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# M26-14

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Math Expert
Joined: 02 Sep 2009
Posts: 47918

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16 Sep 2014, 01:25
1
11
00:00

Difficulty:

75% (hard)

Question Stats:

60% (02:49) correct 40% (03:13) wrong based on 143 sessions

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After $$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed, it turned out that $$\frac{3}{4}$$ of those numbers were non-negative. 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?

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

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Math Expert
Joined: 02 Sep 2009
Posts: 47918

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16 Sep 2014, 01:25
4
4
Official Solution:

After $$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed, it turned out that $$\frac{3}{4}$$ of those numbers were non-negative. 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?

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

When choosing variable for set $$A$$, there will be too many fractions to manipulate with, so pick some smart number: let us imagine set $$A$$ contains 18 numbers.

"$$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed" hence 4 numbers were observed and $$18-4=14$$ numbers left to observe;

"$$\frac{3}{4}$$ of those numbers were non-negative" hence 3 numbers were non-negative and 1 number was negative;

Ratio of negative numbers to non-negative numbers to be 2 to 1 there should be total of $$18*\frac{2}{3}=12$$ negative numbers, so in not yet observed part there should be $$12-1=11$$ negative numbers. Thus $$\frac{11}{14}$$ of the remaining numbers in set $$A$$ must be negative.

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Joined: 11 Sep 2013
Posts: 156
Concentration: Finance, Finance

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28 Nov 2014, 03:00
7
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 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 negative has to be =24-2 =22
Remaining numbers = 36-8 = 28

fraction =22/28 = 11/14
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Joined: 26 Jan 2014
Posts: 3
Location: India
Concentration: Operations, Entrepreneurship
GMAT Date: 05-02-2014
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WE: Engineering (Energy and Utilities)

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06 Aug 2016, 22:54
how 18 * 2/3 ???
from where does 2/3
factor comes in picture.. plz explain..
Thnx
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Joined: 17 May 2016
Posts: 30
GMAT 1: 740 Q46 V46

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11 Aug 2016, 12:22
1
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,
Manager
Joined: 17 Mar 2015
Posts: 121

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26 Dec 2016, 06:18
4
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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29 Jul 2017, 10:02
I think this is a high-quality question and I agree with explanation. I think that the quality would have been much better if the phrase "remaining numbers" was clearer. As from this remaining numbers can be inferred put as Total - observed or total - non-negative.
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28 Aug 2017, 23:38
Are there more questions like this to practice? Would appreciate links if any!
Math Expert
Joined: 02 Sep 2009
Posts: 47918

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28 Aug 2017, 23:45
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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12 Sep 2017, 11:49
Zhenek wrote:
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.

I also solved it the same way, but the last highlighted part is not clear.
Can someone please explain that part as i got my answer as 11/18 which is not in the options.
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21 Nov 2017, 22:07
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.
Math Expert
Joined: 02 Sep 2009
Posts: 47918

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21 Nov 2017, 22:57
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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23 Nov 2017, 18:22
Bunuel wrote:
Official Solution:

After $$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed, it turned out that $$\frac{3}{4}$$ of those numbers were non-negative. 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?

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

When choosing variable for set $$A$$, there will be too many fractions to manipulate with, so pick some smart number: let us imagine set $$A$$ contains 18 numbers.

"$$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed" hence 4 numbers were observed and $$18-4=14$$ numbers left to observe;

"$$\frac{3}{4}$$ of those numbers were non-negative" hence 3 numbers were non-negative and 1 number was negative;

Ratio of negative numbers to non-negative numbers to be 2 to 1 there should be total of $$18*\frac{2}{3}=12$$ negative numbers, so in not yet observed part there should be $$12-1=11$$ negative numbers. Thus $$\frac{11}{14}$$ of the remaining numbers in set $$A$$ must be negative.

Can u please explain the last part of the question ? M still confused

Sent from my Redmi 3S using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 47918

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23 Nov 2017, 21:16
Spongebob02 wrote:
Bunuel wrote:
Official Solution:

After $$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed, it turned out that $$\frac{3}{4}$$ of those numbers were non-negative. 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?

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

When choosing variable for set $$A$$, there will be too many fractions to manipulate with, so pick some smart number: let us imagine set $$A$$ contains 18 numbers.

"$$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed" hence 4 numbers were observed and $$18-4=14$$ numbers left to observe;

"$$\frac{3}{4}$$ of those numbers were non-negative" hence 3 numbers were non-negative and 1 number was negative;

Ratio of negative numbers to non-negative numbers to be 2 to 1 there should be total of $$18*\frac{2}{3}=12$$ negative numbers, so in not yet observed part there should be $$12-1=11$$ negative numbers. Thus $$\frac{11}{14}$$ of the remaining numbers in set $$A$$ must be negative.

Can u please explain the last part of the question ? M still confused

Sent from my Redmi 3S using GMAT Club Forum mobile app

In observed pool: 3 numbers were non-negative and 1 number was negative.

We want the TOTAL ratio of negative numbers to non-negative numbers be 2 to 1. So, there should be total of 18*2/3 = 12 negative numbers. So, in not yet observed part (14) there should be 12-1=11 negative numbers. Thus $$\frac{11}{14}$$ of the remaining numbers in set $$A$$ must be negative.

Hope it's clear.
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11 Jul 2018, 10:33
Bunuel wrote:
Official Solution:

After $$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed, it turned out that $$\frac{3}{4}$$ of those numbers were non-negative. 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?

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

When choosing variable for set $$A$$, there will be too many fractions to manipulate with, so pick some smart number: let us imagine set $$A$$ contains 18 numbers.

"$$\frac{2}{9}$$ of the numbers in a data set $$A$$ were observed" hence 4 numbers were observed and $$18-4=14$$ numbers left to observe;

"$$\frac{3}{4}$$ of those numbers were non-negative" hence 3 numbers were non-negative and 1 number was negative;

Ratio of negative numbers to non-negative numbers to be 2 to 1 there should be total of $$18*\frac{2}{3}=12$$ negative numbers, so in not yet observed part there should be $$12-1=11$$ negative numbers. Thus $$\frac{11}{14}$$ of the remaining numbers in set $$A$$ must be negative.

I don´t know how you always manage to make an answer to a difficult question look super easy.

Is it generally a good idea to select a number which is a multiple of the denominator for ration probles?

Regards,
Chris
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Re: M26-14 &nbs [#permalink] 11 Jul 2018, 10:33
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# M26-14

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