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

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Math Expert
Joined: 02 Sep 2009
Posts: 61549
If ab = -9, what is the value of ab(a + b)?  [#permalink]

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09 Dec 2019, 00:04
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Difficulty:

65% (hard)

Question Stats:

48% (02:04) correct 52% (02:09) wrong based on 77 sessions

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

(1) $$a - b = √100$$

(2) $$ab^2 = -81$$

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

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09 Dec 2019, 02:25
1
given ab=-9
possiblities ; -9,1 and 9,-1
#1
a-b=10
9-(-1) or 1-(-9)
so
$$ab(a + b)$$ = we get +/-72
insufficinet
#2$$ab^2 = -81$$
possible only when a= -1 and b=9
sufficient
IMO B

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

(1) $$a - b = √100$$

(2) $$ab^2 = -81$$

Are You Up For the Challenge: 700 Level Questions
Senior Manager
Joined: 13 Feb 2018
Posts: 499
GMAT 1: 640 Q48 V28
Re: If ab = -9, what is the value of ab(a + b)?  [#permalink]

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09 Dec 2019, 23:47
1 stm -- seems sufficient at a glance, as we have two variables and two equations, but hold on.
after solving we get either a=1 b=-1 or a=-1 b=-9. Not Sufficient

2 stm -- $$ab^2=ab*b=-81$$, We know ab=-9 so -9b=-81 b=9; Sufficient

I will bet on B
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Joined: 24 Nov 2016
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If ab = -9, what is the value of ab(a + b)?  [#permalink]

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13 Dec 2019, 08:28
Bunuel wrote:
If $$ab = -9$$, what is the value of $$ab(a + b)$$ ?

(1) $$a - b = √100$$

(2) $$ab^2 = -81$$

(1) $$a - b = √100$$ insufic

$$a - b = √100…(a-b)^2=100…a^2+b^2-2ab=100…a^2+b^2=82$$

(2) $$ab^2 = -81$$ sufic

$$ab^2 = -81…ab*|b|=-81…-9*|b|=-81…(a,b)=(1,-9;-1,9)$$
$$b^2>0…a<0…(a,b)=(-1,9)$$

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

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12 Jan 2020, 07:02
Archit3110 wrote:
given ab=-9
possiblities ; -9,1 and 9,-1
#1
a-b=10
9-(-1) or 1-(-9)
so
$$ab(a + b)$$ = we get +/-72
insufficinet
#2$$ab^2 = -81$$
possible only when a= -1 and b=9
sufficient
IMO B

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

(1) $$a - b = √100$$

(2) $$ab^2 = -81$$

Are You Up For the Challenge: 700 Level Questions

Hi archit,

your soln to first statement is wrong,
a and b are not integers. a = 4.5 b = -2 can also be there.
Re: If ab = -9, what is the value of ab(a + b)?   [#permalink] 12 Jan 2020, 07:02
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