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If n is a positive integer, which one of the following numbe

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If n is a positive integer, which one of the following numbe [#permalink] New post 30 May 2018, 01:19
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If n is a positive integer, which one of the following numbers must have a remainder of 3 when divided by any of the numbers 4, 5, and 6?

(A) 12n + 3

(B) 24n + 3

(C) 80n + 3

(D) 90n + 2

(E) 120n + 3
[Reveal] Spoiler: OA

Last edited by Carcass on 30 May 2018, 15:53, edited 1 time in total.
Edited by Carcass
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Re: If n is a positive integer, which one of the following numbe [#permalink] New post 28 Jun 2018, 21:17
shahul wrote:
If n is a positive integer, which one of the following numbers must have a remainder of 3 when divided by any of the numbers 4, 5, and 6?

(A) 12n + 3

(B) 24n + 3

(C) 80n + 3

(D) 90n + 2

(E) 120n + 3


Hi,

Firstly we have to find the number that is divisible by 4, 5, and 6. LCM(4,5,6) = 60. Any multiple of 60 will be divisible by 4,5, and 6.
Hence, in general term, any number of the form 60n will be divisible by 4,5, and 6, where n is a non-negative integer.

To get remainder 3, we have to add 3 in the above number. Hence, the required number is of form 60n + 3.

There is no such option available. But option(E) can be converted into the above form. 120n + 3 = 60*2*n + 3.

Hence, the answer is (E).

Thanks.
Re: If n is a positive integer, which one of the following numbe   [#permalink] 28 Jun 2018, 21:17
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If n is a positive integer, which one of the following numbe

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