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Re: M26-14 [#permalink]
how 18 * 2/3 ???
from where does 2/3
factor comes in picture.. plz explain..
Thnx
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Re: M26-14 [#permalink]
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aks231186 wrote:
how 18 * 2/3 ???
from where does 2/3
factor comes in picture.. plz explain..
Thnx


Hi AKS,

The RATIO of non negative to negative is 2:1 Hence the total (2+1 =3) is composed by \(\frac{2}{3}\) of Non Negative + \(\frac{1}{3}\) of negative.

It is the tricky part of ratios and fractions

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Re: M26-14 [#permalink]
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I just drew the picture and then wrote an easy equation:

\(\frac {x + \frac {1}{18}}{\frac{1}{6}+ \frac{7}{9} - x } = 2\)

\(x = \frac{11}{18}\).

Now in order to calculate the answer we need to divide this number by a total of remaining numbers (\(\frac {7}{9}\)), which gives \(\frac {11}{14}\) as an answer.
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Re: M26-14 [#permalink]
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Are there more questions like this to practice? Would appreciate links if any!
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Re: M26-14 [#permalink]
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Madhavi1990 wrote:
Are there more questions like this to practice? Would appreciate links if any!


Check this: https://gmatclub.com/forum/there-are-87 ... 61001.html
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Re: M26-14 [#permalink]
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. i am unable to under why ratio is coming to be 2:1 when it should be 3:1 because 3 are non-negative and 1 is negative.
Please clarify
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Re: M26-14 [#permalink]
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VSJ wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. i am unable to under why ratio is coming to be 2:1 when it should be 3:1 because 3 are non-negative and 1 is negative.
Please clarify


In 4 numbers observed 3 numbers were non-negative and 1 number was negative. But the question asks: What fraction of the remaining numbers in set \(A\) must be negative so that the total ratio of negative numbers to non-negative numbers be 2 to 1?
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Re: M26-14 [#permalink]
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Here's how I solved it:

First \(\frac{2}{9}\) of Set A
Non Negative: \(\frac{2}{9}\) * \(\frac{3}{4}\) = \(\frac{6}{36}\)

Negative: \(\frac{2}{9}\) * \(\frac{1}{4}\) = \(\frac{2}{36}\)

Now we need the ratio of Negative to non negative to be 2:1

So Negative must be \(\frac{24}{36}\) and non negative must be \(\frac{12}{36}\)

We already have 2/36 negative, so I need 22/36 more negative.

Make x be the fraction of negative numbers of the remaining 7/9.

\(\frac{7}{9}\) * x = \(\frac{22}{36}\)

x = \(\frac{22}{36}\) * \(\frac{9}{7}\)

x = \(\frac{22}{36}\) * \(\frac{9}{7}\) = \(\frac{198}{252}\) = \(\frac{99}{126}\) = \(\frac{33}{42}\) = \(\frac{11}{14}\)

Took about 3 minutes.
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Re: M26-14 [#permalink]
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I think that this is a high-quality question and I agree with the explanation.

I spent 4 mins on this question - I should have skipped it and moved on.
That's why I was looking for a quicker approach in this thread.

Since we're dealing with fractions, let's assume that there are 36 numbers in set A.
[\(LCM(9,4)=36\)]

We know: \(Non-negative : Negative = 2:1\)
Observed\(=\frac{2}{9}*36=8\)
Non-Negative & Observed\(=\frac{3}{4}*8=6\)

This information is sufficient to fill up the 2x2 below:

Not ObservedObservedTotal
Non -ve6612
-ve22224
Total28836


\(Fraction=\frac{22}{28}=\frac{11}{14}\)
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Re: M26-14 [#permalink]
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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