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
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 Jay@ManhattanReview
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Say the quotient when the integer n is divided by 6, with the remainder 3 is q.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
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
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When the integer n is divided by 6, the remainder is 3.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
When we are given this wording, the smallest option for n is THE REMAINDER ITSELF.
Test n=3 in the answer choices:
(A) n  3 = 33 = 0
(B) n + 3 = 3+3 = 6
(C) 2n = 2*3 = 6
(D) 3n = 3*3 = 9
(E) 4n = 4*3 = 12
Only D is not a multiple of 6.
The correct answer is D.
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We can let n = 9. We see that all the expressions in the given answer choices will be a multiple of 6 except 3n.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
Answer: D
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