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655-705 (Hard)|   Algebra|      
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demodrenyc
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a^2/b=-8 then what is the value of a(a-b) Updated on: 15 Jun 2012, 09:22
Originally posted by demodrenyc on 14 Feb 2010, 11:33.
Last edited by Bunuel on 15 Jun 2012, 09:22, edited 1 time in total.
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a^2/b=-8 then what is the value of a(a-b)

(1) a/b=-2
(2) a-b=6


Hi All, I came upon a math problem and have a very simple question.

The equation came down to be: 4b^2=-8b

Now per Kaplan explanation they just divided both sides by (b) but that only gives us only 1 answer of (-2) is that correct? I thought it is not good idea to divide squares as we don't know what sign it is. The way I did it was 4b^2+8b=0 and solved for b, which came out to be (0, and -2)
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gurpreetsingh
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a^2/b=-8 then what is the value of a(a-b) Updated on: 14 Feb 2010, 12:54
Originally posted by gurpreetsingh on 14 Feb 2010, 12:25.
Last edited by gurpreetsingh on 14 Feb 2010, 12:54, edited 1 time in total.
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You can divide in equation only if it is not zero, doesnt matter positive negative.

In inequation sign will matter.

1. in equation one a/b = -2 that means b is not equal to 0, so you can cancel b on both sides.
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a^2/b=-8 then what is the value of a(a-b) 14 Feb 2010, 12:48
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demodrenyc
Hi All, I came upon a math problem and have a very simple question.

The equation came down to be: 4b^2=-8b

Now per Kaplan explanation they just divided both sides by (b) but that only gives us only 1 answer of (-2) is that correct? I thought it is not good idea to divide squares as we don't know what sign it is. The way I did it was 4b^2+8b=0 and solved for b, which came out to be (0, and -2)


The problem was: a^2/b=-8 then what is the value of a(a-b)

(1) a/b=-2
(2) a-b=6
Show more

A.. for me..

S1: a/b = -2
this gives -2a = -8 which gives a = 4.... this gives b = -2.. SUFF

S2: a-b = 6
\(a^2 = -8b\)
\(a^2 = -8(a-6)\)
\(a^2 = -8a + 48\)
\(a^2 + 8b - 48 = 0\)
This gives a = 4, -12...... and b = -2 and -18.... gives two values for a(a- b)... NOT SUFF...
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a^2/b=-8 then what is the value of a(a-b) 14 Feb 2010, 14:39
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demodrenyc
Hi All, I came upon a math problem and have a very simple question.

The equation came down to be: 4b^2=-8b

Now per Kaplan explanation they just divided both sides by (b) but that only gives us only 1 answer of (-2) is that correct? I thought it is not good idea to divide squares as we don't know what sign it is. The way I did it was 4b^2+8b=0 and solved for b, which came out to be (0, and -2)


The problem was: a^2/b=-8 then what is the value of a(a-b)

(1) a/b=-2
(2) a-b=6
Show more

Given: \(\frac{a^2}{b}=-8\) --> \(a^2=-8b\). Q: \(a(a-b)=?\)

(1) \(\frac{a}{b}=-2\) --> as per Kaplan: \(4b^2=-8b\). Usually you can not divide equation by variable (or expression with variable) if you are not certain that variable (or expression with variable) does not equal to zero. So generally we should write: \(4b^2=-8b\) --> \(b^2+2b=0\) --> \(b(b+2)=0\) --> \(b=0\) or \(b=-2\). But in this case we can exclude \(b=0\) as a solution, as given that \(\frac{a^2}{b}=-8\) (and also in the statement \(\frac{a}{b}=-2\)): here \(b\) is in denominator and it can not be zero as in this case it won't make any sense (division by zero is undefined). So that is why Kaplan is safely dividing by \(b\). Though I think it's not a good question as, almost always, when GMAT provides some fraction and there is variable in denominator it states that variable does not equal to zero. As for the sign of \(b\): for equation it does not matter, you should only know that it does not equal to zero. Sign matters when you are dividing an inequality: in this case you should not only know that the variable (or expression with variable) does not equal to zero but also the sign of this variable (or expression with variable) to do the safe division/multiplication.

Now in our original question as only valid value of \(b\) is \(b=-2\) --> \(a=4\) and you can calculate \(a(a-b)\).

So this statement is sufficient.

(2) \(a-b=6\) --> \(a=b+6\) --> \(b^2+20b+36=0\) --> \(b=-18\) or \(b=-2\). Two values for \(b\), hence two values for \(a\) --> two values for \(a(a-b)\). Not sufficient.

Hope it's clear.
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a^2/b=-8 then what is the value of a(a-b) 14 Feb 2010, 21:42
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given A^2/b=-8
1. a/b=-2
2.a-b=6

1. if we substitute choice 1 in the eq. we get
a^2=-8b==>
a^2=4a==>a^2-4a=0
so a=0 or a=4
if a=0 then b=0
if a=4 then b=-2
so insufficient
stmt 2 alone clearly insufficient

combining 1 & 2
only a=4 and b=-2 statisfies the stmt 2
so the ans has to be C

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a^2/b=-8 then what is the value of a(a-b) 15 Feb 2010, 05:52
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silasaaa2
given A^2/b=-8
1. a/b=-2
2.a-b=6

1. if we substitute choice 1 in the eq. we get
a^2=-8b==>
a^2=4a==>a^2-4a=0
so a=0 or a=4
if a=0 then b=0
if a=4 then b=-2
so insufficient
stmt 2 alone clearly insufficient

combining 1 & 2
only a=4 and b=-2 statisfies the stmt 2
so the ans has to be C

Posted from my mobile device
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\(\frac{a^2}{b}=-8\) means that neither \(a\) nor \(b\) can equal to zero, hene only valid solution is \(a=4\) and \(b=-2\)
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a^2/b=-8 then what is the value of a(a-b) 15 Jun 2012, 09:18
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demodrenyc
Hi All, I came upon a math problem and have a very simple question.

The equation came down to be: 4b^2=-8b

Now per Kaplan explanation they just divided both sides by (b) but that only gives us only 1 answer of (-2) is that correct? I thought it is not good idea to divide squares as we don't know what sign it is. The way I did it was 4b^2+8b=0 and solved for b, which came out to be (0, and -2)


The problem was: a^2/b=-8 then what is the value of a(a-b)

(1) a/b=-2
(2) a-b=6

Given: \(\frac{a^2}{b}=-8\) --> \(a^2=-8b\). Q: \(a(a-b)=?\)

(1) \(\frac{a}{b}=-2\) --> as per Kaplan: \(4b^2=-8b\). Usually you can not divide equation by variable (or expression with variable) if you are not certain that variable (or expression with variable) does not equal to zero. So generally we should write: \(4b^2=-8b\) --> \(b^2+2b=0\) --> \(b(b+2)=0\) --> \(b=0\) or \(b=-2\). But in this case we can exclude \(b=0\) as a solution, as given that \(\frac{a^2}{b}=-8\) (and also in the statement \(\frac{a}{b}=-2\)): here \(b\) is in denominator and it can not be zero as in this case it won't make any sense (division by zero is undefined). So that is why Kaplan is safely dividing by \(b\). Though I think it's not a good question as, almost always, when GMAT provides some fraction and there is variable in denominator it states that variable does not equal to zero. As for the sign of \(b\): for equation it does not matter, you should only know that it does not equal to zero. Sign matters when you are dividing an inequality: in this case you should not only know that the variable (or expression with variable) does not equal to zero but also the sign of this variable (or expression with variable) to do the safe division/multiplication.

Now in our original question as only valid value of \(b\) is \(b=-2\) --> \(a=4\) and you can calculate \(a(a-b)\).

So this statement is sufficient.

(2) \(a-b=6\) --> \(a=b+6\) --> \(b^2+20b+36=0\) --> \(b=-18\) or \(b=-2\). Two values for \(b\), hence two values for \(a\) --> two values for \(a(a-b)\). Not sufficient.

Hope it's clear.
Show more


My query

a^2/b=-8 main equation

1) a/b = -2 ( statement 1)

now we use main equation and statement 1) to get b= -2
to obtain the value of a , I was of the opinion that I could use either either of the two equations .
why can't I use b= -2 and put it in the main equation to get the value of a .( putting b= -2 in a^2/b=-8 )
but if I do that, I get a^2 = 16 which gives me a = 4 and a = -4 making this in sufficient.

why are we only substituting b= -2 in statement 1 to obtain the value of a


Please do clarify.
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a^2/b=-8 then what is the value of a(a-b) 15 Jun 2012, 09:27
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demodrenyc
Hi All, I came upon a math problem and have a very simple question.

The equation came down to be: 4b^2=-8b

Now per Kaplan explanation they just divided both sides by (b) but that only gives us only 1 answer of (-2) is that correct? I thought it is not good idea to divide squares as we don't know what sign it is. The way I did it was 4b^2+8b=0 and solved for b, which came out to be (0, and -2)


The problem was: a^2/b=-8 then what is the value of a(a-b)

(1) a/b=-2
(2) a-b=6

Given: \(\frac{a^2}{b}=-8\) --> \(a^2=-8b\). Q: \(a(a-b)=?\)

(1) \(\frac{a}{b}=-2\) --> as per Kaplan: \(4b^2=-8b\). Usually you can not divide equation by variable (or expression with variable) if you are not certain that variable (or expression with variable) does not equal to zero. So generally we should write: \(4b^2=-8b\) --> \(b^2+2b=0\) --> \(b(b+2)=0\) --> \(b=0\) or \(b=-2\). But in this case we can exclude \(b=0\) as a solution, as given that \(\frac{a^2}{b}=-8\) (and also in the statement \(\frac{a}{b}=-2\)): here \(b\) is in denominator and it can not be zero as in this case it won't make any sense (division by zero is undefined). So that is why Kaplan is safely dividing by \(b\). Though I think it's not a good question as, almost always, when GMAT provides some fraction and there is variable in denominator it states that variable does not equal to zero. As for the sign of \(b\): for equation it does not matter, you should only know that it does not equal to zero. Sign matters when you are dividing an inequality: in this case you should not only know that the variable (or expression with variable) does not equal to zero but also the sign of this variable (or expression with variable) to do the safe division/multiplication.

Now in our original question as only valid value of \(b\) is \(b=-2\) --> \(a=4\) and you can calculate \(a(a-b)\).

So this statement is sufficient.

(2) \(a-b=6\) --> \(a=b+6\) --> \(b^2+20b+36=0\) --> \(b=-18\) or \(b=-2\). Two values for \(b\), hence two values for \(a\) --> two values for \(a(a-b)\). Not sufficient.

Hope it's clear.


My query

a^2/b=-8 main equation

1) a/b = -2 ( statement 1)

now we use main equation and statement 1) to get b= -2
to obtain the value of a , I was of the opinion that I could use either either of the two equations .
why can't I use b= -2 and put it in the main equation to get the value of a .( putting b= -2 in a^2/b=-8 )
but if I do that, I get a^2 = 16 which gives me a = 4 and a = -4 making this in sufficient.

why are we only substituting b= -2 in statement 1 to obtain the value of a


Please do clarify.
Show more

We have a^2/b=-8 and a/b=-2. Now, the values of a and b must satisfy BOTH equations, but a=-4 and b=-2 does not satisfy the second one, so a=-4 is not a valid solution.

Hope it's clear.
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a^2/b=-8 then what is the value of a(a-b) 15 Jun 2012, 09:35
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Indeed that is very clear now ..
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a^2/b=-8 then what is the value of a(a-b) 15 Jun 2012, 12:32
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is this really sub-600 level? this seems fairly challenging, at least 600-700..
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a^2/b=-8 then what is the value of a(a-b) 09 Jan 2022, 02:06
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