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# If ab = -9, what is the value of ab(a + b) ? (1) a - b = 100

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Manager
Joined: 16 Feb 2010
Posts: 226
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Kudos [?]: 150 [0], given: 16

If ab = -9, what is the value of ab(a + b) ? (1) a - b = 100 [#permalink]  29 Aug 2010, 05:05
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Difficulty:

55% (hard)

Question Stats:

60% (02:44) correct 40% (01:47) wrong based on 58 sessions
If ab = -9, what is the value of ab(a + b) ?

(1) a - b = √100

(2) ab^2 = -81
[Reveal] Spoiler: OA
Manager
Joined: 09 Jun 2010
Posts: 116
Followers: 2

Kudos [?]: 72 [0], given: 1

Re: GrockIt: ab(a+b) [#permalink]  29 Aug 2010, 08:06
ab = -9, what is the value of ab(a + b) ?

(1) a - b = √100

a-b = + 10.
Substituting value from ab = -9 we get a= 9,1,-9,-1 & respectively b = -1,-9,1,9.
Value of (a+b) = +8 or -8 therefore insufficient.

(2) ab^2 = -81

combining with ab = -9 we get b=9 & a = -1 = > (a+b) = 8 ; sufficient.

Manager
Joined: 16 Feb 2010
Posts: 226
Followers: 2

Kudos [?]: 150 [0], given: 16

Re: GrockIt: ab(a+b) [#permalink]  29 Aug 2010, 09:49
thanks....anyone with the algrebraic (non)solution of (A)...?
Manager
Joined: 16 Feb 2010
Posts: 226
Followers: 2

Kudos [?]: 150 [0], given: 16

Re: GrockIt: ab(a+b) [#permalink]  29 Aug 2010, 10:01
zisis wrote:
thanks....anyone with the algrebraic (non)solution of (A)...?

If ab = -9, what is the value of ab(a + b) ?

(1) a - b = √100

(2) ab^2 = -81

for (a)
square both sides

$$(a-b)^ = 100$$

$$a^2 - (2ab) + b^2 = 100$$
substitute b=-9/a
$$a^2 -2(\frac{-9}{a}) + b^2 = 100$$

therefore you end up with
$$a^3 - 82a -9 = 0$$
factorise it and use it.....

no?
Manager
Joined: 16 Mar 2010
Posts: 189
Followers: 2

Kudos [?]: 79 [0], given: 9

Re: GrockIt: ab(a+b) [#permalink]  31 Aug 2010, 04:18
(1) a - b = √100
This means that a-b is +ve. For GMAT sqrt of something can not be -ve.
So, a-b=10
((a-b)^2)+4ab = (a+b)^2 = 100-36 = 64
(a+b) = 8 or -8
Not Enough.
2) Enough
Re: GrockIt: ab(a+b)   [#permalink] 31 Aug 2010, 04:18
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