Algebra
cadabra
cadabra
The sum of two numbers is 10 and their difference (the larger minus the smaller) is 4. What are the two numbers?
7 and 3
A square has a diagonal length of 10 root 2. What is the area of square?
100
What is the smallest two-digit number that is both a perfect square and a perfect cube?
64
If you flip two fair coins, what is the probability that you get one heads and one tails (in any order)?
1/2
On a farm, chickens and rabbits have 30 heads and 100 legs in total. How many rabbits are there?
20
The product of two consecutive positive integers is 56. What are the two integers?
7 and 8
If you double the length of a rectangle and halve its width, how does the area change?
It stays the same
What is the units (ones) digit of 745?
7
If you roll two six-sided dice, what is the probability that the sum of the two dice is 7?
1/6
In a meeting, each person shakes hands with everyone else exactly once. If there were 66 handshakes total, how many people were in the meeting?
12
Solve the equation ∣2x−5∣=3
x=4 or x=1
Two triangles are similar with corresponding side lengths in the ratio 2:3. If the smaller triangle’s area is 8 square units, what is the area of the larger triangle?
18 square units
Find the smallest positive integer that leaves a remainder of 1 when divided by 2, a remainder of 2 when divided by 3, and a remainder of 3 when divided by 4
11
A bag contains 5 red marbles and 3 blue marbles. If you draw 2 marbles without replacement, what is the probability that both marbles are red?
5/14
What three positive numbers give the same result when multiplied together as when added together?
1,2 and 3.
A two-digit number is such that reversing its digits gives a number 27 greater than the original. The sum of its digits is 9. What is the original number?
36
A large cube 3×3×3 is painted on all faces and then cut into 27 small unit cubes. How many of the small cubes have paint on exactly one face?
6
Find the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5.
59
You flip a fair coin 5 times. What is the probability of getting exactly 3 heads?
5/16
On an island of knights (truth-tellers) and knaves (liars), you meet two people, A and B. A says, “At least one of us is a knave.” B says nothing. Is A a knight or a knave (and what is B)?
A is a knight (telling the truth) B is knave
The function f(x)=ax2+bx+c has roots at x=1 and x=4, and passes through the point (2,3). Find the value of a.
a=-3/2
A regular hexagon is inscribed in a circle with radius 6 cm. What is the total length of all the diagonals of the hexagon?
36+36root3
Find the smallest positive number that is divisible by 5, 6, 7, and 8 but leaves a remainder of 1 when divided by 9.
3360
A 3-digit number is formed at random using digits 1–9 (each digit used only once). What is the probability that the number is divisible by 5?
1/9
A palindrome is a number that reads the same forward and backward. How many 3-digit palindromes are divisible by 3?
30