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 11^{2} and 3^{3} are factors of the number a * 4^{3} * 6^{2} * 13^{11}, then what is the smallest possible value of 'a'?

- 121
- 3267
- 363
- 33
- None of the above

@ INR

a * 4^{3} * 6^{2} * 13^{11} can be expressed in terms of its prime factors as a * 2^{8} * 3^{2} * 13^{11}

11^{2} is a factor of the given number.

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

If 11^{2} is a factor of the number, 11^{2} should be a part of 'a'

3^{3} is a factor of the given number.

If we do not include 'a', the number has only 3^{2} in it.

Therefore, if 3^{3} has to be a factor of the given number 'a' has to contain 3^{1} in it.

Therefore, 'a' should be at least 11^{2} * 3 = 363 if the given number has 11^{2} and 3^{3} as its factors.

The question is **"what is the smallest possible value of 'a'?"**

The smallest value that 'a' can take is **363**

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