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Integers

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by BTGmoderatorDC » Sun Sep 10, 2017 1:58 pm
What is the value of a positive integer n?

1) n has only 2 different prime factors 2 and 3.
2) the number of different factors of n is 6.

Can some experts help me with this? How to come up with the correct answer?
Need thorough explanation regarding this one. Thanks

OA E
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Sep 10, 2017 10:19 pm
lheiannie07 wrote:What is the value of a positive integer n?

1) n has only two different prime factors 2 and 3.
2) The number of different factors of n is 6.

Can some experts help me with this? How to come up with the correct answer?
Need thorough explanation regarding this one. Thanks

OA E
Statement 1: n has only two different prime factors 2 and 3.

We cannot get the unique value of n. For example, 12 (= 2^2 * 3) has only two different prime factors 2 and 3, and 24 (= 2^3 * 3) also has only two different prime factors 2 and 3. Insufficient.

Statement 2: The number of different factors of n is 6.

Certainly insufficient.

If n = 12, then n has 6 factors: 1, 2, 3, 4, 6, and 12.
If n = 32, then n has 6 factors: 1, 2, 4, 8, 16, and 32.

No unique value!

Statement 1 and 2:

Both 12 and 32 have only two prime factor, thus the unique value of n cannot be ascertained. Insufficient.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
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by BTGmoderatorDC » Thu Oct 12, 2017 2:21 pm
Jay@ManhattanReview wrote:
lheiannie07 wrote:What is the value of a positive integer n?

1) n has only two different prime factors 2 and 3.
2) The number of different factors of n is 6.

Can some experts help me with this? How to come up with the correct answer?
Need thorough explanation regarding this one. Thanks

OA E
Statement 1: n has only two different prime factors 2 and 3.

We cannot get the unique value of n. For example, 12 (= 2^2 * 3) has only two different prime factors 2 and 3, and 24 (= 2^3 * 3) also has only two different prime factors 2 and 3. Insufficient.

Statement 2: The number of different factors of n is 6.

Certainly insufficient.

If n = 12, then n has 6 factors: 1, 2, 3, 4, 6, and 12.
If n = 32, then n has 6 factors: 1, 2, 4, 8, 16, and 32.

No unique value!

Statement 1 and 2:

Both 12 and 32 have only two prime factor, thus the unique value of n cannot be ascertained. Insufficient.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Thanks a lot Jay!
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by Matt@VeritasPrep » Fri Oct 13, 2017 11:36 am
S1:

We could have 2 * 3, or 2 * 3 * 3, or 2 * 2 * 3, or ...

S2:

We could have 2�, or 2² * 3, or 3² * 2, or 3� ...

(If finding the number of unique factors of a number is a new idea, check out this great link.)

S1+S2:

We could have 2² * 3 or 3² * 2 ...
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