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Divisiblity Difficulty

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Divisiblity Difficulty

by nakul17 » Mon Oct 14, 2013 10:41 am
For positive integer k, is the expression (k + 2)²(k² + 4k + 3) divisible by 4?

(1) k is divisible by 8.

(2) k+1/3 is an odd integer.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient
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Source: — Data Sufficiency |
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by sanjoy18 » Mon Oct 14, 2013 11:23 am
EACH statement ALONE is sufficient.
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by [email protected] » Mon Oct 14, 2013 5:04 pm
Hi nakul17,

What is the source for this DS question? I only ask because you can actually answer it without needing either of the two Facts (which is not how the GMAT designers write their DS questions). As long as k is a positive integer, the expression will be divisible by 4.

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by [email protected] » Mon Oct 14, 2013 5:38 pm
Hi Rich,

How is it self sufficient? Especially the second statement, can you please explain! Thanks

[email protected] wrote:Hi nakul17,

What is the source for this DS question? I only ask because you can actually answer it without needing either of the two Facts (which is not how the GMAT designers write their DS questions). As long as k is a positive integer, the expression will be divisible by 4.

GMAT assassins aren't born, they're made,
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by mevicks » Tue Oct 15, 2013 4:05 am
There is a typo in the original post; the corrected version is already posted here: www.beatthegmat.com/post458391.html#458391
nakul17 wrote:For positive integer k, is the expression (k + 2)²(k² + 4k + 3) divisible by 4?

(1) k is divisible by 8.

(2) k+1/3 is an odd integer.
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by Brent@GMATPrepNow » Tue Oct 15, 2013 6:58 am
For positive integer k, is the expression (k + 2)²(k² + 4k + 3) divisible by 4?
As Rich already stated, the question (as stated above) can be answered without any extra information. Unfortunately, the original poster transcribed the question incorrectly. The (k+2) should not be raised to the power of 2.

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by [email protected] » Tue Oct 15, 2013 3:43 pm
Hi shibsriz,

We're told that K is a positive integer. We're asked if (K+2)^2(K^2 +4K +3) is divisible by 4?

If you rewrite the question, you'll have (K+2)(K+2)(K+1)(K+3)

If K = odd, then you'd have (odd)(odd)(even)(even).
If K = even, then you'd have (even)(even)(odd)(odd).

You'll notice that in all situation, you'll end up with a 2 odds and 2 evens multiplied together. When you multiply two even numbers together, you'll have a result that is divisible by 4 (the other two numbers, in this case "odds", won't change that). Thus, the question can be answered without any additional information (and the answer would ALWAYS BE YES). That is NOT how the GMAT designs its DS questions.

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