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NDA 2024 · PYQ · Permutations / Divisibility · medium

Four digit numbers are formed by using the digits 1, 2, 3, 5 without repetition of digits. How many of them are divisible by 4?

  1. A.120
  2. B.24
  3. C.12
  4. D.6✓ Correct

Explanation

A number is divisible by 4 if its last two digits form a number divisible by 4. From {1,2,3,5}, possible last-two-digit combinations divisible by 4: 12, 32, 52. That's 3 combinations. For each, the first two digits can be arranged from the remaining 2 digits in 2! = 2 ways. Total = 3 × 2 = 6.
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