BTGmoderatorDC wrote:When the integer n is divided by 6, the remainder is 3, Which of the following is NOT a multiple of 6?
(A) n - 3
(B) n + 3
(C) 2n
(D) 3n
(E) 4n
OA D
Source: Official Guide
Say the quotient when the integer n is divided by 6, with the remainder 3 is q.
Thus, n = 6q + 3
Let's take each option one by one.
(A) n - 3 => n - 3 = 6q + 3 - 3 = 6q. We see that 6q is a multiple of 6; thus, not the correct answer.
(B) n + 3 => n + 3 = 6q + 3 + 3 = 6q + 6 = 6(q + 1). We see that 6(q + 1) is a multiple of 6; thus, not the correct answer.
(C) 2n => 2n = 2*(6q + 3)= 12q + 6 = 6(2q + 1). We see that 6(2q + 1) is a multiple of 6; thus, not the correct answer.
(D) 3n => 3n = 3*(6q + 3) = 9(2q + 1). We see that 9(2q + 1) is NOT a multiple of 6; thus, it is the correct answer.
(E) 4n => Since 4n is a multiple of 2n and 2n is a multiple of 6, 4n is also a multiple of 6; thus, not the correct answer.
The correct answer:
D
Hope this helps!
-Jay
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(B) n + 3
(C) 2n
(D) 3n
(E) 4n
