If x is a positive integer, is the remainder 0 when (3^x + : GMAT Data Sufficiency (DS)
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# If x is a positive integer, is the remainder 0 when (3^x +

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If x is a positive integer, is the remainder 0 when (3^x + [#permalink]

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23 Aug 2010, 07:58
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If x is a positive integer, is the remainder 0 when (3^x + 1)/10?
(1) x = 3n + 2, where n is a positive integer.
(2) x > 4

Pls explain the logic.
[Reveal] Spoiler: OA
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23 Aug 2010, 09:05
to have remainder of 0 the Numberator MUST be a multiple of 10 like 10,20,30,40 etc.
1. if x=3n+2 then we know X follows pattern 2,5,8,11,14.
we find the pattern of 3 raised to power and it is 1,3,9,7,1,3 etc... notice that the only time we can get remainder 0 is when 3 is raised to a power and result in units digit of 9 since 9+1 =10. it is irrelevant the tens,hundreds etc. digits are for this problem.

so going back to the pattern 2,5,8,11,14. if you try first couple you see 3^2=9 which is good. but, 3^5 gets us 3 in the units digit which is no good. so 1 is INSUFF
2. this goes by same logic, since x >4 we will have unit digits of 9 and others so INSUFF.

combining them doesnt help either since it just makes the pattern start at 17. so INSUFF

so E
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31 Aug 2010, 22:12
Is zero a positive integer? I don't think so...Correct me if I am wrong!
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01 Sep 2010, 00:22
Wooooo..... there is something wrong in my understanding or the eplaination above...
(3^x + 1)/10 to be an integer, i.e., remainder 0, x has to be 2,6,10,14...
for n=1,2,3 (3^x + 1)/10 will not be an integer, but for n=4 it will be... so not suff...
2 clearly not suff
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01 Sep 2010, 09:20
x=3n+2, so x = 5, 8, 11, 14,...
(3^x+1)/10 is an integer when x = 2, 6, 10, 14,...
Thus, when x = 8 , (3^x+1)/10 is not an integer
When x = 14, (3^x+1)/10 is an integer
x > 4 does not provide the necessary constraints to limit the possible values of x
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11 Sep 2010, 22:41
Similar problem at: need-some-help-92726.html
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Re: Divisibility DS   [#permalink] 11 Sep 2010, 22:41
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