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If a * b = −8, what is the value of a+b?

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If a * b = −8, what is the value of a+b? [#permalink]

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If a * b = −8, what is the value of a+b?

(1) a − b = 6

(2) (a^2 )* b=32
[Reveal] Spoiler: OA

Kudos [?]: 9 [1], given: 21

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Status: MBA Mentor
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Posts: 67

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Location: Korea, Republic of
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Re: If a * b = −8, what is the value of a+b? [#permalink]

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New post 20 Nov 2014, 16:37
Correct answer is B ( Statement 2 is sufficient but Statement 1 is not sufficient)

Solution
a-b = 6
a^2b = 32

[A] a-b=6
(a+b)^2 = a^2 +b^2 + 2ab eq 1
(a-b)^2 = a^2 + b^2 - 2ab eq2

Subtract eq 2 from eq 1
(a+b)^2 - (a-b)^2 = 4ab

Substituting ab = -8 and a-b=6
(a+b)^2 - 36 = -32
(a+b)^2 = 4
a+b = +2 or -2 (We can't answer correctly)
Hence, statement 1 is not sufficient


a^2b = 32
we know ab=-8
Substituting ab
a(ab) = 32
a*-8 = 32
a = -4
b=2
a+b = -2
Hence, we can answer with certainty , -2

Therefore, the answer is [B]

Cheers !
Dhiraj


muktaumarani wrote:
[b]If a * b = −8, what is the value of a+b?

(1) a − b = 6

(2) (a^2 )* b=32

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Dhiraj Jha
http://www.globalmba-gyan.com
MBA 2011 - SDA Bocconi School of Management (Milan, Italy)
Global Account Management, Samsung Electronics Headquarters (Korea)

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Re: If a * b = −8, what is the value of a+b? [#permalink]

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New post 04 Dec 2017, 05:30
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Re: If a * b = −8, what is the value of a+b? [#permalink]

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New post 04 Dec 2017, 05:55
easy700 wrote:
If a * b = −8, what is the value of a+b?

(1) a − b = 6

(2) (a^2 )* b=32





(1) \(a-b=6\)..
square both sides ..
\((a-b)^2 = 6^2.......... a^2+b^2-2ab=a^2+b^2+2ab-4ab = (a+b)^2-4ab =36........(a+b)^2-4*-8=36...........(a+b)^2=36-32=4\)
so a+b = 2... or a+b=-2
insuff

(2) \(a^2*b=32\)
subtract the main equation from this..
\(a^2*b-ab=32+8...............ab(a-1)=40..........(-8)(a-1)=40.........a-1=-5............a=-4\)
so \(b = \frac{-8}{-4}=2\)
a+b=-4+2=-2
sufficient

B

Ofcourse statement I should be \(a-b=-6\)
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Re: If a * b = −8, what is the value of a+b?   [#permalink] 04 Dec 2017, 05:55
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