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

Question

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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effatara · Accepted Answer

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  .

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.

EgmatQuantExpert · Answer

Solution 
  Given:  
In this question, we are given that
 • 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. 
• 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.
• All the students who were eligible for the scholarship applied for the scholarship.

To find:  
 • The maximum possible number of students who applied for scholarship but did not get.

Approach and Working:  
Let us assume that out of 60 students, n number of students obtained Grade A and applied for scholarship.

As 1 out of every 5 students who applied for scholarship got it, we can say
 • Number of students who got scholarship = n/5
• Hence, number of students who didn’t get scholarship = 60 – n/5

As per the given condition,
 • (n/5): (60 – n/5) ≤ 1/9
Simplifying, we get n ≤ 30

So, the maximum value of n = 30
 • Therefore, the maximum value of 4n/5 = 30 * 4/5 = 24

Hence, the correct answer is option C.

Answer: C

aks456 · Answer

As per me, answer is 24

kql5112 · Answer

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

Nevernevergiveup · Answer

soln.png 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

EgmatQuantExpert · Answer

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

keats · Answer

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 ______________________ 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

) 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

Nevernevergiveup · Answer

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

iliavko · Answer

"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?

Nevernevergiveup · Answer

Of-course Scholarship. Is there anyway to apply for a grade? NO right?

iliavko · Answer

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

gps5441 · Answer

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

Bambi2021 · Answer

I think this sentence is a bit ambiguous:

"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."

If the ratio is "not more than 1:9", it sounds like it could be less than 1:9. Actually, it sounds as if everybody could have got a scholarship.

Assuming 1:9 gives:

60/10 = 6 students got a scholarship.

6*4 = 24 students did not get a scholarship.

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