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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## When 5 ##### This topic has 2 expert replies and 1 member reply ### Top Member ## When 5 $$When\ 5^{11}\ and\ 2^n7^2\ have\ the\ same\ number\ of\ factors,\ what\ is\ the\ value\ of\ n?$$ A. 2 B. 3 C. 4 D. 5 E. 6 Can someone show me how to solve this? OA B ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply lheiannie07 wrote: $$When\ 5^{11}\ and\ 2^n7^2\ have\ the\ same\ number\ of\ factors,\ what\ is\ the\ value\ of\ n?$$ A. 2 B. 3 C. 4 D. 5 E. 6 Can someone show me how to solve this? OA B Fun factoid: If $$T = a^x * b^y * c^z$$, where a, b, and c are distinct prime bases, then we can find the number of factors in T, by calculating (x + 1)(y +1)(z+1). Put another way, we can find the number of factors of any number by first taking the prime factorization of that number, then adding one to each exponent and multiplying the results. So we know that 5^11 has 11+1 = 12 factors. Similarly, 2^n * 7^2 will have (n +1)( 2+1) factors. We want this to equal 12, so (n +1)(2+1) = 12, and (n+1)(3) = 12, or n+1 = 4, and n = 3. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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lheiannie07 wrote:
$$When\ 5^{11}\ and\ 2^n7^2\ have\ the\ same\ number\ of\ factors,\ what\ is\ the\ value\ of\ n?$$

A. 2
B. 3
C. 4
D. 5
E. 6
The total number of factors 5^11 has is 11 + 1 = 12 and the total number of factors 2^n x 7^2 has is (n + 1)(2 + 1) = 3(n + 1). Thus we can say:

12 = 3(n + 1)

4 = n + 1

3 = n

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### Top Member

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DavidG@VeritasPrep wrote:
lheiannie07 wrote:
$$When\ 5^{11}\ and\ 2^n7^2\ have\ the\ same\ number\ of\ factors,\ what\ is\ the\ value\ of\ n?$$

A. 2
B. 3
C. 4
D. 5
E. 6

Can someone show me how to solve this?

OA B
Fun factoid:

If $$T = a^x * b^y * c^z$$, where a, b, and c are distinct prime bases, then we can find the number of factors in T, by calculating (x + 1)(y +1)(z+1). Put another way, we can find the number of factors of any number by first taking the prime factorization of that number, then adding one to each exponent and multiplying the results.

So we know that 5^11 has 11+1 = 12 factors.

Similarly, 2^n * 7^2 will have (n +1)( 2+1) factors. We want this to equal 12, so (n +1)(2+1) = 12, and (n+1)(3) = 12, or n+1 = 4, and n = 3. The answer is B
Thanks a lot!

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