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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

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10 Mar 2015, 20:07

Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.

Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.

hi soniasawhney.. it does not require any parenthesis as any sign in front of a fraction modifies the entire fraction irrespective of the term.. just an example.. let the fraction be - \(\frac{7-9}{2}\).. two ways to do it .. first change signs first and then find answer... \(\frac{-7+9}{2}\)=\(\frac{2}{2}\)=1...

second simplify and then change the signs... - \(\frac{7-9}{2}\)=- \(\frac{-2}{2}\)=-(-1)=1..

so both ways answer is same, which means parentheses is not required and a sign in front of a fraction automatically means that the entire fraction is inside bracket....
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Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.

To clarify further: There are 3 ways in which you can make a fraction negative \(\frac{-3}{5}\)

\(-\frac{3}{5}\) Take this to mean \(\frac{-3}{5}\)

and \(\frac{3}{-5}\)

Each one of these fractions is the same as \(\frac{-3}{5}\)

Now what happens in case you have multiple terms in numerator:

\(\frac{-x + 2}{4}\) The negative is only in front of x.

\(-\frac{x+2}{4}\) The negative is in effect, in front of the entire numerator. So this is the same as \(\frac{-(x+2)}{4}\)
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Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

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12 Mar 2015, 19:40

Mountain14 wrote:

After Solving the equation , I got A

Because you didn't distribute the first negative sign on the first fraction. I made the same mistake. 8th grade rules but still find them hard to remember.
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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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Given that, k - (3 - 2k^2)/k = x/k Take LCM of denominators, So, [k^2 - (3 - 2k^2)]/k = x/k So, [k^2 - 3 + 2k^2]/k = x/k Canceling out k from the denominators of both sides, So, [k^2 - 3 + 2k^2] = x So, 3k^2 - 3 = x Hence option C.

I am assuming I can't move the denominator to the right side because of the first term (k), just not sure why.

1. k - [3-2k^2][/k] = [x][/k]

2. k - 3 + 2k^2 = x

Hi Apollon,

If you see, only two of the three terms have the denominator k. In order to cancel out the denominator from all the terms, you need to have the same denominator in each term.

In the given case,

1. k - (3-2k^2)/ k = x / k We need to make sure that the denominator of the first term is also the same.

Hence k^2/k - (3-2k^2)/ k = x / k From here on, we can cancel the terms. k^2 - 3 + 2k^2 = x Or x = 3k^2 - 3 Option C

Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

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30 Apr 2017, 01:26

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Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

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30 Apr 2017, 01:33

VeritasPrepKarishma wrote:

soniasawhney wrote:

Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.

To clarify further: There are 3 ways in which you can make a fraction negative \(\frac{-3}{5}\)

\(-\frac{3}{5}\) Take this to mean \(\frac{-3}{5}\)

and \(\frac{3}{-5}\)

Each one of these fractions is the same as \(\frac{-3}{5}\)

Now what happens in case you have multiple terms in numerator:

\(\frac{-x + 2}{4}\) The negative is only in front of x.

\(-\frac{x+2}{4}\) The negative is in effect, in front of the entire numerator. So this is the same as \(\frac{-(x+2)}{4}\)

Thank you, VeritasPrepKarishma

I too fell for this rule.

So basically in this exercise.

\(-\cfrac { 3-2{ k }^{ 2 } }{ k } \neq \cfrac { -3-2{ k }^{ 2 } }{ k } \\ \\ -\cfrac { 3-2{ k }^{ 2 } }{ k } \rightarrow \cfrac { -\left( 3-2{ k }^{ 2 } \right) }{ k }\)
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