# International Mathematical Olympiad For Senior Level Problem and Solutions Vol. 001

International Mathematical Olympiad For Senior Level (Problem and Solutions Vol. 001)

1. The value of 2-2 + 2-6  is

(A) 1/16 (B) 3/16 (C) 3/32 (D) 3/34 (E) 17/64

2-2 = 1/22  = 1/4
2-6  = 1/26  = 1/64
So,

2-2 + 2-6 = 1/4 + 1/64 = 16/64 + 1/64 = 17/64

2.  Five consecutive integers add up to 50. The smallest one is

(A) 5 (B) 6 (C) 7 (D) 8  (E) 9

x + (x+1) + (x+2) + (x+3) + (x+4) = 50
5x +10 = 50
5x = 40

x = 8

3. On a road map, if a 7 cm length represents 56 km, how many kilometers does a 19 cm length represent?

(A) 124     (B) 152   (C)107       (D) 160     (E) 133

If 7 cm represents of 56 km
19 cm represents of X km
So,  X/19 = 56/7
X = 56/7 x 19 = 152

4. If Aaron Mokoena runs 12 kilometers in a 90 minutes soccer match, then his average speed in km/h, is

(A) 10   (B) 8         (C) 12    (D) 5 (E) 9

If, 60 minutes = 1 hour and 90 minutes = 1,5 hour
For example X   to average speed,
X = 12 km/1.5 h
X = 12 x 10/5 (km/h)
X = 8 km/h

5.  Given any two numbers whose sum is m and whose product is n. The sum of the squares of the numbers can be empressed as

(A) mn       (B) m2 – n2          (C) m2 + 2n              (D) m2 – 2n        (E) (m – n)2