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,
Rich

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.

Cheers,
Brent

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.

GMAT assassins aren't born, they're made,
Rich