Is the product of integers A, B, and C even ? (1) A*B is odd (2) B*C

Argument 1:

Don’t have any info about C. So NS

Argument 2:

If A>0 then even but if A=0 the its also even as 0 considered as Even. -- so Sufficient

Correct answer B

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Target is product of abc even or not
#1
Ab is odd
C is not known
Insufficient
#2
BC is even
A is not known and may be 0 insufficient
From 1&2
Ab is odd and c is even so abc is even
Sufficient option c

But zero is an even number. Would it make any difference if A=0?

Posted from my mobile device

Target is product of abc even or not
#1
Ab is odd
C is not known
Insufficient
#2
BC is even
A is not known and may be 0 insufficient
From 1&2
Ab is odd and c is even so abc is even
Sufficient option c

Zero is an even number, so even if A is zero we get even number as result of the product.

Step 1: Analyse Question Stem

A, B and C are integers; therefore, they are either even or odd.
We have to find out if the product of these integers is even.

The product of a set of integers is even if at least one of them is even; therefore, if one out of A, B and C is even, their product will be even.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: A*B is odd

We have no information about the nature of C

If C = even, A * B * C = even
If C = odd, A * B * C = odd

The data in statement 1 is insufficient to answer the question with a definite YES or NO.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: B*C is even

This means that at least one of B and C is even.
Therefore, the product of A, B and C MUST be even.

The data in statement 2 is sufficient to answer the question with a definite YES.
Statement 2 alone is sufficient. Answer option C and E can be eliminated.

The correct answer option is B.