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Is an integer Q divisible by 11? (1) Q is a multiple of 777

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Is an integer Q divisible by 11? (1) Q is a multiple of 777 [#permalink] New post 09 Nov 2005, 18:21
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Is an integer Q divisible by 11?

(1) Q is a multiple of 777
(2) Q is a multiple of 7
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Director
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 [#permalink] New post 09 Nov 2005, 19:14
E

A) Insuff.
Q = 777*11 -> Yes
Q = 777 -> No

B) Insuff.
Q = 7 -> No
Q = 77 -> Yes

Together, 777 and 777*11 satisfy both A and B, but
Q = 777 is not divisible by 11
Q = 777*11 is divisible by 11
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 [#permalink] New post 09 Nov 2005, 22:19
(1) Insufficient

Q/777 gives an integer. However, we still don't know whether Q/11 gives an integer

(2)

Q/7 same as the above reasoning


(1/2)

Q/7 we get an integer N, then

Q/777 = Q/(7*111) = N/111

However, now we don't know whether N is divisible by 11.


I pick E
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Re: DS [#permalink] New post 09 Nov 2005, 22:50
E.

Let Q be 777, this is multiple of 777 but not divisible by 11. Let Q be 777*11 which is a multiple of 777 and also divisible by 11. Hence stmt 1 is insufficient.

Stmt2: Let Q be 7 which is multiple of 7 but not divisible by 11. Let Q be 77 which is multiple of 7 and divisible by 11. Hence stmt2 by itself is insufficient.

Combing both. Let Q be 777 which is a multiple of 777 and 7 but not divisible by 11. Let Q be 777*11 which is a multiple of 777 and 7 and also divisible by 11. Hence insufficient.

So the answer is E.
Re: DS   [#permalink] 09 Nov 2005, 22:50
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