Is ab odd? (1) a is even (2) a is an integer

1. If a is even and b can be fraction which is 1/a and the value of ab is odd.
But if a is even and b is also an integer, then the product of ab is even. Not sufficient.

2. 'a' being an integer is not sufficient to tell us anything about ab,
since we have no information about b. Here ab could be either even or odd. Not sufficient

On combining the information present in both the statements,
we know a is an integer and even, but we have no information about b.
Hence, the value of ab can either be odd or even as already explained in statement 1's explanation (Option E)

IMHO E

No info is given whether B is an integer


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ST 1: a is even. no idea about b as it could be a fraction, decimal etc. INSUFFICIENT
ST 2: a is integer. no idea about b as it could be a fraction, decimal etc. INSUFFICIENT

St1 & St 2: a is even integer, no idea about b as it could be a fraction, decimal etc. INSUFFICIENT

In the Veritas prep book, there is this thinking process called "Why are you here?". I am guessing this applies here (idk, maybe someone from Veritas can confirm this?). I answered this question and got it wrong. I.e. I answered A because here is my thinking process:

Statement 1: a is even. Quoting pushpitkc, If a is even, b being odd/even wouldn't make any difference, because the product will always be even. Hence statement 1 is sufficient because it gives us a definite NO. And hence sufficient.

Statement 2: a is an integer. My thinking is, this has nothing to do with ab being odd or even. Hence, not sufficient.

So in theory, according to OA, I am wrong because I did not think about the "Why are you here?" element. But I somehow cannot brain the "Why are you here?" element in this question.

Hi sarahfiqbal,

I had not considered the possibility of b being a fraction.
Eg1 Let a=2, b=\(\frac{1}{2}\). The product of ab is 1 which is odd.
Eg2 Let a=2, b=1. Product of ab is 2, which is even.

Hence the information present in both the statements is not enough to answer that question
So, the answer must be Option E, not A as I had previously marked. Made the necessary changes.

Also, hope that helps you!

pushpitkc Yes, I did the same thing- I didn't consider it to be a fraction. And my thought now is that Statement 2 gives that clue that we are suppose to think about fractions. Which is why I highlighted the Veritas prep books. It has that element of "Why are you here?". So I should practice this way of thinking more.

But thank you for the clarification. Good luck.

+1 for option E.

St 1 - No info on whether a is an integer or any info on b.
St 2 - NS ; No input on whether or not a is an integer.

Both - NS. We still don't know if ab will be an integer or not. The entire product must be divisible by 2. Hence E
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Target question: Is ab odd?
Since there's no information stating that b is an integer, we can jump straight to.....

Statements 1 and 2 combined
There are several values of a and b that satisfy BOTH statements. Here are two:
Case a: a = 2 and b = 1, in which case ab = (2)(1) = 2. So, ab is NOT odd
Case b: a = 2 and b = 1.5, in which case ab = (2)(1.5) = 3. So, ab IS odd
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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