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
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
Divisiblity Difficulty
This topic has expert replies
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
-
[email protected]
- Master | Next Rank: 500 Posts
- Posts: 429
- Joined: Wed Sep 19, 2012 11:38 pm
- Thanked: 6 times
- Followed by:4 members
Hi Rich,
How is it self sufficient? Especially the second statement, can you please explain! Thanks
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,
Rich
-
mevicks
- Master | Next Rank: 500 Posts
- Posts: 269
- Joined: Thu Sep 19, 2013 12:46 am
- Thanked: 94 times
- Followed by:7 members
There is a typo in the original post; the corrected version is already posted here: www.beatthegmat.com/post458391.html#458391
Vivek
Regards,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.
Vivek
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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.For positive integer k, is the expression (k + 2)²(k² + 4k + 3) divisible by 4?
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
