n=15*a=3*5*a?
stmt1,
n=20*a=4*5*a
We dont know whether 3 is a factor of n.
Insuff
stmt2,
n+6=3a
n=3a-6=3(a-2)
n=3,6,9..
n is multiple of 3.
We dont know whether 5 is a factor of n.
Insuff
Combining 1 and 2,
3&5 are factors of n.
n is a multiple of 15
Suff
Pick C
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Integers
Source: Beat The GMAT — Data Sufficiency |
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fskilnik@GMATH
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Answer: C
(1) BIFURCATES:
> Take n = 0 , then n is both multiple of 20 (as necessary) and of 15 (answering the question in the affirmative)
> Take n = 20, then n is a multiple of 20 (necessary) but 20 is not a multiple of 15 (answering in the negative)
(2) BIFURCATES:
> Take n = -6, then 0 is a multiple of 3 (as necessary), but -6 is not divisible by 15 (answers in the negative)
> Take n = 15, then 21 is a multiple of 3 (necessary) and 15 is divisible by itself (answers in the positive)
(1+2) DECIDES!
Focus in the question stem, we are looking for factors 3 and 5... From statement (1) we know that n has a factor of 5, from statement (2) we know that n has a factor of 3 (more below), therefore n is divisible by 15.
In fact: n+6 multiple of 3 implies n = (n+6) - 6 divisible by 3 (as a subtraction of two multiples of 3)
Therefore (1+2) answers the question asked, that is, DECIDES about the question concerned!!
Regards,
Fábio
[/quote]
(1) BIFURCATES:
> Take n = 0 , then n is both multiple of 20 (as necessary) and of 15 (answering the question in the affirmative)
> Take n = 20, then n is a multiple of 20 (necessary) but 20 is not a multiple of 15 (answering in the negative)
(2) BIFURCATES:
> Take n = -6, then 0 is a multiple of 3 (as necessary), but -6 is not divisible by 15 (answers in the negative)
> Take n = 15, then 21 is a multiple of 3 (necessary) and 15 is divisible by itself (answers in the positive)
(1+2) DECIDES!
Focus in the question stem, we are looking for factors 3 and 5... From statement (1) we know that n has a factor of 5, from statement (2) we know that n has a factor of 3 (more below), therefore n is divisible by 15.
In fact: n+6 multiple of 3 implies n = (n+6) - 6 divisible by 3 (as a subtraction of two multiples of 3)
Therefore (1+2) answers the question asked, that is, DECIDES about the question concerned!!
Regards,
Fábio
[/quote]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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English-speakers :: https://www.gmath.net
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