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# If x is a positive integer, is the remainder 0 when 3x + 1

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If x is a positive integer, is the remainder 0 when 3x + 1 [#permalink]  19 Jan 2008, 10:53
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If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10?
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4
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Re: remainders [#permalink]  19 Jan 2008, 10:58
Basically is X an integer with 3 in the units digit: 3, 13, 23, 33, etc

1. Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32 etc. None of these numbers + 2 will give us 3 in the units digit SUFFICIENT
2. x>4 doesn't help us because X could be 12 (not work) or 13 (works) INSUFFICIENT

taken together we learn nothing new either

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Re: remainders [#permalink]  19 Jan 2008, 11:04
should be A.

You can see from A that 4n+2 always gives an even number, and plugging the result into 3x+1 always gives an odd number. All multiples of ten are even numbers, so you'll never have a perfect multiple of 10.

With B, you can have n=5 which doesnt give a remainder of 0, or n=13, which does. Insuff.
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Re: remainders [#permalink]  19 Jan 2008, 11:21
Should be A as explained by eschn3am
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Re: remainders [#permalink]  19 Jan 2008, 12:02
marcodonzelli wrote:
If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10?
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4

1: Suff. Notice that X must be even. b/c 4(n) is even and 2 is even and E+E= even.

Also notice that only when x has a 3 in its units digit can 3x+1 be divisible by 10. Since E+E will never equal an odd. the remainder cannot be 0.

2: X can be 5 or 13.
Re: remainders   [#permalink] 19 Jan 2008, 12:02
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