FREE AIME Mathematical Reasoning Questions and Answers

Question 1

A 4-digit number is such that the sum of its digits is 20. How many such numbers are divisible by 9?

Accepted Answer

5

Answer

4

Answer

6

Answer

7

Question 2

In a triangle, the lengths of the sides are in the ratio 3:4:5. If the perimeter of the triangle is 36,
what is the area of the triangle?

Accepted Answer

24

Answer

30

Answer

36

Answer

48

Question 3

What is the smallest positive integer 𝑛 such that 7𝑛 is a multiple of 35?

Accepted Answer

5

Answer

7

Answer

10

Answer

35

Question 4

What is the sum of all positive integers less than 50 that are divisible by 7?

Accepted Answer

168

Answer

98

Answer

140

Answer

245

Question 5

How many positive integer solutions are there to the equation x+2y=10?

Accepted Answer

5

Answer

4

Answer

6

Answer

7