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# When 15n is divided by 6, the remainder is x. What is value

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Joined: 24 Sep 2009
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When 15n is divided by 6, the remainder is x. What is value [#permalink]  06 Oct 2009, 01:06
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When 15n is divided by 6, the remainder is x. What is value of x?

1/ When n is devided by 2, the remainder is 0
2/ When n is divided by 3, the remainder is 0
Senior Manager
Joined: 31 Aug 2009
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Location: Sydney, Australia
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Re: Divisibility/ Remainders [#permalink]  06 Oct 2009, 02:34
1/ When n is divided by 2, the remainder is 0
This means n is even. 15x2 = 30. 15n will always be divisible by 30. You can test this by using n=4,6,8 etc. 30/6 has remainder 0.
Sufficient.

2/ When n is divided by 3, the remainder is 0
n = 3,6,9...
n=3 15n=45 45/6 has remainder 3
n=6 15n=90 90/6 has remainder 0
Not sufficient.

ANS = A.
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Re: Divisibility/ Remainders [#permalink]  07 Oct 2009, 12:55
Here is another solution.

When 15n is divided by 6, the remainder is x. Simplyfing the equation 15 * / 6 results in 5n/2 and also states that x is the remainder.

When a number is divided by 2, the reaminder can be 0 thru n-1 which means in our case x can be either 0 or 1. Now the question is to find the value or X. In 5n/2, 5 is not divisible by 2. So the value of x depends on whether n is even(in which case x = 0) or n is odd(in which case x = 1).

Clue 1 When n is divided by 2, remainder is 0. Clearly n is even and hence x is zero. Sufficient.
Clue 2 When n is divided by 3, remainder is 0. Here n can be odd(for ex - 9) or even(for ex - 6) So x can be 1 or 1. Not sufficient.

Ans = A
Re: Divisibility/ Remainders   [#permalink] 07 Oct 2009, 12:55
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