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x divisible by 6?

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x divisible by 6?

by josh80 » Sun Dec 15, 2013 3:12 pm

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Is the integer x divisible by 6?

1) x + 3 is divisible by 3.

2) x + 3 is an odd number

OA C
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by Stuart@KaplanGMAT » Sun Dec 15, 2013 6:55 pm

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josh80 wrote:Is the integer x divisible by 6?

1) x + 3 is divisible by 3.

2) x + 3 is an odd number

OA C
Hi there!

Not much to dissect for the q stem: we can rephrase it as "is x a multiple of 6?" No info provided, so we know nothing!

(1) (x+3) is a multiple of 3, which means that x is also a multiple of 3.

if x=3, then x is NOT divisible by 6.
if x=6, then x IS divisible by 6.
Maybe no, maybe yes: insufficient... eliminate A and D.

(2) (x+3) is odd, which means that x is even.

if x=2, then x is NOT divisible by 6.
if x=6, then x IS divisible by 6.
Maybe no, maybe yes: insufficient... eliminate B.

Together: x is an even multiple of 3, i.e. x is a multiple of both 2 and 3.

Well, if x is a multiple of both 2 and 3, then x MUST be a multiple of 6. Sufficient... choose C!
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by Jeff@TargetTestPrep » Tue Dec 19, 2017 9:15 am

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josh80 wrote:Is the integer x divisible by 6?

1) x + 3 is divisible by 3.

2) x + 3 is an odd number
We need to determine whether x/6 = integer.

Statement One Alone:

x + 3 is divisible by 3.

Statement one is not sufficient to answer the question. If x = 3, then x is not divisible by 6; however, if x = 6, then x is divisible by 6.

Statement Two Alone:

x + 3 is an odd number.

Statement two is not sufficient to answer the question. If x = 2, then x is not divisible by 6; however, if x = 6, then x is divisible by 6.

Statements One and Two Together:

Using statements one and two, we see that x + 3 is an odd multiple of 3, such as 3, 9, 15, etc. Thus, x must be an even multiple of 3. Since all even multiples of 3 are multiples of 6, x/6 is an integer.

Answer:C

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