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Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Thu May 26, 2011 9:29 am

If p is positive integer, what is remainder when p is divided by 4?
a. When P is divided by 8 remainder is 5
b. P is the sum of the squares of two consecutive positive integers.

OA is D

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Source: Beat The GMAT — Problem Solving | Thu May 26, 2011 9:29 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu May 26, 2011 9:50 am

Hi,
From(1) : P = 8k+5 = 4(2k+1)+1.
So, when divided by 4, p leaves remainder 1
Sufficient

From(2) : P = n^2+(n+1)^2 = n^2 + n^2 +2n +1 =2n^2+2n+1 = 2n(n+1)+1
n(n+1) is always a product of even and odd number.so, the product is even of the form 2.x
So, P= 2(2x)+1 =4x+1
So, when divided by 4, p leaves remainder 1
Sufficient

Hence, answer D

Cheers!

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