IMO Practice Test — Logical Reasoning
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
Find the missing number: 1, 2, 6, 24, 120, ?
240
360
480
720
Explanation: Multiply by consecutive integers: ×2, ×3, ×4, ×5, ×6 → 120×6=720
Question 2 of 6
In a group of 60 people, 35 like tea, 40 like coffee, 15 like both. How many like neither?
0
5
10
15
Explanation: n(T∪C)=35+40-15=60, so 60 like at least one, neither=0
Question 3 of 6
If in a code, GOLD is written as 715124, how is SILVER written?
199122518
199122518
199122518
199122518
Explanation: Letters to positions: S=19,I=9,L=12,V=22,E=5,R=18 → 19 9 12 22 5 18 = 199122518
Question 4 of 6
Find the odd one out: 2, 3, 5, 7, 11, 13, 17, 19, 23
2
3
11
23
Explanation: All are prime numbers. 2 is even prime, others odd primes. Still all primes. No odd one. Actually all are primes. Perhaps 2 is the only even prime. So 2 is the odd one.
Question 5 of 6
Complete the sequence: A, D, I, P, ?
V
W
X
Y
Explanation: Positions: 1,4,9,16,25 → squares: A(1), D(4), I(9), P(16), Y(25)
Question 6 of 6
If 18 × 3 = 54, 27 × 4 = 108, then 36 × 5 = ?
180
200
150
210
Explanation: Pattern is simple multiplication: 18×3=54, 27×4=108, 36×5=180