GMAT Maths | Number Properties Q1

This GMAT sample question is a number theory, number properties practice question testing your understanding of factors/divisors of a number. You could get 2 to 4 questions testing concepts in number properties and number theory in the GMAT quant section.

Question 1: If both 11² and 3³ are factors of the number a * 4³ * 6² * 13¹¹, then what is the smallest possible value of 'a'?

1. 121
2. 3267
3. 363
4. 33
5. None of the above

Video Explanation

Explanatory Answer

Step 1 of solving this GMAT Number Properties Question: Prime factorize the given expression

a * 4³ * 6² * 13¹¹ can be expressed in terms of its prime factors as a * 2⁸ * 3² * 13¹¹

Step 2 of solving this GMAT Number Properties Question: Find factors missing after excluding 'a' to make the number divisible by both 11² and 3³

11² is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 11² is a factor of the number, 11² should be a part of 'a'

3³ is a factor of the given number.
If we do not include 'a', the number has only 3² in it.
Therefore, if 3³ has to be a factor of the given number 'a' has to contain 3¹ in it.

Therefore, 'a' should be at least 11² * 3 = 363 if the given number has 11² and 3³ as its factors.

The question is "what is the smallest possible value of 'a'?"
The smallest value that 'a' can take is 363

Choice C is the correct answer.