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16 Sep 2014, 00:25
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 nonnegative. What fraction of the remaining numbers in set \(A\) must be negative so that the total ratio of negative numbers to nonnegative 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 \(184=14\) numbers left to observe; "\(\frac{3}{4}\) of those numbers were nonnegative" hence 3 numbers were nonnegative and 1 number was negative; Ratio of negative numbers to nonnegative 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 \(121=11\) negative numbers. Thus \(\frac{11}{14}\) of the remaining numbers in set \(A\) must be negative. Answer: A
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M2614
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Updated on: 05 Nov 2018, 11:01
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 nonnegative. So, the negative was 2
The Required ratio of negative to nonnegative =2:1
So Total negatives will be 2/3 of 36 = 24 and nonnegative = 12
So, new negative numbers have to be =242 =22 (Because we already have 2 from observed data) Remaining numbers = 368 = 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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Re: M2614
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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
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
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 highquality 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  nonnegative.



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28 Aug 2017, 22:38
Are there more questions like this to practice? Would appreciate links if any!



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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 highquality 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 nonnegative and 1 is negative. Please clarify



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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 nonnegative. What fraction of the remaining numbers in set \(A\) must be negative so that the total ratio of negative numbers to nonnegative 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 \(184=14\) numbers left to observe; "\(\frac{3}{4}\) of those numbers were nonnegative" hence 3 numbers were nonnegative and 1 number was negative; Ratio of negative numbers to nonnegative 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 \(121=11\) negative numbers. Thus \(\frac{11}{14}\) of the remaining numbers in set \(A\) must be negative.
Answer: A 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 nonnegative. What fraction of the remaining numbers in set \(A\) must be negative so that the total ratio of negative numbers to nonnegative 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 \(184=14\) numbers left to observe; "\(\frac{3}{4}\) of those numbers were nonnegative" hence 3 numbers were nonnegative and 1 number was negative; Ratio of negative numbers to nonnegative 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 \(121=11\) negative numbers. Thus \(\frac{11}{14}\) of the remaining numbers in set \(A\) must be negative.
Answer: A Can u please explain the last part of the question ? M still confused Sent from my Redmi 3S using GMAT Club Forum mobile appIn observed pool: 3 numbers were nonnegative and 1 number was negative. We want the TOTAL ratio of negative numbers to nonnegative 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 121=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 nonnegative. What fraction of the remaining numbers in set \(A\) must be negative so that the total ratio of negative numbers to nonnegative 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 \(184=14\) numbers left to observe; "\(\frac{3}{4}\) of those numbers were nonnegative" hence 3 numbers were nonnegative and 1 number was negative; Ratio of negative numbers to nonnegative 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 \(121=11\) negative numbers. Thus \(\frac{11}{14}\) of the remaining numbers in set \(A\) must be negative.
Answer: A 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: M2614
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29 Aug 2018, 11:05
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 nonnegative =2:1
So Total negatives will be 2/3 of 36 = 24 and non negative = 12
So negative has to be =242 =22 Remaining numbers = 368 = 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 : nonneg 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 nonnegative =2:1
So Total negatives will be 2/3 of 36 = 24 and non negative = 12
So negative has to be =242 =22 Remaining numbers = 368 = 28
fraction =22/28 = 11/14 Hi, Can you please explain this step : "So negative has to be =242 =22 Remaining numbers = 368 = 28" I fail to understand it. Thanks!



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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 nonnegative =2:1
So Total negatives will be 2/3 of 36 = 24 and non negative = 12
So negative has to be =242 =22 Remaining numbers = 368 = 28
fraction =22/28 = 11/14 Hi, Can you please explain this step : "So negative has to be =242 =22 Remaining numbers = 368 = 28" I fail to understand it. Thanks! Hey ajtmatchCarefully 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? 242 = 22 correct? And this 22 is from the remaining total numbers. So how many numbers are remaining other than the 2/9th? 368 = 28 Hope this made sense!










