Odd integer

[cartera]

If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?


A. a/2

B. b/2

C. (a+b)/2

D. (a+2)/2

E. (b+2)/2

Official Guide in the next post

[supersuj]

good question!

i get D

since a/b= even , a=even*b and thus a=even
a-b= even, so b MUST be even as well

a=even*b ( a MUST be even and MUST be divisible by 4)

(a+2)/2 will always be ODD since a must be divisible by 4

Answer is D

[cartera]

You are right Official Answer: D

[Jen1984]

Yes but what if I use

a = 8
b = 2

Then, (a-b) = 6 and (a/b) = 4

In this case, the answer would be B.

From what the question tells us why can I not solve the problem like this?

[serGINho]

I`ve got the the same question actually

[cartera]

Yes but what if I use

a = 8
b = 2

Then, (a-b) = 6 and (a/b) = 4

In this case, the answer would be B.

From what the question tells us why can I not solve the problem like this?

The questions says which number must be an odd number. This implies the number is always an odd number.

[cramya]

Good question! The question reads must be and not could be. One thats always true (must be->woks for any set of numbers)

If a/b is an even integer a has to be even . b could be odd or even. Since a-b is also even b also has to be even

Elimate a,b and c .Between d and e

a=12 b=6

b+2/2 is even

a+2/2 -> odd

Choose D) wihout picking any more numbers since we have eliminated A,B,C and E

[gmat_t1]

(D) clearly