If A and B are positive integers, is the product AB even?

SOLUTION

If A and B are positive integers, is the product AB even?

Since A and B are integers, then in order the product AB to be even at least one of them must be even.

(1) The sum A + B is odd. A and B cannot both be odd, since odd+odd=even, so either A or B must be even. Sufficient.

(2) A is even. Sufficient.

Answer: D.
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If A and B are positive integers, is the product AB even?

(1) The sum A + B is odd.
(2) A is even.

Stat1:
Since A+B = odd implies that one number is even and other is odd so product of AB will be even in any case.

Stat2
A is even.
Since A is even and B is any positive integer so AB will be even in any case.

So, Answer will be D
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A, B= Positive Integers

Is AB=Even? Rephrase question to Is either A or B Even?
Y/N question.

I started with statement 2.
A= Even= Sufficient. Anything times an even number=a even number

Statement1
A+B=ODD
only ODD+Even=ODD therefore sufficient
Answer is D

We need to determine whether the product of positive integers AB is even. We must recall that the product of an even integer and any other integer is always even. Thus, if we can determine that either A or B (or both) is even, then we can answer the question.

Statement One Alone:

The sum A + B is odd.

In order for the sum of two integers to be odd, one of them must be even and the other must be odd. That is, either A is even and B is odd OR A is odd and B is even. In either case, the product AB is even, since one of them is even. Thus, statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and E.

Statement Two Alone:

A is even.

Since we know that the product of an even integer and any other integer is always even, we know that the product AB will always be even.

Statement two is also sufficient.

The answer is D.
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Here is my solution ->
Here we need the Even odd nature of A*B
as A and B are integers
A*B will be even if anyone of A or B is even OR both A and B are even

Statement 1
A+B=odd
A+B will be odd only when A and B will have the Different Even/odd nature
Hence If A is odd => B will be even
And if B is odd => A id even
Hence one out of A and B will always be Even
Hence Sufficient
Statement 2
A is even
As is even => A *B will Even
Hence Sufficient
Hence D
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A,B>0 (They are positive)

A*B=Even
Only if:
A B
Even Even
Even Odd
Odd Even

(1) A+B=Odd

One of these (A and B) is odd. (Odd+Even=Odd e.g. 1+2=3)

Sufficient. (AD)

(2) A is even.
No need to solve. Sufficient.

D

#2 If a is even ab has to be even number

#1, only possible combination-> odd+even=odd, so ab has to be even.

Each statement independently sufficient.

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