M26-14

Question

After observing  \frac{2}{9}  of the numbers in data set  A , it was found that  \frac{3}{4}  of those numbers were non-negative. What fraction of the remaining numbers in  A  must be negative so that the ratio of negative numbers to non-negative numbers in  A  is 2 to 1?

A.  \frac{11}{14}  
B.  \frac{13}{18}  
C.  \frac{4}{7}  
D.  \frac{3}{7}  
E.  \frac{3}{14}

Bunuel · Accepted Answer

Official Solution:

After observing  \frac{2}{9}  of the numbers in data set  A , it was found that  \frac{3}{4}  of those numbers were non-negative. What fraction of the remaining numbers in  A  must be negative so that the ratio of negative numbers to non-negative numbers in  A  is 2 to 1?

A.  \frac{11}{14}  
B.  \frac{13}{18}  
C.  \frac{4}{7}  
D.  \frac{3}{7}  
E.  \frac{3}{14}

To simplify calculations, instead of assigning a variable, we can choose a convenient number, such as 18, for the size of  A .
 
Since we observed  \frac{2}{9}  of the numbers in  A , we observed 4 numbers, and there are 14 numbers left to observe.
 
Given that  \frac{3}{4}  of the observed numbers were non-negative, we know that 3 of the observed numbers were non-negative, and 1 was negative.
 
To achieve a ratio of 2 to 1 between negative numbers and non-negative numbers in  A , we need a total of  18 *\frac{2}{3} = 12  negative numbers. Since we already have 1 negative number, we need 11 more negative numbers in the remaining 14 numbers of  A . Therefore,  \frac{11}{14}  of the remaining numbers in  A  must be negative.

Answer: A

Raihanuddin · Answer

Take L.C.M of 4 and 9 = 36(Let total)
So 2/9 of 36 = 8 was observed

Out of 8, 3/4*8=6 was non-negative. So, the negative was 2

The Required ratio of negative to non-negative =2:1

So Total negatives will be 2/3 of 36 = 24 and non-negative = 12

So, new negative numbers have to be =24-2 =22 (Because we already have 2 from observed data)
Remaining numbers = 36-8 = 28 (Our goal is to find the fraction of remaining numbers. By remaining, we mean the numbers which we haven't observed yet)

fraction =22/28 = 11/14

aks231186 · Answer

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

nickimonckom · Answer

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,

Zhenek · Answer

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.

Madhavi1990 · Answer

Are there more questions like this to practice? Would appreciate links if any!

Bunuel · Answer

Check this: https://gmatclub.com/forum/there-are-87 ... 61001.html

VSJ · Answer

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

Bunuel · Answer

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 ?

MikeScarn · Answer

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.

kaladin123 · Answer

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 Observed  Observed  Total  
  Non -ve  6  6  12  
  -ve   22   2  24  
  Total   28   8  36

Fraction=\frac{22}{28}=\frac{11}{14}

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

GimmeSomQuant · Answer

Hello,

could you please explain me what am I doing wrong here ?

so we have 3/4 of 2/9 that is 1/6 as non-negative

so in order to have our 2:1 ratio we need to have 2/6 so 1/3 of negative ones

then what fraction of 1-2/9 = 7/9 (the remaining ones) gives us 1/3 ?

that is X*7/9 = 1/3
==> X=7/3

any help would be appreciated

Bunuel · Answer

Out of 2/9 numbers, 3/4 are non-negative, so 2/9 * 3/4 = 1/6 are non-negative.
Out of 2/9 numbers, 1/4 are negative, so 2/9 * 1/4 = 1/18 are negative.

Out of the remaining numbers, so out of 7/9 of the numbers, x is negative and 7/9 - x is non-negative.

So, total negative = 1/18 + x and total non-negative = 1/6 + (7/9 - x).

negative/nonnegative = (1/18 + x)/(1/6 + (7/9 - x))=2

x = 11/14

The fraction 11/14 is of 2/9 equals to (11/14) / (2/9) = 11/14.

So, it's much better to substitute numbers in this question.

Varshal · Answer

I did not quite understand the solution. Official solution feels more verbose, less mathematical (and easy to follow) than fraction representation

Bunuel · Answer

Relying solely on algebra is not the proper way to prepare for the exam. You should have other tools in your arsenal. The approach used in the solution is precise and can be applied to many similar questions. If you are still looking for alternative solutions, please check the discussion above.

alrightalright · Answer

I like the solution - it’s helpful.

MegB07 · Answer

Hi,

I dont quite understand what the question is asking for? Could you please explain in terms of fraction of what the question is asking?

Here is how i interpreted it total negative numbers/remaining numbers/negative number + 2/total - negative (non negative) = 2/1

Bunuel · Answer

The question is not asking for total negatives divided by all numbers. It is asking: among the numbers that remain unobserved, what fraction of those must be negative so that the overall set ends up with the required 2 to 1 ratio.

M26-14

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