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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Re: If n is an integer, is n even? [#permalink]
26 Aug 2012, 02:13

Expert's post

SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> n^2-1=odd --> n^2=odd+1=even. Now, since n is an integer, then in order n^2 to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some irrational number (square root of an even number), for example \sqrt{2}, so not an even integer.

(2) 3n + 4 is an even integer --> 3n + 4=even --> 3n=even-4=even. The same here, since n is an integer, then in order 3n to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some fraction, for example \frac{2}{3}, so not an even integer.

Re: If n is an integer, is n even? [#permalink]
30 Aug 2012, 10:32

(1) n^2 - 1 is odd. The next consecutive integer is n^2 and is therefore even. This means that n must be even too, because squaring a number does NOT change this. --> sufficient

(2) 3n + 4 is even. So 3n is even, too. This means that the prime factorization of 3n includes at least one 2. Dividing by 3 (to get from 3n to n) does NOT eliminate recude the number of twos in the prime factorization, so n is even. --> sufficient

The correct answer is D. Both statements are individually sufficient.

Re: If n is an integer, is n even? [#permalink]
30 Aug 2012, 18:56

i will go with d both options individually can get the required info -as its an integer no more fractions integer when squared gives the same type value i.e odd gives odd and even gives even same way multiplying odd with even gives even and odd with odd gives odd

hence both are individually sufficient
_________________

Re: If n is an integer, is n even? [#permalink]
31 Aug 2012, 01:33

Expert's post

SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> n^2-1=odd --> n^2=odd+1=even. Now, since n is an integer, then in order n^2 to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some irrational number (square root of an even number), for example \sqrt{2}, so not an even integer.

(2) 3n + 4 is an even integer --> 3n + 4=even --> 3n=even-4=even. The same here, since n is an integer, then in order 3n to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some fraction, for example \frac{2}{3}, so not an even integer.

Re: If n is an integer, is n even? [#permalink]
16 Mar 2014, 17:55

Bunuel wrote:

SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> n^2-1=odd --> n^2=odd+1=even. Now, since n is an integer, then in order n^2 to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some irrational number (square root of an even number), for example \sqrt{2}, so not an even integer.

(2) 3n + 4 is an even integer --> 3n + 4=even --> 3n=even-4=even. The same here, since n is an integer, then in order 3n to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some fraction, for example \frac{2}{3}, so not an even integer.

Re: If n is an integer, is n even? [#permalink]
16 Mar 2014, 22:45

Expert's post

X017in wrote:

Bunuel wrote:

SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> n^2-1=odd --> n^2=odd+1=even. Now, since n is an integer, then in order n^2 to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some irrational number (square root of an even number), for example \sqrt{2}, so not an even integer.

(2) 3n + 4 is an even integer --> 3n + 4=even --> 3n=even-4=even. The same here, since n is an integer, then in order 3n to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some fraction, for example \frac{2}{3}, so not an even integer.

Answer: D.

Since n is a integer, can we not try with n as 0?

Yes, n can be 0 but 0 is even too.
_________________