# GMAT Sample Questions | Permutation Q14

#### Numbers and Digits | Permutation Combination

This GMAT quant question is a combinatorics problem solving question. The concept tested is to find the number of ways the digits of a number can be rearranged after factoring a divisibility constraint. A medium difficulty permutation question.

Question 14: How many five-digit positive integers comprising only the digits 1, 2, 3, and 4, each appearing at least once, exist such that the number is divisible by 4?

1. 120
2. 24
3. 72
4. 60
5. 54

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### Explanatory Answer | GMAT Numbers and Digits

#### Step 1 of solving this GMAT Permutation Question: List Down the Constraints

The conditions that the number should satisfy
1. It is a 5-digit number
2. Digits should comprise only 1, 2, 3, and 4.
3. Each digit should appear at least once in the 5-digit number.
4. The number is divisible by 4

Test of divisibility for 4
The last two digits (rightmost two digits) should be divisible by 4.