What is the value of (a+b)?

Question

What is the value of a + b?

(1) a^2 - b^2 = 133.
(2) a - b = 7.

shonakshi · Answer

a2-b2=133
(a-b)(a+b)=133

also given (a-b)=7
substitut in eq 1 we get :7*(a+b)=133
so (a+b)=133/7

ans is C

Divyadisha · Answer

(1) a^2 - b^2 = 133.
(a+b) (a-b)= 133
We don't know the value of (a-b) or (a+b). Not Sufficient.

(2) a - b = 7.
We can not get the value of (a+b) by this expression. Not sufficient.

Combining both statements
(a+b) (a-b)= 133
(a+b) *7= 133
(a+b) = 19 
Sufficient. C is the answer

Pachu · Answer

Hi,

I have a small doubt.
Statement 1: From this statement we can understand (a+b)(a-b)=133. We know 133 = 19*7.
Therefore, it can be easily understood that a+b=19 and a-b=7. (Assuming a and b are positive)
Hence i felt, D should be the right choice. :roll:

Please help me with this. Thanks

Kurtosis · Answer

(a + b)(a - b) = 19 * 7 or 7 * 19 or -19 * -7 or -7 * -19
So each statement alone is not sufficient to conclude the value of (a + b)

Bunuel · Answer

You made two wrong assumptions:
1. We are not told that a and b are positive;
2. We are not told that a and b are integers.

If you take the above into the account you'll end up with infinitely many solutions for a^2 - b^2 = 133.

What is the value of (a+b)?

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