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>
