If n is an integer, is n even?

Question

(1) 2n is divisible by 4 
(2) n^2 is even

oss198 · Answer

(1)  2n  divisible by 4 means that n contains at least one 2 as a factor. Therefore the statement is sufficient.

(2) 
odd*odd = odd
even*even = even

as  n^2  is even, n must be even. Sufficient.

Answer D.

Bunuel · Answer

If n is an integer, is n even?

(1) 2n is divisible by 4 --> 2n = 4k --> n = 2k = even. Sufficient.

(2) n^2 is even --> since n is an integer, then n^2 can be even only if n is even. Sufficient.

Answer: D.

Infxel · Answer

If n is an integer, is n even?

(1)  2n is divisible by 4  
(2) n^2 is even

Hello Bunuel, I got confused when I was solving this question. First let's agree on a couple of points, 0 is an integer, 0 is neither even nor odd, & 0 is divisible by everything.

So when I look at the first statement it says 2n is divisible by 4, what if n=0, this statement would still be correct, however 0 is neither even nor odd, so how is statement one sufficient on it's own.

Regards,
YA

EMPOWERgmatRichC · Answer

Hi youssefhabouseif,

0 IS an EVEN integer, by definition. Here's why:

On a number line, consecutive integers fall into the pattern....even....odd.....even....odd.....even....odd....etc.

-2 = even
-1 = odd
0 = even
1 = odd
2 = even
Etc.

Knowing that 0 IS EVEN, you likely would have picked the correct answer, but it's important to keep this rule in mind - you'll likely use it on Test Day at least once.

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

ZERO: 1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. Check more here: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030

stonecold · Answer

Here given n is an integer we need to see if its even or odd
Statement 1 => 2n/4=Integer => N is divisible by 2 => Its even  ]
Statement 2 => n^2=even => n must be even as POWER DOES NOT EFFECT THE EVEN OR ODD NATURE OF ANY NUMBER.

Krishh9119 · Answer

For the 2nd case, what if n is negative and n^2 is even. ex: n=-2. then n^2=4. should we consider n (which is negative as even).
The question boils down to whether negative numbers are considered odd/even in GMAT?

Bunuel · Answer

Negative integers can be even or odd  generally , not only on the GMAT. GMAT does not have its own math.

An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2, 0, 2, 4, ... are all even integers.

An odd number is an   integer   that is not evenly divisible by 2. So, ..., -3, -1, 1, 3, 5, ... are all odd integers.

CrackverbalGMAT · Answer

From the question stem, we know that n is not a fraction or a root.

From statement I alone, 2n is divisible by 4.

Therefore, 2n = 4, 8, 12, …. and so on. This means n = 2 or 4 or 6 and so on. 
For all values, we see that n is even
Statement I alone is sufficient. Answer options B, C and E can be eliminated.

From statement II alone,  n^2  is even.

The square of an integer is even only when the integer is even. Therefore, n is even.
Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

Hope that helps!
Aravind B T

jaydavido · Answer

What if n is 13? A would be not sufficient?

Posted from my mobile device

Bunuel · Answer

(1) says that 2n is divisible by 4. If n = 13, 2n=26, which is not divisible by 4, so n cannot be 13.

ItzSam · Answer

In the statement 1, what if we assume if n=1, then also 2n is divisible by 4, hence when n is odd then also it satisfies, and if n=2 then also it satisfies. Isn't it insufficient in that case?

Bunuel · Answer

If n = 1, then 2n = 2, which is not divisible by 4. So your assumption there is incorrect. For 2n to be divisible by 4, n itself must be even, because then n contributes at least one factor of 2, making 2n divisible by 4.

If n is an integer, is n even?

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