CAT 2025 Inequalities Question (Hard)

Question

Let p, q and r be three natural numbers such that their sum is 900, and r is a perfect square whose value lies between 150 and 500. If p is not less than 0.3q and not more than 0.7q, then the sum of the maximum and minimum possible values of p is

Accepted Answer

We have p q r 900, and r is a perfect square lying between 150 and 500. Let q be a non-variable number that does not have a range. We have 0.3q leq p leq 0.7q, or q 0.3q leq p q leq q 0.7q or 1.3q leq p q leq 1.7q Also, we can rewrite p q 900-r Therefore, 1.3q leq 900-r leq 1.7q Since the extreme va

CAT 2025

Quantitative

Inequalities

Hard

Let p, q and r be three natural numbers such that their sum is 900, and r is a perfect square whose value lies between 150 and 500. If p is not less than 0.3q and not more than 0.7q, then the sum of the maximum and minimum possible values of p is

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