Is b even? (1) a/b is even (2) (a+1)b is even

Question

Is b even?

(1) a/b is even

(2) (a+1)b is even

DavidTutorexamPAL · Answer

This is a bit of a trick question as we're not explicitly told that a,b are integers.
As such, since we're only given general information about the product and quotient of a and b, (E) will be our answer.
For example in (1) if we set b=1/2 than a/b = 2a which is even for any integer a and in (2) we can keep using fractions such as a=2 and b=2/3. Similarly, when combining, we can find fractions that work in both cases such as a=3 and b=1/2

If we assume that a,b are integers, then a more standard solution would be:

As we're asked about number-properties (even/odd) we'll look for a theoretical solution (one without calculation).
This is a Logical approach.

(1) If a/b is even then it is divisible by 2. Since a/b is a factor of a, this means that a is divisible by 2. It tells us nothing about b, however. (For example, consider a = 20, b=2 or a=20, b=5)
Insufficient.

(2) If a product is even, then at least one of its factors is even. So, at least one of (a+1) and b are even. As we don't know which one, we cannot answer.
Insufficient.

Combined: From (1) we know that a is even meaning that a+1 is odd. Therefore, by (2), b must be even.
Sufficient!

In this case (C) is our answer.

GMATBusters · Answer

(1) a/b is even
Not sufficient. (A,B) can be (6,2) or (6,3) or even non integers.
(2) (a+1)b is even 
B can be even or odd or non integers. (a,b) can be (1,2) or (1,1)
Not sufficient.

after combing st1 &2 , multiplying st1&2 , we get a(a+1) is even integer. That means a is an integer.
Now if a is integer, then as per statement 2, b is also a integer as (a+1)*b is an even integer.
Now if both a and b are integers, and a/b is even, a is even integer.
Now using a as even integer, (a+1) is odd integer, hence b is even integer as (a+1)*b is even.

Sufficient.

answer c

amanvermagmat · Answer

I think the answer should be E.

We are not given that a/b are integers, so they can take fractional/decimal values also.

Lets take an example of a=3, b=1.5. Here a/b = 3/1.5 = 2, which is even. And (a+1)b = 4*1.5 = 6, which is also even.

Now lets take an example of a=8, b=2. Here a/b = 8/2 = 4, which is even. And (a+1)b = 9*2 = 18, which is also even.

Looking at the above two cases, b can be even, or it can take a decimal value also. So even after combining the statements are not sufficient.  Hence E

DavidTutorexamPAL · Answer

Good point. But then the question becomes kind of pointless, doesn't it? (as if they aren't integers you can do whatever you like)

Bunuel · Answer

Yes, in its current form the answer must be E. C would be correct if the question were "Is integer b even?".

GMATBusters · Answer

One of the trickiest question Sir...

You are awesome

Good point. But then the question becomes kind of pointless, doesn't it? (as if they aren't integers you can do whatever you like)

Yes, in its current form the answer must be E. C would be correct if the question were "Is integer b even?".

shmba · Answer

agree. i've seen a lot of questions like this in gmatclub. quite tricky. but most likely you won't see it in real gmat tests.
when it comes to odd/even, gmat prompt always states numbers are integers. otherwise, it'll be pointless. good question but pretty much out of scope.

Is b even? (1) a/b is even (2) (a+1)b is even

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Is b even? (1) a/b is even (2) (a+1)b is even

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