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If x is a positive integer, is the remainder 0 when (3^x +

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Manager
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If x is a positive integer, is the remainder 0 when (3^x + [#permalink]  28 Oct 2005, 07:04
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

OA is E but i think ans should be A. Pls comment.
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Re: D/s : remainder [#permalink]  28 Oct 2005, 07:10
trickygmat wrote:
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

OA is E but i think ans should be A. Pls comment.

1) x=5(n=1) --> 3^5= 243 ---> 3^5+1= 244 divided by 10 has remainder of 4--->insuff
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Re: D/s : remainder [#permalink]  28 Oct 2005, 07:22
trickygmat wrote:
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

OA is E but i think ans should be A. Pls comment.

(2) is quite clear I think... X could be 5, and then the remainder is 4 or X could be 6 then the reminder is zero..

(1) is a bit weird... E is seems correct, however I had to use a calculator to verify this...

the equation leaves a remainder of zero, when X = 2,6,10,14.. always +4(here I needed the calculator to verify its always +4).
So if n is a +ve integer and X shoud equal one of the numbers.. you try to find an n for x = 2, or 6 or 10. 2 is not possible because n is positive.. 6 is not possible if n needs to be an integer. 10 is als not possible.. but 14 is. if n = 4 then x = 14.. and the equation from the stem leaves a remainder of 0.... so insuff.
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Oops never mind...I didn't get it...

Last edited by mohish on 28 Oct 2005, 07:30, edited 1 time in total.
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Re: D/s : remainder [#permalink]  28 Oct 2005, 21:24
trickygmat wrote:
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
OA is E but i think ans should be A. Pls comment.

both statements, (i) and (ii), are insufficinet to answer the question.

suppose in (i), if
1. n=1, x = 5, (n is not = 0, since n is a +ve integer). the unit digit of x is 3. so reminder of (3^x + 1)/10 is not 0.
2. n=2, x = 8. the unit digit of x is 1, so the reminder of (3^x + 1)/10 is not 0.
3. n=3, x = 11. the unit digit of x is 7. so still the reminder of (3^x + 1)/10 is not 0.
4. n=4, x = 14. now the unit digit of x is 9. so the reminder of (3^x + 1)/10 is 0. so not suff.

from (ii) also same result derrives. so not suff. togather too not suffcient...............
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You guys are brilliant!
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