This sample GMAT Math question is a Permutation problem solving question. The concept tested is to find the number of integers that meet a set of constraints stated in this permutation question. An interesting GMAT 600 to 650 level counting methods question.

Question 12: How many odd 4-digit positive integers that are multiples of 5 can be formed without using the digit 3?

- 900
- 729
- 3240
- 648
- 1296

From INR

It is a 4-digit number.

It is an odd number.

It is a multiple of 5.

It should not contain 3 as one of its digits.

**Let us start with condition 3:** The number is a multiple of 5

Deduction: The right most digit (units place) is either 0 or 5.

**Let us include condition 2:** It is an odd number

Deduction: The unit digit has to be 5.

It is a 4-digit number with 5 as its unit digit. So, the units place has only 1 option.

The left most place cannot be 0. It cannot be 3. So, we have (10 – 2) = 8 options.

The hundreds and tens place can take values from 0 to 9 except 3. So, 9 options for each of the two digits.

Number of such 4-digit numbers = 8 × 9 × 9 × 1 = 648

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