Question
The product of two natural numbers P and Q is 364. P is a perfect even composite number and Q is a prime number. The HCF of P and Q is 50% of R. Find the relation between A, B and C:
A. Sum of P and Q minus R
B. 42.85% of P less than the product of Q and R
C. Product of the smallest perfect number and R
Solution
ATQ, P is a perfect even composite number, so possible values are 6 and 28. If P = 6, then Q = 364/6, not possible If P = 28, then Q = 364/28 = 13, which is prime So, P = 28 Q = 13 HCF of P and Q = 1 1 = 50% of R R = 2 A => 28 + 13 - 2 = 39 B => 13 × 2 - 3/7 × 28 = 26 - 12 = 14 C => 6 × 2 = 12 Therefore, A > B > C
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