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# If w, x and y are different positive integers, and wxy = 24,

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If w, x and y are different positive integers, and wxy = 24, [#permalink]

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Updated on: 31 Aug 2017, 06:51
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Difficulty:

75% (hard)

Question Stats:

56% (01:48) correct 44% (01:04) wrong based on 90 sessions

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If w, x and y are different positive integers, and wxy = 24, is xy divisible by 6?

(1) wy is not divisible by 6.

(2) x is even.

[Reveal] Spoiler:
Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

Each statement ALONE is sufficient to answer the question.

Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.
[Reveal] Spoiler: OA

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Originally posted by shrive555 on 04 Oct 2010, 11:51.
Last edited by abhimahna on 31 Aug 2017, 06:51, edited 1 time in total.
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Posts: 44636
If w, x and y are different positive integers, and wxy = 24, [#permalink]

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04 Oct 2010, 12:04
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Expert's post
If w, x and y are different positive integers, and wxy = 24, is xy divisible by 6?

(1) wy is not divisible by 6 --> if $$w=3$$ and $$y=1$$ then $$x=8$$ and $$xy=8$$ so not divisible by 6 but if $$w=1$$ and $$y=3$$ then $$x=8$$ and $$xy=24$$ so divisible by 6. Two different answers. Not sufficient.

(2) x is even --> clearly insufficient.

(1)+(2) Example from (1) is still valid. Not sufficient.

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Re: If w, x and y are different positive integers, and wxy = 24, [#permalink]

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04 Oct 2010, 12:57
shrive555 wrote:
If w, x and y are different positive integers, and wxy = 24, is xy divisible by 6?

(1) wy is not divisible by 6.

(2) x is even.

Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

Each statement ALONE is sufficient to answer the question.

Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

(1) Let w=1, y=2, x=12 xy divisible by 6
Let w=3, y=1, x=8 xy not divisible by 6
Insufficient

(2)In both cases above x is even. Not sufficient

(1+2) : Again two examples above work

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Re: If w, x and y are different positive integers, and wxy = 24, [#permalink]

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09 Dec 2017, 17:29
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Hi All,

Certain Quant questions include 'restrictions' that limit the number of possible outcomes. In those situations, it can often be useful to list out all of the possibilities BEFORE you actually approach the rest of the prompt.

Here, we're told that W, X and Y are DIFFERENT positive integers and that (W)(X)(Y) = 24. Based on this information, these are the only possibilities:
1, 2 and 12
1, 3 and 8
1, 4 and 6
2, 2, and 6
2, 3 and 4

We're asked if (X)(Y) is divisible by 6. This is a YES/NO question.

1) (W)(Y) is NOT divisible by 6...

IF... W=1, Y=4, X=6 then the answer to the question is YES.
IF... W=3, Y=1, X=8 then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) X is EVEN.

We can use the same 'TESTs' from Fact 1 in Fact 2....
IF... W=1, Y=4, X=6 then the answer to the question is YES.
IF... W=3, Y=1, X=8 then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we already have to different examples that 'fit' BOTH Facts and provide two different results (a "YES" and a "NO"), so there's no more work needed.
Combined, INSUFFICIENT

[Reveal] Spoiler:
E

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Re: If w, x and y are different positive integers, and wxy = 24,   [#permalink] 09 Dec 2017, 17:29
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