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# For a non-negative integer n, if the remainder is 1 when 2n

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VP
Joined: 30 Jun 2008
Posts: 1007
For a non-negative integer n, if the remainder is 1 when 2n [#permalink]

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18 Sep 2008, 02:47
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0% (00:00) correct 0% (00:00) wrong based on 1 sessions

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For a non-negative integer n, if the remainder is 1 when 2n is divided by 3, then which of
the following must be true?
I. n is greater than zero.
II. 3^n = (-3)^n
III. √2^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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VP
Joined: 17 Jun 2008
Posts: 1477

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18 Sep 2008, 03:08
A.

Since, n is non-negative, it can be zero or positive. Also, 2n = 3x + 1 for x = 0,1,2,3,.....
Hence, n cannot be 0.

Possible values of 2n = 1,4,7,10,13,16,19,22.....
But, since n is integer hence possible values of n are 2,5,8,11,.....

Hence, II and III are out and only I is true.

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Re: PS: non-negative integer   [#permalink] 18 Sep 2008, 03:08
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# For a non-negative integer n, if the remainder is 1 when 2n

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