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# M26-14

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how 18 * 2/3 ???
from where does 2/3
factor comes in picture.. plz explain..
Thnx
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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

Regards,
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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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Are there more questions like this to practice? Would appreciate links if any!
Math Expert
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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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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.
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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.

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

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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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