Mahmud6 wrote:

A number \(N^2\) has 35 factors. How many factors can \(N\) have?

A. 6 or 10 factors

B. 8 or 14 factors

C. 10 or 16 factors

D. 12 or 18 factors

E. 14 or 20 factors

D is the answer as follows.

Sometime in GMAT where we have time crunch we have to consider specific case based on the answer options provided.

Here, particularly in this question just by considering a single prime factor will be sufficient to answer the question.

Lets assume \(a^p = N^2\) => since it has 35 factors including N^2, hence p = 34

For N the number of factors will be 17 (\(\frac{34}{2}\)). Considering N as one of the factor the number of factors will become 18.

Only D satisfies the condition, hence no need to consider the case of multiple prime factors.

Hope, I am clear.

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