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

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Bunuel
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If ab = -9, what is the value of ab(a + b)? [#permalink] New post   09 Dec 2019, 01:04
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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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Archit3110
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Re: If ab = -9, what is the value of ab(a + b)? [#permalink] New post   09 Dec 2019, 03:25
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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) \(ab^2 = -81\)


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LevanKhukhunashvili
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Re: If ab = -9, what is the value of ab(a + b)? [#permalink] New post   10 Dec 2019, 00:47
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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If ab = -9, what is the value of ab(a + b)? [#permalink] New post   13 Dec 2019, 09:28
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] New post   12 Jan 2020, 08:02
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.
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Re: If ab = -9, what is the value of ab(a + b)? [#permalink]
12 Jan 2020, 08:02
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Bunuel
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