CAT 2025 Number System Question (Hard)

Question

If m and n are integers such that m 2 n 2 m n 27 , then the maximum possible value of 2 m - 3 n is

Accepted Answer

Sure! We can solve it without explicitly introducing new variables for substitution. We are given m 2n 2m n 27 and we want to maximize 2m-3n Because m and n are integers, both m 2n and 2m n are going to be integers. Factor pairs of 27 including negatives are 1,27 , 3,9 , 9,3 , 27,1 , -1,-27 , -3,-9

CAT 2025

Quantitative

Number System

Hard

If ( m ) and ( n ) are integers such that ( ( m + 2 n ) ( 2 m + n ) = 27 ), then the maximum possible value of ( 2 m - 3 n ) is

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