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Re: Positive integer Q gives a remainder of 5 when divided by 7. Find the
[#permalink]
09 Jul 2021, 08:54
1
Carcass wrote:
Positive integer Q gives a remainder of 5 when divided by 7. Find the remainder when 2Q is divided by 7.
(A) 2 (B) 3 (C) 5 (D) 7 (E) 9
-------------ASIDE------------------ When it comes to remainders, we have a nice property that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. --------------------------------------
Positive integer Q gives a remainder of 5 when divided by 7. So, the possible values of Q are: 5, 12, 19, 26, 33, . . . etc
Find the remainder when 2Q is divided by 7. Let's test one of the possible values of Q. The easiest value to test is Q = 5 So, 2Q = 2(5) = 10, and 10 divided by 7 leaves remainder 3