What is the value of (a + b)^2 ?

Question

(1) a = 15/b 
(2) (a – b)^2 = 4

anupamadw · Answer

What is the value of (a + b)^2 ?
(a+b)^2 = a^2+b^2+2ab

(1) a = 15/b --> ab =15 insuff

(2) (a – b)^2 = 4
a^2+b^2 = 2ab+4 insuff

(a+b)^2 = a^2+b^2+2ab
 = 2ab+4+2ab ( from stmnt2)
 = 4ab+4
 = 4*15 ( from stmnt1)

IMO C, could you please confirm the answer?

BassanioGratiano · Answer

Thanks for step the by step. Just to point out you forgot to add the +4 to your last step. Other than that, thank you so much!

anupamadw · Answer

Thanks for pointing out, but I am not sure about OA. So let's wait for Bunuel to confirm answer.

Bunuel · Answer

_____________
The OA is C.

akumar5 · Answer

Since we know (a+b)^2-(a-b)^2=4ab

so we need values both for ab and (a-b)

1) a=15/b 
2)(a-b)^2=4

from above two options we can have the required value for (a+b)^2

ANSWER IS C

jerinpeter · Answer

We can determine the value of (a + b)^2 in one of three ways: by figuring out the sum of a and b, by determining what a and b are separately, or by determining the value of a^2 + 2ab + b^2 (which is the quadratic form of our product of factors).

(1) INSUFFICIENT: After multiplying both sides by b, we can determine that ab = 15, but we know nothing else.

(2) INSUFFICIENT: If we FOIL (a – b)2 we can learn that a2 – 2ab + b2 = 4. However, this does not allow us to determine the sum of a and b, the respective values of a and b individually, or the value of a2 + 2ab + b2.

(1) AND (2) SUFFICIENT: Statement 1 tells us ab = 15. If we substitute this into the quadratic equation from the second statement, we can determine the value of a^2 + b^2 in the following manner:

a^2 – 2(15) + b^2 = 4 
a^2 – 30 + b^2 = 4 
a^2 + b^2 = 34

If we know the value of a^2 + b^2, and the value of ab, we can determine the value of a^2 + 2ab + b^2.
a^2 + 2ab + b^2 = a^2 + b^2 + 2ab = 34 + 2(15) = 64
 
The correct answer is C

What is the value of (a + b)^2 ?

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