CAT 2022 Number System Question (Hard)

Question

A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the stud

Accepted Answer

Let s Break Down the Conditions Given N equiv 4 mod 9 N equiv 4 mod 10 N equiv 4 mod 12 N equiv 4 mod 25 N equiv 0 mod 11 --- Step 1 Combine the Moduli with Remainder 4 We want to find numbers such that N equiv 4 mod 9, 10, 12, 25 Compute LCM LCM of 9 and 10 90 LCM of 90 and 12 180 since LCM 90, 12

CAT 2022

Quantitative

Number System

Hard

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