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.