XAT 2023 Number System Question (Medium)

Question

The addition of 7 distinct positive integers is 1740. What is the largest possible greatest common divisor of these 7 distinct positive integers?

Optima Learn · Accepted Answer

Let the gcd be g. Then the seven integers can be written as g a_1, g a_2, ..., g a_7 where the a_i are distinct positive integers with gcd 1. Their sum is g a_1 a_2 ... a_7 1740, so g divides 1740 and S a_1 a_2 ... a_7 1740 g. For 7 distinct positive integers, the minimum possible sum is 1 2 3 4 5 6

XAT 2023 Number System — Previous Year Question

XAT 2023

Quantitative

Number System

Medium

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