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

Question

Is the integer n odd?

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

They say that n(n-2) becomes divisible by 4 as soon as n is even, so n must be odd. 
 Well what about n=2? -->Isn't n^2-2n=0, an even integer? Did Manhattan Gmat forget about that option?

heyholetsgo · Answer

Damn, 0 is divisible by 4. Thanks man;)

gmat6nplus1 · Answer

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

follows  n(n-2) is not a multiple of 4

find out in which points the equation yields zero, zero is a multiple of 4 as well as a multiple of any number except zero itself. 
value a=0 and value b=2 thus n must not be any of those two values because otherwise the expression would result in a multiple of 4 
-n can be both positive or negative, the only restriction is that n is an integer- since o and 2 are out of the pool 4 would be the first positive even number applicable to n. Every other positive even number would cause the expression to be a multiple of 4. We can safely say that n is for sure not an even number. before submitting the answer let's quickly check how the expression behaves with negatives.

if n=-2 the greatest negative even integer plugged  n^2-2n  results in a multiple of 4 then for sure n is odd.
 
Sufficient.

2. n is a multiple of 3. 
Non sufficient, n could be zero.

unceldolan · Answer

(1) n²-2n ==> n(n-2) = 0. Thus, n = 2 or n = 0. Both are multiples of 4. Every other even integer (also the negatives) result in a multiple of 4. Thus n is clearly odd. 
You could also just plug in numbers....

(2) n is a multiple of 3 --> clearly IS. could be 6 or 9 or 12 or 15 and so on.

GMATinsight · Answer

Given : n is an Integer

Question : Is n odd?

Statement 1 : n^2-2n is not a multiple of 4 
i.e. n(n-2) is a multiple of 4
but since n and (n-2) are separated by 2 therefore, they will both be either even or both be odd
Since the product is even so they must be even. Hence
 SUFFICIENT

Statement 2 : n is a multiple of 3 
a multiple of 3 may be even (e.g. 6 or 12) or may be odd (e.g. 3 or 9). Hence,
 NOT SUFFICIENT

Answer: Option A

BrentGMATPrepNow · Answer

Target question :    Is the integer n odd?

Given : n is an INTEGER

Statement 1 : n² - 2n is not a multiple of 4.  
Factor to get:  n(n - 2)  is NOT a multiple of 4

Underlying concepts  :

Integer n is 2 greater than n-2
If n is ODD, then n-2 is also ODD, so n(n - 2) = (ODD)(ODD) =  ODD . In this case,  n(n-2)   cannot  be divisible by 4
If n is EVEN, then n-2 is also EVEN, so n(n - 2) = (EVEN)(EVEN) =  EVEN . More importantly, n and n-2 are CONSECUTIVE even integers, and   the product of two CONSECUTIVE even integers is always a multiple of 4

Statement 1 tells us that  n(n - 2)  is NOT a multiple of 4
So, it cannot be the case that n is EVEN
In other words,  it MUST be the case that n is ODD 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : n is a multiple of 3 
There are several values of n that satisfy this condition. Here are two: 
Case a: n = 3, in which case n  n is ODD 
Case b: n = 6, in which case n  n is EVEN 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

dabaobao · Answer

There's a slight mistake (bolded in red) there. If both n & (n-2) are even (example: {2,0} or {4,2}), then they would always be a multiple of 4, violating stmt 1. Hence, they both have to be odd. Therefore, n = odd.

argerniki · Answer

Bunuel , I think the question should get proper formatting.

I tried out different values and didn't get a sufficient answer from A, because I thought that the argument is  n^{2-2n} .
When n = 1,  n^{2-2n}  becomes  1^0 = 1 , which isn't a multiple of 4 and n is odd.
But when you plug in n = 2, it becomes  2^{2-2*2} = 2^{2-4} = 2^{-2} = \frac{1}{4} , which isn't a multiple of 4 as well and n is even.
Therefore 2 different answers -> insufficient.

It would be much clearer if the question was written as  n^2-2n

Bunuel · Answer

n^2 - 2n can only mean  n^2 - 2n . If it were  n^{2 - 2n}  it would have been written as n^(2 - 2n). Still edited. Thank you.

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

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