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Of the 60 students in a class, only the students who had obtained Grad

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Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post Updated on: 07 Aug 2018, 01:15
1
18
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (02:03) correct 55% (02:44) wrong based on 309 sessions

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Question 2 of The e-GMAT Sets Triad

Of the 60 students in a class, only the students who had obtained Grade A in Science could apply for a scholarship. Only 1 out of every 5 students who applied for a scholarship got it. If the ratio of the number of students who got the scholarship to the number of students who did not get the scholarship is not more than 1:9, what is the maximum possible number of students who applied for but did not get the scholarship? Assume that all the students who were eligible for the scholarship applied for it.

(A) 6
(B) 12
(C) 24
(D) 30
(E) 54

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Originally posted by EgmatQuantExpert on 13 May 2015, 07:42.
Last edited by EgmatQuantExpert on 07 Aug 2018, 01:15, edited 3 times in total.
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post Updated on: 14 May 2015, 23:49
1
3
The correct answer is option C

The given information can be tabulated as below:

Image

Given:

\((\frac{Y}{5})/(60- \frac{Y}{5})\) ≤ \(\frac{1}{9}\)

That is, \(\frac{Y}{5}\) ≤ \(\frac{1}{9}*(60- \frac{Y}{5})\)
9Y ≤ 300-Y

Y ≤ 30

So, the maximum possible value of Y = 30
So, the maximum possible value of \(\frac{4Y}{5}\) = 24
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Originally posted by EgmatQuantExpert on 13 May 2015, 08:06.
Last edited by EgmatQuantExpert on 14 May 2015, 23:49, edited 1 time in total.
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 13 May 2015, 10:27
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As per me, answer is 24
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 13 May 2015, 19:14
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x students got the scholarship. 5x students applied for it. y students didn't apply. 5x+y=60. find the maximum 4x
x/(4x+y)<=1/9 and y=60-5x
simplify everything x<=6 so 4x<=24
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 14 May 2015, 11:43
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Attachment:
soln.png
soln.png [ 14.93 KiB | Viewed 3840 times ]

G+a+b+c=60
According to assumption b=0
G+a+c=60
\(\frac{G}{(a+c)} > \frac{1}{9}\)
9G>a+c
10G>60(since a+c+G=60)
G>6
G=7,8,9………
But G=4a {8,12,16………..}
a={2,3,4……….}
Thus 4a+a+c=60
Thus 5a+c=60
Inorder to maximize a we can take values for c as greater than or equal to 0.
Thus maz values of a according to options can be 12.
Option B is the right answer
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 14 May 2015, 23:55
aks456, kql5112, Mechmeera: Good job done with this question! :)

Mechmeera: Kudos for the well-drawn tree structure! The single point where you erred was in the inequality:

\(\frac{G}{(a+c)}>\frac{1}{9}\)

The sign of inequality there should have been ≤. Try solving it again and am sure you would get the right answer! :)

Best Regards

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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 14 May 2015, 23:58
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Of the 60 students in a class, only the students who had obtained Grade A in Science could apply for a scholarship. Only 1 out of every 5 students who applied for a scholarship got it. If the ratio of the number of students who got the scholarship to the number of students who did not get the scholarship is not more than 1:9, what is the maximum possible number of students who applied for but did not get the scholarship? Assume that all the students who were eligible for the scholarship applied for it.

(A) 6
(B) 12
(C) 24
(D) 30
(E) 54

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I like doing things algebraically :-D . So, I'll try to make some quick equations here.

Total # of students = 60
Let us assume that x students finally got the scholarship. This means that 5x students applied for the scholarship (These are the one's who have got an A grade in Science, smart students :P )
This means that there are 4x students who applied BUT did not got the scholarship, and there are some students who in the first place could not get in A in Science.
Let us assume that the # of students who could not apply be y
This means y =60-5x

And the ratio given in the question is
x/(4x+y) <=1/9
We know that x and y are positives (they are students) so we can cross multiply

And finally on solving we can get x <=4
Or 4x <=24

Therefore, maximum possible value of 4x can be 24

Option C
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 15 May 2015, 00:13
1
EgmatQuantExpert wrote:
aks456, kql5112, Mechmeera: Good job done with this question! :)

Mechmeera: Kudos for the well-drawn tree structure! The single point where you erred was in the inequality:

\(\frac{G}{(a+c)}>\frac{1}{9}\)

The sign of inequality there should have been ≤. Try solving it again and am sure you would get the right answer! :)

Best Regards

Japinder


Yes you are right.
Thank You EgmatQuantExpert for mentioning the point.
\(\frac{G}{a+c}≤\frac{1}{9}\)
9G<a+c
10G<60
\(G\leq{6}\)

And I mistakenly wrote G=4a but actually a=4G
therefore inorder to maximise a value we need to tkae manimum G value which is 6.
Therefore a=4*6=24
C is the answer
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 14 Feb 2017, 11:55
"A in Science could apply for a scholarship. Only 1 out of every 5 students who applied for a scholarship got it."

Got it what? the grade or the scholarship?
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 14 Feb 2017, 20:15
Top Contributor
iliavko wrote:
"A in Science could apply for a scholarship. Only 1 out of every 5 students who applied for a scholarship got it."

Got it what? the grade or the scholarship?


Of-course Scholarship. Is there anyway to apply for a grade? NO right?
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 15 Feb 2017, 04:07
I would disagree with the "of course" claim..

This can be read as applied for scholarship and got it (the grade) maybe people applied without having the grade, it would (could) change the problem. Anyways instead of "it" the noun "it" refers to would be better :)
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 19 Feb 2017, 01:04
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If you apply a bit of logic, the solution to this problem is very simple. The trick is to clearly understand the two conditions given:

(1) "1 out of every 5 students who applied for the scholarship got it".
This means if 5 applied, 1 got it and 4 didn't; if 10 applied, 2 got it and 8 didn't; and so on.
The second take-away is: the greater the number of students who applied for and got the scholarship, the greater the number who applied and didn't. So if we can find the
greatest number of students who could have got the scholarship (subject to the constraint imposed by the 2nd condition), we will have our answer simply by multiplying that number by 4. Which brings us to the 2nd condition:

(2) "The ratio of the number of students who got the scholarship to the number of students who didn't is NOT MORE THAN 1:9".
This means that the greatest number of students who could have got the scholarship is 6 because any number more than that would not be in compliance with the ratio of = to or <1:9 [e.g. if 7 students got the scholarship, 63 students (or more) would have to be unsuccessful in order to comply with the ratio which means the total number of
students would have to be 70 or more].

So, given the above conditions, if the greatest number of students who could have got the scholarship is 6, the maximum number of students who applied for but did not get it must be 6 x 4=24.
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Re: Of the 60 students in a class, only the students who had obtained Grad  [#permalink]

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New post 16 Nov 2017, 23:27
1
Total student=60
Got Scholarship: Did Not get Scholarship
1:9
or
6:54 (10x=60 or x=60/10=6)

The ratio between
Got scholarship: Applied for scholarship
1:5
ie 6=1/5x or x=30 ie the total students who qualified for the scholarship.
Student who applied and did not get= Total student who applied-student who got the schloarship=30-6=24
Re: Of the 60 students in a class, only the students who had obtained Grad &nbs [#permalink] 16 Nov 2017, 23:27
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