Is the integer n a multiple of 15?
(1) n is a multiple of 20
(2) n+6 is a multiple of 3.
The OA is C.
How can I use both statements together to determine whether n is multiple of 15 or not?
Is the integer n a multiple of 15?
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- ceilidh.erickson
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In order for an integer to be a multiple of 15, it must have factors of 3 and 5.
Target question: is n a multiple of both 3 and 5?
(1) n is a multiple of 20
This tells us that n has at least two factors of 2 and one factor of 5. Since it doesn't tell us whether it has a factor of 3, it is not enough to answer the question. Insufficient.
(2) n+6 is a multiple of 3
There is a divisibility rule that states: any multiple of a given integer x plus or minus another multiple of x will yield a multiple of x.
E.g. 10a + 15b must equal some multiple of 5 (as long as a and b are integers).
Therefore, if n + 6 = a multiple of 3, then n + [a multiple of 3] = [a multiple of 3], and therefore n must be a multiple of 3.
By itself this does not answer the full question. Insufficient.
(1) & (2) Together:
Statement (1) told us that n was a multiple of 5, and (2) told us that n was a multiple of 3. Therefore, using the statements together, n must be a multiple of both 3 and 5, i.e. 15. Sufficient.
The answer is C.
Target question: is n a multiple of both 3 and 5?
(1) n is a multiple of 20
This tells us that n has at least two factors of 2 and one factor of 5. Since it doesn't tell us whether it has a factor of 3, it is not enough to answer the question. Insufficient.
(2) n+6 is a multiple of 3
There is a divisibility rule that states: any multiple of a given integer x plus or minus another multiple of x will yield a multiple of x.
E.g. 10a + 15b must equal some multiple of 5 (as long as a and b are integers).
Therefore, if n + 6 = a multiple of 3, then n + [a multiple of 3] = [a multiple of 3], and therefore n must be a multiple of 3.
By itself this does not answer the full question. Insufficient.
(1) & (2) Together:
Statement (1) told us that n was a multiple of 5, and (2) told us that n was a multiple of 3. Therefore, using the statements together, n must be a multiple of both 3 and 5, i.e. 15. Sufficient.
The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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- ceilidh.erickson
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Please also POST YOUR SOURCE. It's a copyright violation to post questions without citing your source.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
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Vicen, following up on the above.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education