Is the integer n odd? (1) n^2 - 2n is not a multiple of 4. (2) n is

Question

Is the integer n odd?

(1) n^2 - 2n is not a multiple of 4.
(2) n is a multiple of 3.

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GMATinsight · Answer

Question: Is n odd?

Statement 1 :n^2 - 2n is not a multiple of 4.

n^2 - 2n =n*(n-2)

n and n-2 should both be either Consecutive Even integers or Consecutive ODD integers

If they were consecutive Even integers then n*(n-2) musthave been divisible by 4
Since n*(n-2) is NOT divisible by 4 therefore n and n-2 both MUST BE ODD INTEGERS
answer to the question is Definitely NO hence

SUFFICIENT

Statement 2 : n is a multiple of 3.

i.e.n may be 3 (odd) or 6 ( even) hence

NOT SUFFICIENT

ANSWER: OPTION A

RayanCHB · Answer

for statement 1 : n could be equal to 2 so n x (n-2) is not divisible by 4 and yet n is not odd.

statements 1 + 2 : n is definitely odd hence I believe it should be C.

HarshiSingh · Answer

What about n = 0 OR 2?

Shikhar22 · Answer

exactly. it should be c

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vivek1810971 · Answer

ND104 · Answer

if n=2, n x (n-2) =2*0=0, 0 is DIVISIBLE by 4, resulting 0 as quotient
Zero is divisible by every integer, and so zero is a multiple of all numbers (x*0 = 0, so 0 is a multiple of any number, x)

ND104 · Answer

Is the integer n odd?

(1) n^2 - 2n is not a multiple of 4.
(2) n is a multiple of 3.

Statement 1- 
If n=0, n*(n-2)=0*-2 =0 which  is multiple  of 4,
If n=2, n*(n-2)=2*0 =0 which  is multiple  of 4

Zero is divisible by every integer, and so zero is a multiple of all numbers (x*0 = 0, so 0 is a multiple of any number, x)

If n is even(including n=0 or 2), n-2 will also be even, and so it will be  divisible for 4 
but if n is odd, n-2 will be odd as well, and its product will not be divisible by 4.

Only second case works for Statement1, n=odd, so anwer is YES always

A is the answer

Is the integer n odd? (1) n^2 - 2n is not a multiple of 4. (2) n is

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