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

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29 Aug 2010, 06:05
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65% (hard)

Question Stats:

56% (01:53) correct 44% (01:46) wrong based on 160 sessions

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

(1) a - b = √100

(2) ab^2 = -81
[Reveal] Spoiler: OA

Kudos [?]: 378 [0], given: 16

Manager
Joined: 09 Jun 2010
Posts: 111

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29 Aug 2010, 09:06
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.

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Manager
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29 Aug 2010, 10:49
thanks....anyone with the algrebraic (non)solution of (A)...?

Kudos [?]: 378 [0], given: 16

Manager
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29 Aug 2010, 11:01
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?

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Manager
Joined: 17 Mar 2010
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31 Aug 2010, 05:18
(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

Kudos [?]: 211 [0], given: 9

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

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28 Apr 2016, 18:57
zisis wrote:
If ab = -9, what is the value of ab(a + b) ?

(1) a - b = √100

(2) ab^2 = -81

1. a=10+b
(10+b)b=-9
b^2 +10b +9 = 0
(b+9)(b+1)=0
b=-9
b=-1

b=-9 -> a=1 -> -9(1-9) =72
b=-1 -> a=9 -> -9(9-1) = -72
2 outcomes, A is out.

2. ab^2 = -81
ab=-9
a=-9/b

-9/b * b^2 = -81
-9b = -81
b=9
and a=-1

sufficient.

Kudos [?]: 431 [0], given: 200

Intern
Joined: 28 Feb 2016
Posts: 1

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

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28 Apr 2016, 19:31
I think it should be D

a -b = sq root 100

ab = -9

(a + b)^2 = (a -b)^2 + 4ab
(a + b)^2 = 64;

(a +b) = sqrt (64) ---> Does GMAT considers -ve value of sqrt ?

If not, then answer could be D.

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Math Expert
Joined: 02 Aug 2009
Posts: 5212

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

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28 Apr 2016, 20:05
himmy71 wrote:
I think it should be D

(a + b)^2 = 64;

(a +b) = sqrt (64) ---> Does GMAT considers -ve value of sqrt ?

If not, then answer could be D.

Hi,
GMAT does not consider -ive value of square root , that is $$\sqrt{64}=8$$..
But $$(a + b)^2 = 64$$ means a+b=8 or a+b=-8
and if it is given $$(a +b) =(\sqrt{64}) = 8$$.. these are two different things
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Veritas Prep GMAT Instructor
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Location: Pune, India
Re: If ab = -9, what is the value of ab(a + b) ? (1) a - b = 100 [#permalink]

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28 Apr 2016, 22:42
himmy71 wrote:
I think it should be D

a -b = sq root 100

ab = -9

(a + b)^2 = (a -b)^2 + 4ab
(a + b)^2 = 64;

(a +b) = sqrt (64) ---> Does GMAT considers -ve value of sqrt ?

If not, then answer could be D.

Here is the reason the square root is always positive but a square considers both positive and negative value.

A positive number has two square roots: a positive square root (also called principal square root) and a negative square root. They are depicted as $$\sqrt{x}$$ and $$-\sqrt{x}$$.
So by convention, $$\sqrt{x}$$ implies we are talking about only the positive square root. Hence when you are given $$\sqrt{x}$$ in the question, it implies that this is the principal square root only.

On the other hand, $$x^2 = 4$$ has two solutions: x = 2 or -2 since x could take either of these values.
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Kudos [?]: 17815 [0], given: 235

Re: If ab = -9, what is the value of ab(a + b) ? (1) a - b = 100   [#permalink] 28 Apr 2016, 22:42
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