Data Sufficiency

What is the value of f^2 - g^2?

(1) f = -g + 8
(2) f = g - 2

The OA is C.

Why is not sufficient each statement alone? And, should I solve the system of equations? <i class="em em-neutral_face"></i>

M7MBA wrote:What is the value of f^2 - g^2?

(1) f = -g + 8
(2) f = g - 2

The OA is C.

Why is not sufficient each statement alone? And, should I solve the system of equations? <i class="em em-neutral_face"></i>

Hello M7MBA.

Let's take a look at your question.

First of all, note that the given expression can be rewritten as follows: $$f^{\ 2}-g^2=\left(f+g\right)\left(f-g\right).$$ So, we need to find the values of f+g and f-g.

First statement

(1) f = -g + 8

Here, we can get f+g=8. But, we don't know the value of f-g. Hence, this statement is not sufficient.

Second statement

(2) f = g -2

Here, we can get f-g=-2. But, we don't know the value of f+g. Hence, this statement is not sufficient.

First statement + Second statement

(1) f = -g + 8
(2) f = g -2

Now, we know that f+g=8 and f-g=-2, therefore $$f^{\ 2}-g^2=\left(f+g\right)\left(f-g\right)=\left(8\right)\left(-2\right)=16.$$ So, we could get an answer.

Therefore, using both statements together is sufficient, that implies that the correct answer is the option C.

I hope it help you. <i class="em em-smiley"></i>