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GATE DA 2024 Q3: 4-digit numbers divisible by 3 from {1, 3, 4, 6, 7}

Question

How many 4-digit positive integers divisible by 3 can be formed using only the digits {1,3,4,6,7}\{1, 3, 4, 6, 7\}, such that no digit appears more than once in a number?

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Answer: B (official GATE 2024 final answer key)

Concept used: Divisibility by 3 (digit sum) with permutations of distinct digits.

First step: The five digits sum to 21, so the left-out digit must be a multiple of 3 (3 or 6); each choice of four digits gives 4!=244! = 24 numbers.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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