GMAT Quant Practice Question 12

Counting methods - Numbers and Digits | Permutation Combination

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?

  1. 900
  2. 729
  3. 3240
  4. 648
  5. 1296

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Explanatory Answer | GMAT Counting Methods Q12

Step 1 of solving this GMAT Permutation Question: Understanding the constraints

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.

Step 2 of solving this GMAT Permutation Question: One Constraint at a time

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

Choice D is the correct answer.



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