I'm not sure why the explanation says a and b may or may not be integers. But here is my reasoning.

a and b are integers (both +ve and -ve). Value of ab?

1. (ab)^2 = 16

This means that ab = +/- 4. We have the following scenarios to satisfy ab = +/- 4,
I. a (+ve), b(+ve)
II. a (-ve), b(-ve)
III. a (+ve), b(-ve)
IV. a (-ve), b(+ve)

Insufficient.

2. a=4
No info about b. Insufficient.

Combined,
a=4 and b could be +1 or -1. You get 2 different values of ab.
Insufficient.

LMK27 wrote:I came across the below problem on a practice test and got it wrong. Looking at the explanation I was a little confused. I assumed from the intro that a and b in (1) are integers as well, but according the the explanation they could or could not be integers.....so why does the intro say a and b are integers then?

If a and b are integers, what is the value of ab?

(1) (ab)^2 = 16
(2) a = 4


Answer is E

I dont think the problem is of integers here .

Its given clearly that a and b both are integers so thats true .

We need to find what a x b is ?

(1) (ab)^2 = 16

Take square root both sides

ab = +/- 4 .

Not sufficient .

(2) a = 4 .

Nothing is said about b .

Not Sufficient

Combine (1) and (2)

a = 4 and (a x b ) = +/- 4

So b could be = +/- 1 .

Not sufficient .

E is correct.

Thank you both for your explanations, it makes sense.