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

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What is the value of (a+b)^2? [#permalink] New post 24 Dec 2012, 17:59
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

72% (01:49) correct 28% (01:00) wrong based on 89 sessions
What is the value of (a+b)^2?

(1) ab = 0
(2) (a-b)^2 = 36
[Reveal] Spoiler: OA

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Re: What is the value of (a+b)^2? [#permalink] New post 25 Dec 2012, 04:02
Expert's post
megafan wrote:
What is the value of (a+b)^2?

(1) ab = 0
(2) (a-b)^2 = 36


Each statement alone is clearly insufficient. When we take the statements together we have: ab=0 and a^2-2ab+b^2=36, thus a^2+b^2=36 --> (a+b)^2=a^2+2ab+b^2=36+0=36. Sufficient.

Answer: C.
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Re: What is the value of (a+b)^2? [#permalink] New post 14 May 2015, 03:40
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Re: What is the value of (a+b)^2? [#permalink] New post 14 May 2015, 21:41
Expert's post
Hi All,

This question can be solved with Algebra (and recognizing Classic Quadratics) or by TESTing VALUES.

We're asked for the value of (A+B)^2

Fact 1: AB = 0

This means that either A or B or Both = 0

IF...
A = 0
B = 0
(0+0)^2 = 0

IF....
A = 1
B = 0
(1+0)^2 = 1
Fact 1 is INSUFFICIENT

Fact 2: (A-B)^2 = 36

This ultimately means that (A-B) = 6 or -6

IF.....
A = 6
B = 0
(6+0)^2 = 36

IF....
A = 7
B = 1
(7+1)^2 = 64
Fact 2 is INSUFFICIENT

Combined, we know....
A or B or Both = 0
(A-B) = 6 or -6

IF....
A = 0
B = 6 OR -6
(0+6)^2 = (0-6)^2 = 36

IF....
B = 0
A = 6 OR -6
(0+6)^2 = (0-6)^2 = 36

The answer is ALWAYS 36.
Combined, SUFFICIENT

Final Answer:
[Reveal] Spoiler:
C


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Re: What is the value of (a+b)^2? [#permalink] New post 15 May 2015, 08:46
\((a+b)^2= a^2+b^2+2ab\)

St1
ab=0
=> either a=0 or b=0 or both.
=> \((a+b)^2= a^2+b^2\)
Since we cant determine this value. Insufficient

St2
(\(a-b)^2=36\)
=>\(a^2+b^2-2ab=36\)
Insufficient

St1+St2
since ab=0, \((a-b)^2=a^2+b^2=36 = (a+b)^2\)
Sufficient

Answer C.
Re: What is the value of (a+b)^2?   [#permalink] 15 May 2015, 08:46
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