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24 Dec 2018, 03:38
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D
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Difficulty:
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Question Stats:
87% (01:05) correct
13%
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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
(A) n – 3
(B) n + 3
(C) 2n
(D) 3n
(E) 4n
HKD1710
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
(A) n – 3
(B) n + 3
(C) 2n
(D) 3n
(E) 4n
When n is split into groups of 6, 3 is left over.
If you remove 3 from n, there will be only groups of 6 leftover. So (n - 3) will be divisible by 6.
If you add 3 to n, the remaining will also form a complete group of 6 and hence there will be only groups of 6. So (n + 3) will be divisible by 6.
When you double n, 3 left over will become 6 and so we will have only groups of 6. Hence 2n will be divisible by 6.
If 2n is divisible by 6, 4n must be divisible by 6 too.
When you triple n, 3 will still be left over. So 3n will not be divisible by 6.
Answer (D)
24 Dec 2018, 13:24
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HKD1710
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
(A) n – 3
(B) n + 3
(C) 2n
(D) 3n
(E) 4n
The integer n is divided by 6, the remainder is 3
This meabs that \(n = 6q+3\)
If n is divided by even number and leaves remainder it means that N is ODD number
to prove this just plug any numbers for q
n=9= 6(1)+3
now test 9 in aswer choices
(A) 9 – 3 = 6 (MULTIPLE OF 6)
(B) 9 + 3=12 (MULTIPLE OF 6)
(C) 2(9)=18 (MULTIPLE OF 6)
(D) 3(9)= 27 ( 27 IS NOT MULTIPLE OF 6 )
(E) 4 (9) =36 (MULTPLE OF 6)
IMO: D
