What is the Smallest Positive Integer That is Not a Factor of 15! GMAT Problem Solving

Question: What is the smallest positive integer that is NOT a factor of 15! and NOT a prime number?

1. 25
2. 27
3. 32
4. 34
5. 36

Correct Answer: D
Solution and Explanation:
There is only one approach to this problem.
Approach Solution 1:

The problem statement asks to find the smallest positive integer that is NOT a factor of 15! and NOT a prime number.
15! implies = 1 x 2 x 3 x 4 x 5 x 6........15

Let’s analyze each option to solve the problem.
Option A: 25 = 5 x 5. The above number will have at least 2 fives to cancel. For example: 5 and 10 (5x2). Hence a factor.
Option B: 27 = 3 x 7. The above number will have 3 and 7. Hence a factor.
Option C: 32 = 4 x 8. The above number will have 4 and 8. Hence a factor.
Option D: 34 = 2 x 17. The above no has 2 but no 17. Hence, not a factor and even 34 is not prime.
Option E: 36 = 12 x 3. The above number will have 12 and 3. Hence a factor.

Therefore, option D satisfies the problem statement.
Hence, the smallest positive integer that is NOT a factor of 15! and NOT a prime number = 34.

“What is the smallest positive integer that is NOT a factor of 15!”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Advanced Questions”. The candidates must possess solid knowledge of calculations in order to solve GMAT Problem Solving questions. The candidates can practice different types of questions from GMAT Quant practice papers to improve their knowledge of mathematics.

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