IMO Practice Test — Rational Numbers
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
a + b = 10 and a - b = -6. Find a and b.
a=2, b=8
a=8, b=2
a=2, b=-8
a=-2, b=8
Explanation: Add equations: 2a=4, so a=2. Then b=10-2=8.
Question 2 of 6
hard
(-3) x = 24. If y = x + (-10), find y.
-18
-8
8
18
Explanation: x = -8. Then y = -8 + (-10) = -18.
Question 3 of 6
hard
On a number line, point P is at -7, Q is at 15. What is the midpoint?
-11
-4
4
11
Explanation: (-7+15)/2 = 8/2 = 4
Question 4 of 6
hard
The product of two integers is -36 and their sum is -5. Find the integers.
-9 and -4
-9 and 4
9 and -4
9 and 4
Explanation: -9 x 4 = -36, and -9 + 4 = -5.
Question 5 of 6
hard
A bird flies from a tree at 5 m above ground to a cave at -12 m. What is the vertical distance traveled?
7 m
12 m
17 m
22 m
Explanation: 5 - (-12) = 17 m (absolute vertical distance)
Question 6 of 6
hard
|x + 3| = 7. How many integer solutions does x have?
1
2
3
4
Explanation: x+3=7 gives x=4; x+3=-7 gives x=-10. Two solutions.