Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 20 Jul 2019, 17:21

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.

Close

Request Expert Reply

Confirm Cancel

Every student in a room is either a junior or a senior. There is at le

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56304
Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 04 Dec 2015, 00:53
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:42) correct 23% (01:47) wrong based on 168 sessions

HideShow timer Statistics


Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2356
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 04 Dec 2015, 01:51
1
Let total number of juniors= J
total number of seniors =S
(1/4) J = (3/5) S
=> S = 5/12 J
Total number of students = J+S = (17/12) J

Fraction of the students in the room are juniors = J/(J+S) = J/[(17/12) J]
=12/17

Answer D
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful
Manager
Manager
avatar
Joined: 02 May 2014
Posts: 93
Schools: ESADE '16, HKU'16, SMU '16
GMAT 1: 620 Q46 V30
GMAT ToolKit User
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 06 Dec 2015, 07:26
1
Skywalker18 wrote:
Let total number of juniors= J
total number of seniors =S
(1/4) J = (3/5) S
=> S = 5/12 J
Total number of students = J+S = (17/12) J

Fraction of the students in the room are juniors = J/(J+S) = J/[(17/12) J]
=12/17

Answer D


Hi Skywalker18 ,

As soon as we get S = 5/12 J, we can reduce it to ratio of S:J = 5:12.
Now from the above ratio, we can get that number of S and J are 5x and 12x respectively, x being the multiplier.
We can directly calculate J/(J + S) = 12x/17x i.e. 12/17.

So can we say that when we have a relation between two quantities in the form
a/b = int1/int2, we can directly express the fraction of a or b with respect to whole using this relation alone ?

Thanks!
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2356
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 06 Dec 2015, 12:10
1
sytabish wrote:
Skywalker18 wrote:
Let total number of juniors= J
total number of seniors =S
(1/4) J = (3/5) S
=> S = 5/12 J
Total number of students = J+S = (17/12) J

Fraction of the students in the room are juniors = J/(J+S) = J/[(17/12) J]
=12/17

Answer D


Hi Skywalker18 ,

As soon as we get S = 5/12 J, we can reduce it to ratio of S:J = 5:12.
Now from the above ratio, we can get that number of S and J are 5x and 12x respectively, x being the multiplier.
We can directly calculate J/(J + S) = 12x/17x i.e. 12/17.

So can we say that when we have a relation between two quantities in the form
a/b = int1/int2, we can directly express the fraction of a or b with respect to whole using this relation alone ?

Thanks!


Hi sytabish ,

Yes , it is essentially the same .

let's say a/b = 1/2
The numbers a and b can be x and 2x respectively , where x is some constant.
a+b= x + 2x = 3x

b/(a+b) =2x/3x = 2/3

a/b + 1 = 1/2 +1
=>(a+b)/b = 3/2
=>b/(a+b) =2/3

a/(a+b)=x/3x = 1/3

or b/a = 2
=>b/a + 1 = 2+1
=>(b+a)/a = 3
=>a/(a+b)=1/3

Hope it help!! :)
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4512
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 06 Dec 2015, 12:26
Bunuel wrote:
If 1/4 of the juniors is equal to 3/5 of the seniors, what fraction of the students in the room are juniors?/


\(\frac{1}{4}J\) = \(\frac{3}{5}S\)

So, J = \(\frac{12}{5}s\)

Bunuel wrote:
Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room.


So, Total no of Students in the room is = junior + senior

Or, Total no of Students in the room is = \(\frac{12}{5}s\)+ \(s\)

Or, Total no of Students in the room is = \(\frac{17}{5}s\)

Bunuel wrote:
What fraction of the students in the room are juniors?


Required Fraction is = Juniors/Total Number of Students

Or, Required Fraction is =12s/5/17s/5

Or, The Required Fraction is = 12/17


Hence answer is (D) 12/17

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14597
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 07 Dec 2015, 22:29
3
Hi All,

This question can be solved by TESTing VALUES. The 'key' is to make sure that the NUMERATORS of the two fractions are equal.

We're told that 1/4 of the Juniors = 3/5 of the Seniors

With these two fractions, the easiest way to set the two numbers equal is if we use the number 3...

3 out of 12 Juniors = 3 out of 5 Seniors

So there are 12 TOTAL Juniors and 5 TOTAL Seniors

The question asks what fraction of the students are JUNIORS: 12/17

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 368
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 28 Oct 2016, 17:07
1
Say # of juniors = 120

1/4(120)=(3/5)x
30=3x/5
x=50 (# seniors)

120+50 = 170 (total of people in the room)

ratio --> 120/170 = 12/17
Manager
Manager
User avatar
G
Joined: 29 Nov 2018
Posts: 169
CAT Tests
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 27 May 2019, 01:39
A shorter way to solve:

Given,
1/4 J = 3/5 S

Cross-multiply to get,
5J=12S
or, J/S= 12/5

Represent as ratios,
Part:Part:Whole

12: 5: 17

Now, Junior: Total = 12:17
_________________
Hit Kudos to keep the community alive !
ISB School Moderator
User avatar
G
Joined: 08 Dec 2013
Posts: 530
Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Reviews Badge CAT Tests
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

New post 27 May 2019, 01:43
Bunuel wrote:
Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 1/4 of the juniors is equal to 3/5 of the seniors, what fraction of the students in the room are juniors?

A. 3/20
B. 1/3
C. 5/12
D. 12/17
E. 17/20


(1/4)J = (3/5)S

J/S = 12/5

So J/(J+S) = 12x/(12x+5x)
=> 12/17 D
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.

GMAT Math Book


-I never wanted what I gave up
I never gave up what I wanted-
GMAT Club Bot
Re: Every student in a room is either a junior or a senior. There is at le   [#permalink] 27 May 2019, 01:43
Display posts from previous: Sort by

Every student in a room is either a junior or a senior. There is at le

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne