Arithmetic
What is the value of 1 + 2 − 4 + 8 + 16 − 32?
-9
Given that (x) + (1/x) = 4, what is the value of x2 + (1/x2)?
14
If 2687x is divisible by 9 where x is a digit, what is x?
4
How many 3-digit positive, odd integers are multiples of 5?
90
What is the value of 12(p + 9) – 12(p – 3)?
144
If x+y=5 and x2+y2=21, what is the value of xy?
2
What is the units digit of the product of 1 x 3 x 5 x ... x 2025?
5
Two fair six-sided dice each have faces numbered 1, 1, 2, 3, 5 and 8. If both dice are rolled, how many distinct sums are possible?
12
What is the sum of all odd numbers between 100 and 200?
7500
If b=a2, c=3b-2, what is the product of all values of a for which b=c?
-1
Fernando builds a cube out of 5 8 -inch sugar cubes and another cube out of 1-inch sugar cubes. If the two constructed cubes are the same size, what is the least possible edge length, in inches, of the cubes he builds?
5
Each of the 26 eighth-grade students at Monarch Middle School is in orchestra, algebra or both. Of these students, 20 are in orchestra and 16 are in algebra. How many students are in both orchestra and algebra?
10
6
For some integer k, the first three terms of an arithmetic sequence are k, 2k+3, and 4k+1, in that order. What is the integer value of the fourth term?
29
What is the greatest product of three distinct positive integers that have a sum of 15?
120
Robin rolls two fair octahedral dice, each with faces numbered 1 through 8. What is the probability that the sum of the numbers she rolls is 8? Express your answer as a common fraction.
7/64
For positive integers a, b and c, with a > b > c, the sum a + b + c has the same value as the product a × b × c. What is the value of a – b – c?
0
What is the least integer x for which x (x ^2 − 9) = 1?
-3
What is the sum of the distinct positive divisors of 1024?
2047
If you flip a fair coin 8 times, what is the probability that you get the same number of heads and tails?
35/128