[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
If n is an integer, is (n+1)^2 an even integer?
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
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
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Some important rules:Max@Math Revolution 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
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN
4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN
Target question: Is (n+1)² an even integer?
This is a good candidate for rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
(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
Cheers,
Brent
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Brent´s solution is perfect and full of important details.
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.
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)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
=>
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).
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).
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
-
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Mon Sep 17, 2018 1:08 am