Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 12 May 2009
Posts: 50

At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
Updated on: 28 Apr 2014, 01:31
Question Stats:
76% (02:22) correct 24% (02:28) wrong based on 406 sessions
HideShow timer Statistics
At College X, the facultytostudent ratio is 1:9. If twothirds of the students are female and onequarter of the faculty is female, what fraction of the combined students and faculty are female? (A) 11/24 (B) 5/8 (C) 25/56 (D) 11/12 (E) It cannot be determined from the information given. Does someone know how to solve this one without picking numbers? This is how far I got:
p/s=1/9 f/s=2/3 f/p=1/4
Equation 2 and 3 give us:
f=2s/3 f=1p/4
Set equal 2s/3=1p/4; Reducing: s/p=3/8 (which does not agree with equation 1). Where did I go wrong?
Thanks Steve
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by enfinity on 03 Oct 2009, 18:22.
Last edited by Bunuel on 28 Apr 2014, 01:31, edited 2 times in total.
Renamed the topic, edited the question and added the OA.



Senior Manager
Joined: 18 Aug 2009
Posts: 279

Re: Ratio: System of Equation (Kaplan)
[#permalink]
Show Tags
03 Oct 2009, 18:32
enfinity wrote: At college x, the ratio of students to students is 1:9. If two thirds of the students are female and one quarter of faculty is female, what fraction of the combined students and faculty are female?
a) 11/24 b) 5/8 c) 23/47 d) 3/4 e) 2/3
Does someone know how to solve this one without picking numbers? This is how far I got:
p/s=1/9 f/s=2/3 f/p=1/4
Equation 2 and 3 give us:
f=2s/3 f=1p/4
Set equal 2s/3=1p/4; Reducing: s/p=3/8 (which does not agree with equation 1). Where did I go wrong?
Thanks Steve Can you please recheck if this is correct question?



Manager
Joined: 12 May 2009
Posts: 50

Re: Ratio: System of Equation (Kaplan)
[#permalink]
Show Tags
03 Oct 2009, 18:35
Sorry, that's the right question:
At college x, the ratio of faculty to students is 1:9. If two thirds of the students are female and one quarter of faculty is female, what fraction of the combined students and faculty are female?



Senior Manager
Joined: 18 Aug 2009
Posts: 279

Re: Ratio: System of Equation (Kaplan)
[#permalink]
Show Tags
03 Oct 2009, 18:48
enfinity wrote: Sorry, that's the right question:
At college x, the ratio of faculty to students is 1:9. If two thirds of the students are female and one quarter of faculty is female, what fraction of the combined students and faculty are female? Faculty/Students = 1/9 Female Faculty = ff = F/4 Female Students = fs = 2S/3 So combined ratio = (ff+fs)/(F+S) = (1/4 + 2*9/3)/(1+9) ratio = 5/8 Answer is B.



Manager
Joined: 18 Jul 2009
Posts: 164
Location: India
Schools: South Asian Bschools

Re: Ratio: System of Equation (Kaplan)
[#permalink]
Show Tags
04 Oct 2009, 07:20
i simply picked 100 but faculty came in fraction....so picked up 200 in nxt interval 125/200 = 5/8 ...i didint take more than a minute to conclude option answer
_________________
Bhushan S. If you like my post....Consider it for Kudos



Manager
Joined: 15 Sep 2009
Posts: 117

Re: Ratio: System of Equation (Kaplan)
[#permalink]
Show Tags
05 Oct 2009, 10:12
faculty = x
Students = 9x.
Female (faculty) = x/4 and female(students) = 6x.
So fraction is = 25x/40x = 5/8
I wud go with option B



Kaplan GMAT Instructor
Joined: 25 Aug 2009
Posts: 635
Location: Cambridge, MA

Re: Ratio: System of Equation (Kaplan)
[#permalink]
Show Tags
05 Oct 2009, 20:34
bhushan252 wrote: i simply picked 100 but faculty came in fraction....so picked up 200 in nxt interval
125/200 = 5/8 ...i didint take more than a minute to conclude option answer Just wanted to chime in here. I know I've been beaten to the math, and the OP wanted to avoid picking numbers. However, for this problem picking numbers will be easier for many test takers. Picking 100 can make it difficult, though. Fortunately, there's a trick to it! A 1:9 ratio has a total of ten parts, we're taking thirds of the the faculty, and quarters of the students. So we need a number divisible by 10, 3, and 4; multiply them out and we get 120. Start there, and things work out much better! 12 faculty, 3 female faculty, 108 students, 72 female students, 75 females gives us 75/120 = 15/24 = 5/8.
_________________
Eli Meyer Kaplan Teacher http://www.kaptest.com/GMAT
Prepare with Kaplan and save $150 on a course!
Kaplan Reviews



Retired Moderator
Joined: 29 Apr 2015
Posts: 848
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
01 Jul 2015, 03:39
enfinity wrote: At College X, the facultytostudent ratio is 1:9. If twothirds of the students are female and onequarter of the faculty is female, what fraction of the combined students and faculty are female? (A) 11/24 (B) 5/8 (C) 25/56 (D) 11/12 (E) It cannot be determined from the information given. Does someone know how to solve this one without picking numbers? This is how far I got:
p/s=1/9 f/s=2/3 f/p=1/4
Equation 2 and 3 give us:
f=2s/3 f=1p/4
Set equal 2s/3=1p/4; Reducing: s/p=3/8 (which does not agree with equation 1). Where did I go wrong?
Thanks Steve The Ratio F:S is 1:9 2/3 of the students are female: 2/3*9 = 6 1/4 of the faculty are female: 1/4*1 = 0.25 So we have a combined fraction of 6.25/10 >>> expand with *4 both the dividend and divisor to get to 25/40 = 5/8
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Senior Manager
Joined: 28 Jun 2015
Posts: 293
Concentration: Finance
GPA: 3.5

Re: At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
01 Jul 2015, 05:35
Let F be Faculty, and S be Students. F : S = 1x : 9x Female_F = 1x/4 Female_S = 9x*2/3 = 6x Total number of people at college X = 1x+9x = 10x. Total Male = 3x/4 + 3x = 3x+12x/4 = 15x/4 Total Female = x/4 + 6x = x +24x/4 = 25x/4 Ratio of Total Female : Total Number of People at College X = 25x/4 : 10x = 25x : 40x = 5:8. Ans is B.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.



Manager
Status: Preparing
Joined: 05 May 2016
Posts: 58
Location: India
Concentration: International Business, Finance

Re: At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
13 Mar 2017, 10:50
Female students: 2/3*9 Female faculty: 1/4 Ratio will be:(2/3*9+1/4)/10=25/40=5/8
Please let me know if my method is wrong!



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
Location: United States (CA)

Re: At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
26 Nov 2017, 12:35
Hi All, This prompt gives us a few facts to work with: 1) The ratio of faculty to students is 1:9 (meaning that the number of students MUST be a multiple of 9) 2) 2/3 of the students are FEMALE 3) 1/4 of the faculty are FEMALE (meaning that the number of faculty MUST be a multiple of 4) We're asked for the fraction of total people that are female. This question can be solved by TESTing VALUES. IF.... Total faculty = 4, then we have 1 female faculty Total students = 36, then we have 24 female students Total females = 25 Total people = 40 The answer to the question is 25/40 = 5/8 The logical question to ask is whether this fraction stays the same if we change the total number of people, so let's TEST another value... IF.... Total faculty = 8, then we have 2 female faculty Total students = 72, then we have 48 female students Total females = 50 Total people =80 You should notice that ALL of the values increased by the same percent, so the answer to the question will be the SAME... The answer to the question is 50/80 = 5/8 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
Rich Cohen
CoFounder & 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!*****



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)

Re: At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
29 Nov 2017, 11:11
enfinity wrote: At College X, the facultytostudent ratio is 1:9. If twothirds of the students are female and onequarter of the faculty is female, what fraction of the combined students and faculty are female?
(A) 11/24 (B) 5/8 (C) 25/56 (D) 11/12 (E) It cannot be determined from the information given. ] We can let the total faculty = f and the total students = n. Thus, (2/3)n are female students and (1/3)n are male. Also, (1/4)f is female faculty and (3/4)f is male. We also know that 1/9 = f/n, so n = 9f. Thus, (2/3)(9f) = 6f are female students and (1/3)(9f) = 3f are male. So the total students and faculty is: 9f + f = 10f, and the combined female students and female faculty is 6f + (1/4)f = 6.25f. Thus, females are 6.25f/10f = 6.25/10 = 625/1000 = 5/8 of the total students and faculty at College X. Alternate Solution: Let 4x represent the number of faculty in College X. Since facultytostudent ratio is 1:9, there are 36x students in College X. Since 1/4 of the faculty are females, there are x female faculty members. Since 2/3 of the students are females, there are (36x)(2/3) = 24x female students. In total, there are x + 24x = 25x females and 4x + 36x = 40x people in College X, giving us a ratio of 25x/40x = 5/8. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
08 Jan 2018, 12:35
enfinity wrote: At College X, the facultytostudent ratio is 1:9. If twothirds of the students are female and onequarter of the faculty is female, what fraction of the combined students and faculty are female?
(A) 11/24 (B) 5/8 (C) 25/56 (D) 11/12 (E) It cannot be determined from the information given. We can express the ratio of faculty to students as x : 9x. Since twothirds of the students are female: (9x)(2/3) = 6x = female Since onequarter of the faculty is female: (1/4)x = x/4 = female Thus, the fraction of the combined students and faculty who are female is: (6x + x/4)/(9x + x) = (24x/4 + x/4)/(10x) = (25x/4)/10x = 25x/40x = 5/8 Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 06 Sep 2016
Posts: 134
Location: Italy
GPA: 3.2
WE: General Management (Human Resources)

Re: At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
16 Feb 2018, 08:59
Total number of people = 400 Total number of faculty = 40 Total number of students = 360 Female faculty members = 10 Female students = 240 So, 250/400 = 5/8 , our answer



Manager
Joined: 22 May 2017
Posts: 90
GMAT 1: 580 Q41 V29 GMAT 2: 580 Q43 V27

Re: At College X, the facultytostudent ratio is 1:9. If twoth
[#permalink]
Show Tags
16 Feb 2018, 09:11
Attachment:
1518797473485.jpeg [ 751.28 KiB  Viewed 938 times ]
Sent from my Redmi Note 3 using GMAT Club Forum mobile app




Re: At College X, the facultytostudent ratio is 1:9. If twoth &nbs
[#permalink]
16 Feb 2018, 09:11






