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M26-14

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M26-14  [#permalink]

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New post 16 Sep 2014, 01:25
1
11
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A
B
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E

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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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Re M26-14  [#permalink]

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New post 16 Sep 2014, 01:25
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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.


Answer: A
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M26-14  [#permalink]

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New post 28 Nov 2014, 03:00
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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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Re: M26-14  [#permalink]

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New post 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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Re: M26-14  [#permalink]

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New post 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

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Re: M26-14  [#permalink]

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New post 26 Dec 2016, 06:18
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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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Re M26-14  [#permalink]

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New post 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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Re: M26-14  [#permalink]

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New post 28 Aug 2017, 23:38
Are there more questions like this to practice? Would appreciate links if any!
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New post 28 Aug 2017, 23:45
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Re: M26-14  [#permalink]

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New post 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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Re M26-14  [#permalink]

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New post 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.
Please clarify
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Re: M26-14  [#permalink]

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New post 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.
Please clarify


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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Re: M26-14  [#permalink]

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New post 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.


Answer: A

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


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Re: M26-14  [#permalink]

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New post 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.


Answer: A

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


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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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M26-14  [#permalink]

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New post 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.


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