GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Dec 2018, 07:56

Starting NOW!

YouTube Live with Cornell Johnson - Join HERE  |  HBS Chat - Decisions at Noon ET  |  HaaS Chat  HaaS calling admits |  Darden Chat

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

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
• The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

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

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51099
Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

03 Dec 2015, 23:53
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:40) correct 23% (01:50) wrong based on 168 sessions

HideShow timer Statistics

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

_________________
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2125
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

04 Dec 2015, 00:51
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

_________________

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
Joined: 02 May 2014
Posts: 100
Schools: ESADE '16, HKU'16, SMU '16
GMAT 1: 620 Q46 V30
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

06 Dec 2015, 06:26
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

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
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2125
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

06 Dec 2015, 11:10
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

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
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4273
Location: India
GPA: 3.5
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

06 Dec 2015, 11:26
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

_________________

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
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13058
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

07 Dec 2015, 21:29
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

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

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/

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

Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 377
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

28 Oct 2016, 16:07
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
Non-Human User
Joined: 09 Sep 2013
Posts: 9116
Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

Show Tags

01 Sep 2018, 06:02
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.
_________________
Re: Every student in a room is either a junior or a senior. There is at le &nbs [#permalink] 01 Sep 2018, 06:02
Display posts from previous: Sort by