If a,b and c are positive integers and only one out of them is even, which of the following must be even?

I. \(\frac{ab}{c}\), where ab/c is an integer.
II. abc
III. a+b+c

A. Only I
B. Only II
C. Only III
D. Only II and III
E. I, II and III

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Given, a,b and c are positive integers & only one out of them is even.

I.\(\frac{ab}{c}\),
Since ab/c is an integer, hence \(Rem(\frac{numerator}{denominator})=0\), so, when one of the integers is even, then numerator/denominator must be a multiple of 2.hence the expression must be even.
II.abc
Since only one out of a,b, and c is odd; hence even*(odd)=Even. hence abc is Even.
Must be even.
III. a+b+c
when a=even, b, c=odd; a+b+c=even+odd+odd=even+even=even
Since a,b, and c are added ;same results would be obtained when b or c is even.
Must be even.
Ans. (E)
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PKN

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