GMAT Quantitative Reasoning Practice Test 6

Question : 12 of 100

Marks: +1, -0

What is the value of

a+b

?
(1)

a^2+b^2=13

(2)

2 b=12 \/ a

Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.
Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.
The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).
The problem can be solved using EITHER statement (1) only or statement (2) only.
The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

Solution:

Remember that

(a+b)^2=a^2+2 a b+b^2

. From statement (1), we know that

a^2+b^2=13

. By cross multiplying in statement

(2)

, we get

2 a b=12

.
Since we know the values of

a^2+b^2

and

2 a b

, and

(a+b)^2=a^2+2 a b+b^2

, we can now take the square root of the sum to find the value of

a + b.

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