If k is an integer, is k even?

Question

(1) k/2 is not an even integer.

(2) 5 - k is an even integer.

Bunuel · Answer

Similar question from OG: https://gmatclub.com/forum/if-m-is-an-i ... 29702.html

sumi747 · Answer

IMO B
Statement 1, if k = 4, k/2=2. If k= 6, k/2= 3. Both cases k is even. Not sufficient.
Statement 2, 5-k= even, odd-odd=even, hence we know k is odd. Sufficient.

EncounterGMAT · Answer

IMO answer is option B

This is how I solved:

Posted from my mobile device

Archit3110 · Answer

#1
k/2 result in fraction /odd value insufficient
#2
5-k is an even integer only when k is odd
IMO B

bebs · Answer

sumi747  I don't think we can test 4 as you did for statement 1 since we are told  \frac{k}{2}  is not an even integer. Please correct me if I am wrong.

bebs · Answer

St 1: if k = 3 ==>  \frac{k}{2}  = 1.5 (not an even integer). If k = 6 ==>  \frac{k}{2} = 3 (not an even integer). Therefore, st 1 is not sufficient since we are able to show that k could be 3 (odd) or 6(even)

St 2: k must be odd since odd - odd = even, therefore st 2 is sufficient.

Answer is   B

If k is an integer, is k even?

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