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

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

Answer (E) : 


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

Answer (D) :


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

Answer (B) :

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

Answer (B) :

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      

Answer (D) :


Example, two numbers = a and b
 a + b = m
 a.b  = n
So,
(a + b)2 = a2 + b2 + 2ab
a2 + b2 = (a + b)2 – 2ab
a2 + b2 = (m)2 – 2(n)

a2 + b2 = m2 – 2n

Juli 19, 2019 - tanpa komentar