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# M26-14

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Math Expert
Joined: 02 Sep 2009
Posts: 50585

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16 Sep 2014, 00:25
1
1
14
00:00

Difficulty:

75% (hard)

Question Stats:

65% (02:28) correct 35% (02:53) wrong based on 228 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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16 Sep 2014, 00:25
4
6
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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Updated on: 05 Nov 2018, 11:01
8
1
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

Originally posted by Raihanuddin on 28 Nov 2014, 02:00.
Last edited by Raihanuddin on 05 Nov 2018, 11:01, edited 1 time in total.
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06 Aug 2016, 21:54
how 18 * 2/3 ???
from where does 2/3
factor comes in picture.. plz explain..
Thnx
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11 Aug 2016, 11:22
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,
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26 Dec 2016, 05:18
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, 09:02
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, 22:38
Are there more questions like this to practice? Would appreciate links if any!
Math Expert
Joined: 02 Sep 2009
Posts: 50585

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28 Aug 2017, 22:45
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, 10:49
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, 21:07
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.
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21 Nov 2017, 21:57
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, 17:22
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
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23 Nov 2017, 20:16
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, 09:33
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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29 Aug 2018, 11:05
1
Raihanuddin wrote:
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

This was a real brain teaser, but it's so simple it hurts!
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29 Aug 2018, 11:23
souvonik2k wrote:
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.

I think the easiest way to think about it is overall you are solving for the 2:1 = neg : non-neg ratio. the items on the right of equals are for 100% (or 9/9) of the ratio, but you only need 7/9 of it. So you divide by 7/9 and get the portion that corresponds to our search, as we are disregarding 2/9.
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13 Sep 2018, 19:31
Raihanuddin wrote:
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

Hi,

Can you please explain this step :
"So negative has to be =24-2 =22
Remaining numbers = 36-8 = 28"

I fail to understand it. Thanks!
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05 Nov 2018, 04:45
ajtmatch wrote:
Raihanuddin wrote:
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

Hi,

Can you please explain this step :
"So negative has to be =24-2 =22
Remaining numbers = 36-8 = 28"

I fail to understand it. Thanks!

Hey ajtmatch
Carefully read the question and observe that it asks us "What fraction of the remaining numbers in set A must be negative".

From Raihanuddin 's awesome explanation we already know two things-
1) that from 2/9th of the numbers we get 2 negatives and
2) we also know that totally we need 24 negatives

So tell me how many of remaining numbers needs to be negative? 24-2 = 22 correct?
And this 22 is from the remaining total numbers. So how many numbers are remaining other than the 2/9th? 36-8 = 28

M26-14 &nbs [#permalink] 05 Nov 2018, 04:45
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# M26-14

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