Non-negative integer

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Thu Jan 07, 2010 5:22 am

For a nonnegative integer n, if the remainder is 1 when 2^n is divided by 3, then which of
the following must be true?

I. n is greater than zero.
II. 3^n = (-3)^n
III. âˆš2^n is an integer.

A. I only
B. II only
C. I and II
D. I and III
E. II and III

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Source: Beat The GMAT — Problem Solving | Thu Jan 07, 2010 5:22 am

ace_gre: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Nov 23, 2009 2:30 pmFollowed by: 1 member; Thanked: 26 times

by ace_gre » Thu Jan 07, 2010 10:45 am

IMO E

First determine the pattern 2 ^0=1, remainder when divided by 3=1
2^1=2, remainder when divided by 3=2
2^2=4, remainder=1
2^3=8 , remainder = 2
2^4=16 ,remainder =1
2^5=32 , remainder =2

Alternating pattern of 1 and 2. In all cases remainder is 1 when n=even.

I is not true. For n=0, remainder =1.
II For n=even, 3^n=(-3)^n. True
III âˆš2 ^ n= integer(for n=0,2,4,..value is integer). True

Hence II and III must be true.

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

by mehravikas » Thu Jan 07, 2010 7:33 pm

Agree answer should be D

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