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If n is an integer, which of the following must be even?

1 2

gupta335

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20 Aug 2018, 01:20

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Any Integer that is a multiple of 2, is even.

Ans. C

Hovkial

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19 Oct 2020, 04:39

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OFFICIAL GMAT EXPLANATION

2n is a multiple of 2 and hence must be even.

vigneshvrk

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Bunuel

If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

Practice Questions
Question: 44
Page: 158
Difficulty: 550

A. This could be either odd or even
B. Same as A.
C. Any integer multiplied by 2 will give us an even integer
D. 1 added to any even integer would give us an odd integer
E. This could be either odd or even

Hence answer is C.

henokgadissa

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26 Aug 2025, 14:18

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What about n = 0? ...................................

Bunuel

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henokgadissa

What about n = 0? ...................................

If n = 0, then 2n = 0, which is an even integer.

ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer.

3. Zero is neither positive nor negative (the only one of this kind)

4. Zero is divisible by EVERY integer except 0 itself (\(\frac{0}{x} = 0\), so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x)

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))

9. \(0^0\) case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), \(0^n = 0\).

11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.

12. \(0! = 1! = 1\).