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jo9: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed Aug 13, 2008 5:52 pm

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by jo9 » Thu Dec 25, 2008 4:22 pm

At College X,the faculty-to-student ratio is 1:9.If two-thirds of the students are female and one-quarter of the faculty is female,what fraction of the combined stdents 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.

Hi guys I found this Q very tough.Jus curious to know if such tough questions are expected in the real test????

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Source: Beat The GMAT — Data Sufficiency | Thu Dec 25, 2008 4:22 pm

amitabhprasad: Master | Next Rank: 500 Posts; Posts: 259; Joined: Thu Jan 18, 2007 8:30 pm; Thanked: 16 times

by amitabhprasad » Thu Dec 25, 2008 4:35 pm

I am getting 'B"
whats OA ?
this is how I solved
pick a number for # of students = 36 LCM of 3,4,9
Thus number of faculty = 4 since ratio is 1:9
# of female student = 2/3 of 36 = 24
# of female faculty = 1/4 of 4 = 1
ratio = (24+1)/(36+4)

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Thu Dec 25, 2008 5:48 pm

Or pick smart numbers and solve for the ratio

ratio 1:9

12 faculty

108 students

2/3*108 = 72

1/4*12 = 3

72+3/120 = 5/8

B)

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vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Thu Dec 25, 2008 5:59 pm

Fac/St =1/9

2/3*S=F
1/4 faculty is female

9,3,4 so the ideal number to plug in 36

so there are 4 faculty, and 36 students

2/3 of students is female thats is 24 female stduents

1/4 female fucaulty is 1

combined is 40 and female bothe faculty and students is 25

25/40 -- > 5/8 it is OA B

vishu

KILL !! DIE !! or BEAT my FEAR !!! de@D END!!

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vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Thu Dec 25, 2008 6:00 pm

Hi guys I found this Q very tough.Jus curious to know if such tough questions are expected in the real test???

I wont be surprised if u get one !!!

vishu

KILL !! DIE !! or BEAT my FEAR !!! de@D END!!

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Fri Dec 26, 2008 1:02 am

Faculty = F
Student = S

S/F = 9

For Students;
Female = 2/3 S

For faculty:
Facultuy = 1/4 F

Now total females/ total people: ( 2/3S + 1/4(S/9) )/ S + S/9 ( using previous equation to convert F into S)
= 5/8

IMO B

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thirst: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Fri Nov 28, 2008 9:47 pm; GMAT Score:720

by thirst » Fri Dec 26, 2008 1:13 am

Questions like these can be difficult if you try to do normal math. It becomes a much easier problem when you pick numbers to attack this problem as the previous posters have demonstrated.

Target scores: 50Q 45V

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pm; Thanked: 33 times; Followed by:4 members

by vittalgmat » Fri Dec 26, 2008 10:47 am

Here is another way.
f:s = 1: 9. So totally 1+9= 10. (here the entire problem deals with ratios; fraction is a synonym for ratio. So we can drop the x ie. we dont need to say f:s = 1x: 9x, so totally 10x)

From the q we have females are
2/3 of 9 and 1/4 of 1 ie. 18/3 + 1/4.

The q asks for ratio (or fraction) of females to combined total.

ie (18/4 + 1/4) / 10.

=> 5/8

HT Helps.

One can be almost sure to expect q of this this type on GMAT. This is a moderately tough question, probably a 600 -650 level.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Fri Dec 26, 2008 11:59 am

This question just asks about a weighted average, and it's just as fast, if not faster, to do with 'normal math' as it is to plug in numbers, at least if you know how to do a weighted average problem.

This is among the more common topics to see tested on the current GMAT, so if you do find this kind of question difficult, I'd strongly recommend learning how to do it and other similar questions.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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