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

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Intern
Joined: 02 May 2014
Posts: 4
If a * b = −8, what is the value of a+b?  [#permalink]

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20 Nov 2014, 15:45
2
2
00:00

Difficulty:

65% (hard)

Question Stats:

53% (01:35) correct 47% (01:36) wrong based on 97 sessions

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

(1) a − b = 6

(2) (a^2 )* b=32
Manager
Status: MBA Mentor
Joined: 28 Oct 2014
Posts: 67
Location: Korea, Republic of
Concentration: Strategy, Other
Schools: SDA Bocconi - Class of 2011
GMAT 1: 700 Q50 V34
GPA: 3.21
WE: Analyst (Telecommunications)
Re: If a * b = −8, what is the value of a+b?  [#permalink]

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20 Nov 2014, 17:37
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

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

_________________

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

Math Expert
Joined: 02 Aug 2009
Posts: 6535
Re: If a * b = −8, what is the value of a+b?  [#permalink]

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04 Dec 2017, 06:55
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If a * b = −8, what is the value of a+b? &nbs [#permalink] 04 Dec 2017, 06:55
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