Is the product of a and b odd?

[gmatnmein2010]

Is the product of a and b odd?

(1) a has exactly 2 factors.

(2) b = 2x + 1, where x is an integer.

[ajith]

Is the product of a and b odd?

(1) a has exactly 2 factors.

(2) b = 2x + 1, where x is an integer.

1) Insufficient - It talks only about a

2) insufficient - it talks only about b

Combining

1) shows that a is a prime number (2,5...)
2) shows that b is an odd number

The product can be odd or even

Hence E

[harsh.champ]

Is the product of a and b odd?

(1) a has exactly 2 factors.

(2) b = 2x + 1, where x is an integer.

1) Insufficient - It talks only about a

2) insufficient - it talks only about b

Combining

1) shows that a is a prime number (2,5...)
2) shows that b is an odd number

The product can be odd or even

Hence E

I agree.
This question could have been more challenging if it was written that 2 is not a factor of a.
In that case,when we consider both the statements together,the product would always be an odd number.
This is because all prime no.s except 2 are odd.
Also,from statement 2 we know that b is an odd integer.
Odd x Odd =Odd
Hence,it could have been C.
That could have been a good trap.

[shashank.ism]

Is the product of a and b odd?

(1) a has exactly 2 factors.

(2) b = 2x + 1, where x is an integer.

St. 1 : a has exactly 2 factors. we know nothing about the factors. even we don't know about b ---------so insuff.
St.2 : b= 2x+1 and x is integer that is clearly and odd number ....since 2x is an even number as it has a factor 2 and when u add or subtract 1 from even number it gives an odd number
so b i an odd no.
but we know nothing about a --------so insuff..
combining : we know abt b is odd but we got no idea abt a ----- insuff.
Ans E