Data Sufficiency

If n is a positive integer and r is the remainder when ( n^2-1) is divided by 8. What is the value of r??

1. n is odd
2. n is not divided by 8

OA A

Explanations please

n^2-1 = (n-1) (n+1)

Stmt I

n is odd which tell us n-1 and n+1 are both consecutive evens. The product of any 2 consecutive evens will always be divisible by 8

Remainder:0

SUFF

Stmt II

n is not divisible by 8

We can pick many n values with different remainders when divided by 8

INSUFF

Choose A

The method that I applied was plugging numbers

n>0 and an integer

1) N is odd

n^2-1; substituting n=3,5,7,9,11 all leads to remainder 0. As it is perfectly divisible by 8

1 is sufficient

2) N is not divisble by 8.
Lets substitute n=4,6,7

n=4; 15/8 remainder 7
n= 6; 35/8 remainder 3
n= 7; 48/8 remainder 0

Inconclusive results: not sufficient

Thus answer is A

BlackArrow,
Picking numbers for remainder problems is a sure shot approach and I too am a big fan of it.

Like u did we must always go with the approach that immediately comes to mind rather than trying to think of a text book solution if one does not come to mind.

Picking numbers works good with remainder probs i.e as soon as u start seeing a pattern for eg. in stament I where the remainder is always 0 when u pick a odd. Most probs can be solved this way.

Just my 2 cents in the mix...

Good luck.

Regards,
CR

another soln.

the problem can be written as
n^2 -1 = 8k + r and we have find r.

stmt 1: n is odd.
We know square of n is always odd if n is odd.
so n^2 -1 is even.
Now choose values for n.
1, 3, 5, 7.
(n^2 -1) is 0, 8, 24, 48.
In every case the remainder is 0 when divided by 8.

So suffiient.

Stmt 2:
n is not divisible by 8.
So the remainder can be any number 1 - 7.
So insufficient.

Ans is A.

HT helps

Thanks a lot guys for sharing the approach.

Cramya,

Can you please let me know how to take the screenshots from the GMAT prep test??

I gave my GMAT prep yesterday and did exceptionally bad, and now I want to discuss some questions.

But I am not able to get the screenshots,some questions require figures and it will be otherwise very time consuming for me to post those questions.

Regards,

Karan

gmat740 wrote:Cramya,

Can you please let me know how to take the screenshots from the GMAT prep test??

I gave my GMAT prep yesterday and did exceptionally bad, and now I want to discuss some questions.

But I am not able to get the screenshots,some questions require figures and it will be otherwise very time consuming for me to post those questions.

Regards,

Karan

I think that should be easy. Just go to the review page, open up the question & use the "Print Scrn" button on your keyboard to take a screen shot of the page. Crop the image as desired, save it as an image & upload in this forum. If you are doing the above & still not able to copy the screen shot, then you are probably having a memory issue. Reboot your machine & try again.