GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Sep 2018, 10:08

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If n is an integer, is (n-1)(n+1) a multiple of 24?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6242
GMAT 1: 760 Q51 V42
GPA: 3.82
If n is an integer, is (n-1)(n+1) a multiple of 24?  [#permalink]

### Show Tags

05 Oct 2017, 03:15
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:01) correct 33% (01:31) wrong based on 49 sessions

### HideShow timer Statistics

[GMAT math practice question]

If n is an integer, is (n-1)(n+1) a multiple of 24?

1) n is odd.
2) n is not divisible by 3.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Joined: 14 Sep 2016
Posts: 145
Re: If n is an integer, is (n-1)(n+1) a multiple of 24?  [#permalink]

### Show Tags

05 Oct 2017, 04:56
According to the question we need to prove (n^2-1)/24 = an integer

1. If n is odd its not sufficient since it can take value as 3
2. If is n is not divisible by 3 then n can be even also hence, in sufficient

taking both 1 & 2 we get n^2-1 is a multiple of 24

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6242
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If n is an integer, is (n-1)(n+1) a multiple of 24?  [#permalink]

### Show Tags

08 Oct 2017, 18:00
=>
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.
We have 1 variable and 0 equation from the original condition. Therefore, D is most likely to be the answer.

Condition 1)
Since n is odd, n-1 and n+1 are consecutive even integers.
One of two consecutive even integers must be a multiple of 4. For example, (2,4), (6,8), (8,10) and (10,12).
Thus (n-1)(n+1) is a multiple of 4, but its divisibility by 3 is not identified.
Counterexamples are n = 3 and n = 5.
(3-1)(3+1) = 2*4 = 8, which is not a multiple of 24.
(5-1)(5+1) = 4*6 = 24, which is a multiple of 24.
This is not sufficient.

Condition 2)
Since n is not a multiple of 3, n = 3k +1 or n = 3k + 2 for some integer k.
For the case, n = 3k +1, (n-1)(n+1) = (3k+1-1)(3k+1+1) = 3k(3k+2) is a multiple of 3. However, we can’t identify if n is a multiple of 24. Counterexamples are n = 4 for which (n-1)(n+1) = 3*5 = 15 is not a multiple of 24 and n = 7 for which (n-1)(n+1) = 6*8 = 48 is a multiple of 24.
For the case, n = 3k +2, (n-1)(n+1) = (3k+2-1)(3k+2+1) = (3k+1)(3k+3) = 3(3k+1)(k+1) is a multiple of 3. However, we can’t identify if n is a multiple of 24. Counterexamples are n = 5 for which (n-1)(n+1) = 4*6 = 15 is a multiple of 24 and n = 6 for which (n-1)(n+1) = 5*7 = 35 is a not multiple of 24.

Condition 1) & 2)
From the condition 1), (n-1)(n+1) is a multiple of 8 and from the condition 2), (n-1)(n+1) is a multiple of 3.
Thus, (n-1)(n+1) is a multiple of 24.
Therefore, unlike our expectation, C is the answer.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If n is an integer, is (n-1)(n+1) a multiple of 24? &nbs [#permalink] 08 Oct 2017, 18:00
Display posts from previous: Sort by

# If n is an integer, is (n-1)(n+1) a multiple of 24?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.