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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Integers
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Jay@ManhattanReview
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Statement 1: n has only two different prime factors 2 and 3.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
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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BTGmoderatorDC
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Thanks a lot Jay!Jay@ManhattanReview wrote:Statement 1: n has only two different prime factors 2 and 3.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
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.
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Matt@VeritasPrep
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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 ...
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 ...
