.
Hypothesis: As they strike the ground, they are effaced.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
|
The cost of the hearing aids is $2500 * 2 = $5000
So insurance covers $5000 * .8 = $4000
That means it cost him $5000 - $4000 = $1000
|
1000
|
gsm8k
|
John ends up damaging his hearing aids. He needs to replace both of them. They cost $2500 each. Insurance covers 80% of the cost. How much does he personally have to pay?
|
The largest asteroids are the size of miniature planets. Mercury is the smallest planet and has a radius of 1,516 miles. New York City is 13.4 miles long and 2.3 miles wide. Mercury weighs 3.285 × 10^23 kg.
|
Yes
|
strategyqa
|
Could largest asteroid crush a whole city?
|
If she changes the box weekly, then in 210 days, she will change the box 210/7=30 times.
At 15 pounds of litter for every box change, she will require 30*15=450 pounds of cat litter in 210 days.
If she buys 45-pound containers, then for 450 pounds she will need to buy 450/45=10 containers of litter.
At $21 per container, to buy enough cat litter for 210 days, it will cost 10 * $21 = $210
|
210
|
gsm8k
|
Janet buys 45-pound containers of cat litter for $21 each. If her cat litter box holds 15 pounds of cat litter, and she changes out the litter weekly, how much will it cost, in dollars, for her to buy enough litter to last 210 days?
|
Feeling popular implies that the person has had a good day with lots of people wanting to talk to them, which is not the case when the person has had a terrible day and no one wanted to speak to them.
|
No
|
FLUTE
|
Consider the staetement "I had a bad day and tried calling two different people and couldn't get anyone". Based on this statement, is "Feel so popular over the fact that I had a terrible day and no one wanted to pick up my call." a true statement? Yes/no/unknown
|
A clean plate at the bottom of a sink is bright and round, and so is the moon.
|
Yes
|
FLUTE
|
Consider the staetement "It hung in the sky, round and bright". Based on this statement, is "It hung in the sky, like a clean plate at the bottom of a scummy sink." a true statement? Yes/no/unknown
|
1, 2, 3, 4, 5, 18→ 6 $30-5-1=24$, $24\div2=12$ $$6+12=18$$
|
D
|
TAL-SCQ5K
|
From $1$ to $30$, how many integers can be chosen at most to ensure that no two of chosen numbers sum to $36$?
Options:
A. $$15$$
B. $$16$$
C. $$17$$
D. $$18$$
E. $$19$$
|
Al ran twice as far as Bob. Split $$18\rm km$$ into two parts, one twice the other, to see that Bob ran $$6\rm km$$ and Al ran twice as far, $$12\rm km$$.
|
[4]
|
TAL-SCQ5K
|
Al ran twice as far as Bob ran. They ran a total off $$18\rm km$$. How far did Al run?
Options:
[1] $$3\rm km$$
[2] $$6\rm km$$
[3] $$9\rm km$$
[4] $$12\rm km$$
|
The sum of the angles around any point is $360^\circ$. Therefore, $5x^\circ+4x^\circ+x^\circ+2x^\circ=360^\circ$ or $12x = 360$ or $x=30$.
|
$30$
|
competition-math
|
In the diagram, what is the value of $x$? [asy]
size(120);
draw(Circle((0,0),1));
draw((0,0)--(.5,sqrt(3)/2));
draw((0,0)--(sqrt(3)/2,.5));
draw((0,0)--(sqrt(3)/2,-.5));
draw((0,0)--(-1,0));
label("$4x^\circ$",(0,0),NNW); label("$5x^\circ$",(0,0),SSW);
label("$2x^\circ$",(.3,0));label("$x^\circ$",(.3,.3));
[/asy]
|
She bought 5 shorts at $7 each so 5*7=$35
She bought 2 pair of shoes at $10 each so 2*10=$20
The shorts and shoes cost her 35+20 = $55
We know she spent 75 total and the shorts and shoes cost $55 which left a difference of 75-55 = $20
She bought 4 tops for a total of $20 so 20/4 = $5
|
5
|
gsm8k
|
Ann's favorite store was having a summer clearance. For $75 she bought 5 pairs of shorts for $7 each and 2 pairs of shoes for $10 each. She also bought 4 tops, all at the same price. How much did each top cost?
|
He can jump 3*60=180 times per minute
So he can jump 180*60=10,800 per hour
So it would take him 54,000/10,800=5 hours
|
5
|
gsm8k
|
Mark wants to set the record for most consecutive ropes jumped. The record is 54,000. He can jump 3 times a second. How many hours would he need to jump rope?
|
A carved out pumpkin is emptied out, so it would not make sense for someone to feel fullness in their chest if it felt like an emptied out pumpkin
|
False
|
FLUTE
|
Context: "He felt a deep sense of fullness in his chest." Claim: "The center of his chest felt like a carved out pumpkin ."
Considering the context, is the claim true, false, or unknown?
|
John bought 50-15 = 35 eBook readers.
John has 35-3 = 32 eBook readers after losing some.
Together they have 50+32 = 82 eBook readers.
|
82
|
gsm8k
|
John and Anna bought some eBook readers. John bought 15 eBook readers less than Anna did. Unfortunately, John lost 3 eBook readers. If Anna bought 50 eBook readers, how many eBook readers do they have altogether?
|
Addie put 72/4=18 stamps in the scrapbook
Parker now has 18+18=36 stamps in his scrapbook
|
36
|
gsm8k
|
There were 18 stamps in Parker’s scrapbook. If Addie put one fourth of her 72 stamps in Parker’s scrapbook, how many stamps does he have now?
|
If the party died as soon as she left, that would suggest that she was the main attraction in the party, however, if there was nothing like a party until she left, that would suggest that the party was much better after she left.
|
Yes
|
FLUTE
|
Given the statement "There was nothing like a party until she left.", is the statement "The party died as soon as she left." wrong?
- Yes
- No
- Unknown
|
The amount of the discount is 20/100 * $90 original price = $18
Charlotte needs to bring the $90 - $18 discount = $72
|
72
|
gsm8k
|
Charlotte needs to know how much money to have with her when she goes to the shoe store. How much money should Charlotte bring to buy a pair of boots, if the original price is $90 and there is a discount of 20%?
|
Having your favourite snacks eaten before dinner by someone else is often very frustrating, especially if they make a mess in the process
|
No
|
FLUTE
|
Context: My son raided the snack cupboard before dinnertime, eating all my favourite snacks, and he made a mess out of it.
Hypothesis: My son ate all my favourite snacks before dinner and made a huge mess of the cupboard in the process
Is the hypothesis incorrect? (Yes, no, or unknown)?
|
She and her dog both have a serving before bed so they eat 1+1 = 2 servings a day
She wants to have enough for 30 days and they eat 2 servings a day so they need 30*2 = 60 servings
Each jar has 15 servings and she needs 60 servings so she will need 60/15 = 4 jars of peanut butter
|
4
|
gsm8k
|
Phoebe eats 1 serving and gives her dog 1 serving of peanut butter for a bedtime snack. Each jar of peanut butter has 15 servings. How many jars will she need to make sure she and her dog have enough to last for 30 days?
|
We will consider the sum $A+B+C+D+E+F+G+H$. We know that the sum of any three consecutive terms is $30$ and that $C=5$, so $A+B+C=A+B+5=30$ and thus $A+B=25$. Now, we have
\[A+B+C+D+E+F+G+H=A+(B+C+D)+(E+F+G)+H=A+30+30+H=A+H+60\]and
\[A+B+C+D+E+F+G+H=(A+B)+(C+D+E)+(F+G+H)=25+30+30=85.\]Equating the two values we obtained for the sum, we find that $A+H+60=85$, so $A+H=25$.
|
$25$
|
competition-math
|
In the eight-term sequence $A,B,C,D,E,F,G,H$, the value of $C$ is $5$ and the sum of any three consecutive terms is $30$. What is $A+H$?
|
设这$$10$$名同学的平均得分是$$x$$分，那么$$10$$名同学的总得分是$$10x$$分，则： $$10x6\times \left( x20 \right)=4\times 150$$，$$10x-6x=480$$，$$\begin{matrix}4x=480 \end{matrix}$$，$$x=120$$， 答 ：这$$10$$名同学的平均得分是$$120$$分.
|
$$120$$
|
TAL-SCQ5K
|
$$10$$名同学参加数学竞赛，前$$4$$名同学平均得分$$150$$分，后$$6$$名同学平均得分比$$10$$人的平均分少$$20$$分，这$$10$$名同学的平均分是（~ ）分．
* $$100$$
* $$140$$
* $$160$$
* $$120$$
|
To taste blood means to feel triumphant over an opponent, but in this context he feels horror and pity for her victims.
|
Yes
|
FLUTE
|
Given the statement "He could hear the screams of her victims, could smell burnt flesh and feel horror and pity for his opponent.", is the statement "He could hear the screams of her victims, could smell burnt flesh and taste blood." wrong?
- Yes
- No
- Unknown
|
People usually get angry when somebody cuts in front of them in a queue because it is an act of rudeness and impatience and not something to be thrilled about.
|
Yes
|
FLUTE
|
Consider the statement "I was at the airport and someone cut me in line.". Is the statement "I was at the airport and was thrilled when I saw how somebody jumped the queue and cut in front of me" false? Yes/no/unknown
|
♥ $$\times$$ ☺ $$=$$ ♦ Since ☺ is an even number,~♦ must also be an even number. ♦ $$-\textasciitilde3$$ is the only option to given an odd answer because even $$-$$ odd $$=$$ odd.
|
A
|
TAL-SCQ5K
|
♥ $$\times$$ ☺ $$=$$ ♦ ☺ is an even number. which of the following gives an odd answer?
Options:
A) ♦ $$-\textasciitilde3$$
B) ☺ $$+$$ ♦
C) ☺ $$\times$$ ☺
D) ♦ $$\times$$~♦
|
First add the fractions of vaccinated and recovered townspeople: 1/3 + 1/3 = 2/3
Then you need to subtract the fraction that are both vaccinated and recovered, since they were double-counted. To do this, start by converting 2/3 to the same denominator as 1/6: 2/3 * 2/2 = 4/6
Then subtract 1/6 from 4/6: 4/6 - 1/6 = 3/6
Then divide the numerator by the denominator and multiply by 100% to express the answer as a percentage: 3/6 * 100% = 50%
|
50
|
gsm8k
|
1/3 of the townspeople have received the full COVID vaccine. 1/3 are immune because they already recovered from COVID. If 1/6 of the townspeople are both vaccinated and already had COVID, what percent of the town is immune in some way?
|
She paid 3 x $15 = $45 for the makeup palettes.
She paid 4 x $2.50 = $10 for the lipsticks.
She also paid 3 x $4 = $12 for the boxes of hair color.
Therefore, Maddie paid a total of $45 + $10 + $12 = $67 for the beauty products.
|
67
|
gsm8k
|
Maddie went to a beauty store and bought some beauty products. She bought 3 different makeup palettes which cost $15 each, 4 lipsticks which cost $2.50, and 3 boxes of hair color which cost $4 each. How much did Maddie pay in total?
|
He makes 20*40=$800 per week
He used to make 16*25=$400 per week
So his raise was 800-400=$400 per week
So he makes 400*52=$20,800 per year more
|
20800
|
gsm8k
|
Jame gets a raise to $20 per hour and works 40 hours a week. His old job was $16 an hour for 25 hours per week. How much more money does he make per year in his new job than the old job if he works 52 weeks a year?
|
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