NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 03:36 It is currently 26 Apr 2024, 03:36
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16843 [71]
Given Kudos: 165
Send PM
Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   Updated on: 07 Aug 2018, 01:15
2
Kudos
69
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

44% (02:55) correct 56% (02:53) wrong based on 708 sessions
Hide Show timer Statistics
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

Previous Question | Next Question

To read all our articles:Must Read articles to reach Q51


ShowHide Answer
Official Answer
C

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.
Most Helpful Reply
User avatar
aks456
Manager
Manager
Joined: 20 Jul 2012
Posts: 92
Own Kudos [?]: 139 [18]
Given Kudos: 559
Location: India
WE:Information Technology (Computer Software)
Send PM
GMAT ToolKit User
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   13 May 2015, 10:27
12
Kudos
6
Bookmarks
As per me, answer is 24
Attachments

_2.PNG
_2.PNG [ 4.56 KiB | Viewed 13868 times ]

User avatar
G
effatara
Manager
Manager
Joined: 09 Nov 2015
Posts: 202
Own Kudos [?]: 320 [8]
Given Kudos: 96
Send PM
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   19 Feb 2017, 01:04
6
Kudos
2
Bookmarks
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.
General Discussion
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16843 [7]
Given Kudos: 165
Send PM
Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   Updated on: 03 Apr 2019, 04:09
2
Kudos
5
Bookmarks
Expert Reply

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

Originally posted by EgmatQuantExpert on 13 May 2015, 08:06.
Last edited by EgmatQuantExpert on 03 Apr 2019, 04:09, edited 2 times in total.
avatar
kql5112
Intern
Intern
Joined: 13 May 2015
Posts: 2
Own Kudos [?]: 4 [2]
Given Kudos: 5
Send PM
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   13 May 2015, 19:14
2
Kudos
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
User avatar
G
Nevernevergiveup
Retired Moderator
Joined: 18 Sep 2014
Posts: 1015
Own Kudos [?]: 2755 [2]
Given Kudos: 79
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   14 May 2015, 11:43
2
Kudos
Attachment:
soln.png
soln.png [ 14.93 KiB | Viewed 13452 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
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16843 [0]
Given Kudos: 165
Send PM
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   14 May 2015, 23:55
Expert Reply
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
User avatar
G
keats
Director
Director
Joined: 28 Nov 2014
Posts: 754
Own Kudos [?]: 1264 [2]
Given Kudos: 86
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Send PM
Reviews Badge
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   14 May 2015, 23:58
1
Kudos
1
Bookmarks
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 :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
User avatar
G
Nevernevergiveup
Retired Moderator
Joined: 18 Sep 2014
Posts: 1015
Own Kudos [?]: 2755 [2]
Given Kudos: 79
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   15 May 2015, 00:13
2
Kudos
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
User avatar
S
iliavko
Senior Manager
Senior Manager
Joined: 08 Dec 2015
Posts: 258
Own Kudos [?]: 117 [0]
Given Kudos: 36
GMAT 1: 600 Q44 V27
Send PM
Reviews Badge
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] 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?
User avatar
G
Nevernevergiveup
Retired Moderator
Joined: 18 Sep 2014
Posts: 1015
Own Kudos [?]: 2755 [0]
Given Kudos: 79
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] 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?
User avatar
S
iliavko
Senior Manager
Senior Manager
Joined: 08 Dec 2015
Posts: 258
Own Kudos [?]: 117 [1]
Given Kudos: 36
GMAT 1: 600 Q44 V27
Send PM
Reviews Badge
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   15 Feb 2017, 04:07
1
Kudos
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 :)
User avatar
B
gps5441
Manager
Manager
Joined: 04 May 2014
Posts: 114
Own Kudos [?]: 72 [2]
Given Kudos: 126
Location: India
WE:Sales (Mutual Funds and Brokerage)
Send PM
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   16 Nov 2017, 23:27
2
Kudos
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
User avatar
S
Bambi2021
Senior Manager
Senior Manager
Joined: 13 Mar 2021
Posts: 338
Own Kudos [?]: 101 [1]
Given Kudos: 227
Send PM
Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   08 Jun 2021, 16:22
1
Kudos
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.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32680
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink] New post   15 Mar 2024, 13:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Of the 60 students in a class, only the students who had obtained Grad [#permalink]
15 Mar 2024, 13:39
Moderators:
Bunuel
Math Expert
92929 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions