Is the product of a and b odd?

The product will be odd if both a and b are odd
1. a has two factors so a is prime...now if a=2,b=odd number then product is not even but if a=any other prime and b=odd number than product is odd...clearly we dont have enough information.. Option A and D ruled out

b=2x+1 so possible values for b=1,3,5,7...b= odd number...B ruled out

Combining both statements we can still have product even or odd..

ans E

From 1, we can say a can be 2, 3, 5, 7 ... any prime number. Donot know the value of b. Therefore, insufficient

From 2, we can say b is odd. But we don't know a. Therefore, insufficient.

Combining a) and b), we can't say whether the product of a and b is odd or even, since it depends on the value of "a" which can either be even (value = 2) or odd (primes other than 2).

E) should be the answer

Step 1: Analyse Question Stem

We have to find if the product of a and b is odd.
If a and b are integers, their product will be odd when both are odd. However, since the question does not mention whether a and b are integers, we need more information from the statements.

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

Statement 1: a has only 2 factors

This means that a is a prime number. However, primes can be even or odd.
Additionally, we do not have any information about b. Therefore, we cannot ascertain if the product of a and b is 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 = 2x + 1, where x is an integer

This means that b is an odd number.
But, we do not have any information about b. Therefore, we cannot ascertain if the product of a and b is odd.

The data in statement 2 is insufficient to answer the question with a definite YES or NO.
Statement 2 alone is insufficient. Answer option B can be eliminated.


Step 3: Analyse Statements by combining

From statement 1: a has only 2 factors
From statement 2: b = 2x + 1, where x is an integer

a is a prime number and b is an odd number.
If a = 2 and b = 1, product of a and b is even
If a = 3 and b = 1, product of a and b is odd

The combination of statements is insufficient to answer the question with a definite YES or NO.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.

The correct answer option is E.

Here we need to prove that A*B is odd
Note => It is not specified whether they are integers or not.
Statement 1 => A = prime => No clue of B
A=2 B=3 => A*B=even
A=3 B=5 => A*b= odd
Not suff
Statement 2 => B must be odd
no clue of A
not suff
combining them we can say if A is 2 then AB is even else Ab will be odd
since no boundary condition on A is given => not suff

Hence E

FROM STATEMENT - I INSUFFICIENT

a can be both Odd / Even ; further we have no knowledge of b so, we can not find ab

FROM STATEMENT - II INSUFFICIENT

If x = odd , 2x + 1 will be even
If x = even , 2x + 1 will be odd

Since a consistent value of b can not be determined we can not find the value of ab...

Thus, Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed, answer will be (E)

This question is just asking- is "a" an even number - simple even and odd properties

Statement 1

This just means "a" is prime; but 2 is an even prime number

Statement 2
This just mean B must be odd because any number multiplied by an even number is even and the sum of an even and odd number is odd. But even if this statement forces B to be odd, we still cannot say what A is.

E

1) a could be any prime number including 2. So it could be either even or odd.
2) b is odd.

E