A is the set of all points (x,y) in the shaded region.
Find the set B consisting of all points (2x, -y)?
A perfect cube is an integer whose cube root is an integer.
For example, 64 and 125 are perfect cubes.
A and B are perfect cubes.
Which of the following will NOT necessarily be a perfect cube?
Xia and Yvonne collect buttons.
Xia only collects the ones with two holes and Yvonne only collects the ones with four holes.
Xia has 10 more buttons than does Yvonne.
The total number of holes found in all of their buttons is 110.
How many buttons do they have?
Nine teams enter a basketball tournament.
Each team plays one match against each of the other teams, getting three points for a win, one point for a draw and none for a defeat.
Which of the following is a possible value of the total number of points earned by the teams at the end of the tournament?
A frog ate 20 flies in a day.
Each day, the frog ate 20 more than on the day before.
In how many days did she eat 1000 flies?
If the admittance rate to a prestigious university is 7.5% and 810 students were admitted, how many people applied to the university?
Mr. Rapid always starts driving on a motorway at exactly 7:00 a.m.
If he drives on cruise control at 45 miles per hour, he arrives at work 3 minutes late.
If he sets the cruise control to 48 miles per hour, he arrives at work 1 minute early.
At what time should he be in his office?
In a city, three-quarters of the men are married to four-fifths of the women.
What is the ratio of men to women in the city?
Mr. Rapid always starts driving on a road at exactly 7:00 a.m.
If he drives on cruise control at 24 miles per hour, he arrives at work late.
If he sets the cruise control to 48 miles per hour, he arrives at work early.
The amount of time he is early is also the amount of time he is late.
How fast should he goes to get to his office exactly on time?
There are N students in a class and only 8 of them are girls.
If 11 boys added to the class, how many students in the class are boys?
This is a typical SAT question.
The rear tires of my car wear out after 40,000 miles, whilst the front tires are done after 20,000 miles.
Estimate how many miles I should drive before the tires (front and rear) are rotated to drive the maximal distance.
Ben ate 100 bananas between Monday and Friday, stopping for the weekend.
Each day he ate six more bananas than on the previous day.
How many bananas did Ben eat on Wednesday?
Which gives the smallest answer if
X and Y are integers,
X is greater than Y and
Y is greater than 1?
On an island, the ratio between the number of adult men and the number of adult women is 2 ∶ 3 and the ratio between the number of adults and the number of children under 16 is 5 ∶ 4. What is the ratio between the number of adult women and the number of children?
It takes two gardeners 6 days to mow a lawn.
One is lazy and one is enthusiastic.
The motivated one would only take 10 days to mow it on his own.
How many days would the lazy guy take to mow the lawn on his own?
Derek dragon became a vegetarian two years ago. Derek likes to eat 3 baskets full of apples and 5 baskets full of berries for his birthday feast. But this year he can’t find many berries so he settles for 4 baskets of apples and only 1 basket of berries instead. Surprisingly, he feels equally satisfied. His mind drifts back to the old times when humans in metal suits used to clank into his cave. They made a nice crunchy breakfast treat!
How many baskets of berries will satisfy this dragon for his next birthday feast?
I participate in a 10-day rally.
The rear tires of my car wear out after 4,000 miles, whilst the front tires are done after 5,000 miles.
I have 5 spare tires and periodically change the tires.
How far can I drive with the tires?