Q1. Let a, b and c be the ages of three persons P, Q and R respectively where a ≤ b ≤ c are natural numbers. If the average age of P, Q, R is 32 years and if the age of Q is exactly 6 years more than that of P, then what is the minimum possible value of c?
A 34 years
B 36 years
C 38 years
D 32 years
EXPLANATION
A
It is given,
a + b + c = 96 and a ≤ b ≤ c
It is also given that age of Q is 6 years more than the age of P, i.e. b = a + 6
Minimum value c can take is equal to b, i.e. a + 6
a + a + 6 + a + 6 = 96
3a = 84
a = 28
Minimum possible value of c = 28 + 6 = 34 years
The answer is option A.
Q2. The number of all integers n for which n2 + 96 is a perfect square, is
A 4
B 6
C 8
D 10
EXPLANATION
Let = k2
k2 − n2 = 96
(k + n)(k − n) = 96
(k + n)(k − n) = 2 × 48, 4 × 24, 6 × 16, 8 × 12, 12 × 8, 16 × 6, 24 × 4, 48 × 2
n can take 8 values, i.e. -23, -10, -5, -2, 2, 5, 10 and 23.
The answer is option C.
Leave a Reply