IMO Practice Test — One-Step & Two-Step Equations
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
Solve: (2x+3)/5 = (x-1)/2
x = 11
x = 8
x = 6
x = 4
Explanation: Cross multiply: 2(2x+3) = 5(x-1) => 4x+6 = 5x-5 => 11 = x
Question 2 of 6
hard
Three consecutive integers sum to 72. Find the middle integer.
23
24
25
26
Explanation: Let the integers be n-1, n, n+1. Sum = 3n = 72 => n = 24.
Question 3 of 6
hard
Solve: 3(2x-4) = 2(3x+5) - 22. How many solutions?
x = 0
x = 2
All real numbers (identity)
No solution
Explanation: 6x-12 = 6x+10-22 => 6x-12 = 6x-12. This is always true, so all real numbers are solutions.
Question 4 of 6
hard
The perimeter of a rectangle is 48 cm. The length is 6 cm more than twice the width. Find the length.
12 cm
15 cm
18 cm
21 cm
Explanation: Let width=w, length=2w+6. 2(w+2w+6)=48 => 2(3w+6)=48 => 3w+6=24 => w=6, length=18 cm
Question 5 of 6
hard
Solve: (2x+5)/3 = 5
x = 5
x = 8
x = 10
x = 12
Explanation: 2x+5 = 15 => 2x = 10 => x = 5
Question 6 of 6
hard
A father is 3 times as old as his son. In 10 years, he will be twice as old as his son. Find the son's current age.
5 years
8 years
10 years
12 years
Explanation: Son=s, Father=3s. 3s+10 = 2(s+10) => 3s+10 = 2s+20 => s=10 years