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

It is currently 23 May 2019, 12:47

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If n is an integer, is (n+1)^2 an even integer?

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

Hide Tags

 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7367
GMAT 1: 760 Q51 V42
GPA: 3.82
If n is an integer, is (n+1)^2 an even integer?  [#permalink]

Show Tags

New post 13 Sep 2018, 01:36
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (00:47) correct 16% (01:24) wrong based on 52 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

If \(n\) is an integer, is \((n+1)^2\) an even integer?

1) \(n-1\) is an even integer
2) \((n-1)^2\) is an even integer

_________________
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 $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Intern
User avatar
B
Joined: 02 May 2018
Posts: 11
GMAT 1: 620 Q46 V29
GMAT ToolKit User
Re: If n is an integer, is (n+1)^2 an even integer?  [#permalink]

Show Tags

New post 13 Sep 2018, 01:46
For \((n+1)^2\) to be even, \(n+1\) should be even.
A) \(n-1\) is even implies that \(n+1\) will be even and hence sufficient.
B) \((n-1)^2\) is even implies that \(n-1\) is even and thus \(n+1\) will be even and hence sufficient.
So answer is D
VP
VP
User avatar
P
Joined: 31 Oct 2013
Posts: 1354
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If n is an integer, is (n+1)^2 an even integer?  [#permalink]

Show Tags

New post 13 Sep 2018, 02:12
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(n\) is an integer, is \((n+1)^2\) an even integer?

1) \(n-1\) is an even integer
2) \((n-1)^2\) is an even integer



we are looking for whether \((n + 1 )^2\) is even or not.

Statement 1: n - 1 = even. we know odd - odd = even. So, n is odd. So n +1 = even. Sufficient.

Statement 2 : \((n - 1 )^2\)= even. We know odd - odd = even and even times even is even. So, n is odd and n + 1 = even. Sufficient .

Note: There is no effect of Exponents in odd even question .

The best answer is D.
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3726
Location: Canada
Re: If n is an integer, is (n+1)^2 an even integer?  [#permalink]

Show Tags

New post 13 Sep 2018, 08:25
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(n\) is an integer, is \((n+1)^2\) an even integer?

1) \(n-1\) is an even integer
2) \((n-1)^2\) is an even integer


Target question: Is (n+1)² an even integer?
This is a good candidate for rephrasing the target question.

Aside: At the bottom of this point, you'll find a video with tips on rephrasing the target question

(n+1)² = (n+1)(n+1). So, in order for (n+1)² to be even, it must be the case that n+1 is EVEN.
Why is this?
Well, if n+1 were ODD, then (n+1)² = (ODD)² = (ODD)(ODD) = ODD, but we want (n+1)² to be EVEN
However, if n+1 were EVEN, then (n+1)² = (EVEN)² = (EVEN)(EVEN) = EVEN. Perfect.
From here, we can see that if n+1 is EVEN, then it must be the case that n is ODD
So, asking Is (n+1)² an even integer? is the same as asking Is n odd?

REPHRASED target question: Is n odd?

Statement 1: n-1 is an even integer
If n-1 is an even integer, then we can be certain that n is odd
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: (n-1)² is an even integer
If (n-1)² is an even integer, then we know that (n-1) is EVEN
If (n-1) is EVEN, then we can be certain that n is odd
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Image
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If n is an integer, is (n+1)^2 an even integer?  [#permalink]

Show Tags

New post 13 Sep 2018, 09:56
I would like to add some comments, related to dangerous situations usually explored in traps for the uncautious students...

\({x^2}\,\,{\text{even}}\,\,\,\,{\text{does}}\,\,{\text{NOT}}\,\,{\text{imply}}\,\,\,\,\,x\,\,{\text{even}}\,\,\,\,\,\,\,{\text{ }}\left( {x = \sqrt 2 \,\,\,{\text{for}}\,\,{\text{example}}} \right)\)

\({y^2}\,\,{\text{odd}}\,\,\,\,{\text{does}}\,\,{\text{NOT}}\,\,{\text{imply}}\,\,\,\,\,y\,\,{\text{odd}}\,\,\,\,\,\,\,{\text{ }}\left( {y = \sqrt 3 \,\,\,{\text{for}}\,\,{\text{example}}} \right)\)

On the other hand, as it is the case in the problem proposed,

\(x\,\,\,\operatorname{int} \,,\,\,\,{x^2}\,\,{\text{even}}\,\,\,\,{\text{imply}}\,\,\,\,\,\,x\,\,{\text{even}}\,\,\,\,\,\,\,{\text{ }}\left( {x\,\,{\text{is}}\,\,{\text{odd}}\,\,{\text{or}}\,\,{\text{even,}}\,\,{\text{but}}\,\,\,{\text{it}}\,\,{\text{is}}\,\,{\text{not}}\,\,{\text{odd}}...} \right)\)

\(y\,\,\,\operatorname{int} \,,\,\,\,{y^2}\,\,{\text{odd}}\,\,\,\,{\text{imply}}\,\,\,\,\,\,y\,\,{\text{odd}}\,\,\,\,\,\,\,{\text{ }}\left( {y\,\,{\text{is}}\,\,{\text{odd}}\,\,{\text{or}}\,\,{\text{even,}}\,\,{\text{but}}\,\,\,{\text{it}}\,\,{\text{is}}\,\,{\text{not}}\,\,{\text{even}}...} \right)\)


This kind of observation follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7367
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If n is an integer, is (n+1)^2 an even integer?  [#permalink]

Show Tags

New post 16 Sep 2018, 18:28
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

\((n+1)^2\) is an even integer
=> \(n+1\) is an even integer
=> \(n\) is an odd integer

Condition 1)
Since “\(n-1\) is an even integer” is equivalent to “\(n\) is an odd integer”, condition 1) is sufficient.

Condition 2)
“\((n-1)^2\) is an even integer” is equivalent to “\(n-1\) is an even integer”, which is condition 1).
Condition 2) is also sufficient.

Therefore, D is the answer.

Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
_________________
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 $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Bot
Re: If n is an integer, is (n+1)^2 an even integer?   [#permalink] 16 Sep 2018, 18:28
Display posts from previous: Sort by

If n is an integer, is (n+1)^2 an even integer?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.