even integer

[magical cook]

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. (2+b) /2

[Suyog]

a-b is an even integer

This is possible only when a and b both are either even or odd
i.e. a = 10 and b = 4
or a = 9 and b = 5

a/b is an even integer

Since we can have both odd or both even a/b is even only when a and b, both are even...

Now from the ans choices...

(a+b) / 2 will provide the odd ans..

Ans C.

[moneyman]

The best strategy is to pick numbers

Since its a must question try plugging in more than 3 values for a and b

I think the answer is D because for all other values there is a yes and a no as an answer

The answer is not C because lets assume a=8 and b=4 then (a+b)/2=12/2=6 which is an even number.

Is the answer D??

[magical cook]

yeah answer is D thanks

[preciousrain7]

The best strategy is to pick numbers

Since its a must question try plugging in more than 3 values for a and b

I think the answer is D because for all other values there is a yes and a no as an answer

The answer is not C because lets assume a=8 and b=4 then (a+b)/2=12/2=6 which is an even number.

Is the answer D??

can't the answer also be E since 4+2=6 and 6/2=3?

[andes1]

hummm???

[samirpandeyit62]

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-b is even so both a& b are either odd or even

a/b is even, possible only if both are even(considering the above case also into account)

so we can say that both a & b are even numbers

also a/b =c (c is even) i.e a = bc

now we have

A a/2 = bc/2 is even ( both b & c have 2 as a factor)
B. b/2 = odd or even
C. (a+b) /2 = (bc + b)/2 = b(c+1)/2 (may be even or odd)
D. (a+2) /2 = a/2 + 1 = even nos + 1 = odd
E. (2+b) /2 = 1 + b/2 (b/2 can be both even as well as odd)

[cris]

I dont see how D can be the answer:

"a" and "b" must be both even integers

D. (a+2)/2 must be odd

Say that "a" is 10 (an even integer)....10+2=12......12/2=6 (and is an even integer)

[rchadha7]

Its D.. as it is given that a/b is even means it cannot be 10/2 as 5 is odd... so a can be 8 or 12.
Then (a+2)/2 is always odd.

[cris]

Got it!!...guess that with the gmat nothing is as simple as ""a" and "b" are both even"...i will try to keep that in mind

Thanks rchadha7!

[cris]

Got it!!...guess that with the gmat nothing is as simple as ""a" and "b" are both even"...i will try to keep that in mind

Thanks rchadha7!

[StarDust845]

a - b = 2m where m GE 0. --(1)
a = 2qb where q GE 0 -- (2)

From (2) a is even. Hence b is also even from (1).

now (a + 2)/2 = (2qb + 2)/2 = qb + 1

b is even implies qb is even implies qb + 1 must be ODD.

Hence (a+2)/2 is odd.

Calista.