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PS: 3 secretaries (m21-02) [#permalink]
 21 Nov 2007, 11:30
Three secretaries working together can type 36 pages of text in half an hour. If the typing speeds of the secretaries are in a 4:3:2 ratio, how long will it take the slowest-typing secretary working alone to type 52 pages of text? (A) 1 hour and 34 minutes (B) 1 hour and 45 minutes (C) 2 hours and 24 minutes (D) 3 hours and 15 minutes (E) 3 hours and 25 minutes Source: GMAT Club Tests - hardest GMAT questions Please explain. Thanks.
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Re: PS: 3 secretaries [#permalink]
21 Nov 2007, 11:34
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GK_Gmat wrote: Three secretaries working together can type 36 pages in half an hour. If the typing speeds of the secretaries are in 4:3:2 ratio, how long will it take the slowest-typing secretary working alone to type 52 pages?
Please explain. Thanks.
4x+3x+2x=72 (1hr) 9x=72 --x=8. The slowest is 2(8) 16pgs in 1 hr.
16t=52 t=52/16 26/8--> 13/4 or 3.25 hrs.
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Combined rate is: 36pg/(0.5)h or 72pg/hr
Slowest typer rate is: 2/9 of 72/h or 16page/h
time = work/rate = 52/16 hours = 3.25hr
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Will try to share my approach (may be to someone it'll be faster or easier to use)
Secretary = S
S1 : S2 : S3
4 : 3 : 2 | total = 9. It means that 1 unit is 36/9 = 4 pages per 1/2 h and 8 pages per h
S3 is the slowest and has 2 units. So 2 units * 8 pager per h = S3 type 16 pages per hour.
52 / 16 = 3.25 hours would take the slowest secretary to type 52 pages.
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Re: PS: 3 secretaries (m21-02) [#permalink]
29 Dec 2009, 04:31
2+3/2+1=9/2 writers
for one writers one hour work 72/8*2=16 pages
for 52 pages= 52/16= 3 hours 15 minutes
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All of you(except Nitin) have applied the correct approach except 1 mistake.
52/16 hrs. = 13/4 hrs. = 3(1/4) = 3hrs and 1/4*60 mins = 3hrs and 15 mins.
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Re: PS: 3 secretaries (m21-02) [#permalink]
29 Dec 2009, 07:11
yea. did it in first attempt in a minute. My Answer is D.
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Re: PS: 3 secretaries (m21-02) [#permalink]
29 Dec 2009, 19:50
The answer is D.
This question is classified as GMAT hardest questions. Do we see these kind of questions at 700+ stage?
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Re: PS: 3 secretaries (m21-02) [#permalink]
29 Dec 2009, 20:27
Ans : D 3.25 h = 3 hour and 15 min
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Re: PS: 3 secretaries (m21-02) [#permalink]
14 Aug 2010, 07:38
Can anyone explain the method once again???
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Re: PS: 3 secretaries (m21-02) [#permalink]
05 Jan 2011, 07:05
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bibha wrote: Can anyone explain the method once again??? You have typing speeds for each secretary as follows 4:3:2. Lets say secretary A, secretary B and secretary C respectively. So A has a speed of 4x, B of 3x and C of 2x The three of them could write 36 pages in half hour so: 36 pages = A effort + B effort + C effort 36 = 4x + 3x + 2x x = 4 So we derive that the secretary C could finish 2x of work that would be 8 pages in the half hour So for C how much would it take to write 52 pages? 52/8 = 6.5 0.5 hour * 6.5 = 3.25 hours That would be 3 hours and 15 minutes Hope this helps
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Re: PS: 3 secretaries (m21-02) [#permalink]
05 Jan 2011, 08:41
Okay so this is how I thought of it...
Lets find how many pages were completed per individual in those 36pages in 30mins
4x + 3x + 2x = 36
9x = 36
x = 4
So the slowest person would be 2x...which only did 8 pages in those 30mins
The question is asking how long it would take this person to type 56 pages
well 8pages * 6 = 48pages remember it is 8 pages for every 30mins so 6*.5 = 3 hours with a left over of 4 pages which is half of 8pages therefore it would be half the mins...30mins/2 = 15mins
in the end we get 3hrs and 15mins
Choice D...this is my exact thought process. there is probably a better way to figure this out after you get x = 4
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Re: PS: 3 secretaries (m21-02) [#permalink]
05 Jan 2011, 10:22
yep D for me as well.. used the same technique as watever. 
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Re: PS: 3 secretaries (m21-02) [#permalink]
05 Jan 2011, 10:46
+1 for D. Here is my solution; lets say x pages were completed per individual in those 36pages in 30mins (x is speed in page per min) 4x + 3x + 2x = 36/30 p/m 9x = 36/30 p/m x = 4/30 p/m =4p/30m So the slowest person would be 2x = 8p/30m since slowest person needs 30 min for 8 pages or, he can complete 8 page in 30 min for 52 page he needs =30*52/8 = 195min = 3 hr 15 min. Choice D..
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Re: PS: 3 secretaries (m21-02) [#permalink]
05 Jan 2011, 23:45
Rate * Time = work
Rate *1/2 = 36
Rate = 72.
Problem stated that the rates of the 3 members are in the ratio 0f 4:3:2. we need rate for the smaller worker which is 2/9.
So 72*2/9 =16 (rate of the smaller worker). Again back to the formula:
Rate * Time = work
16* X= 52
X=52/16=26/8=3.25 (3 hour 15 minutes)
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Re: PS: 3 secretaries (m21-02) [#permalink]
09 Jan 2011, 02:24
52/16=3.25hrs..ans is D
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Re: PS: 3 secretaries (m21-02) [#permalink]
07 Feb 2011, 10:29
D clearly! Although I made some excess calculations 
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Re: PS: 3 secretaries (m21-02) [#permalink]
19 Nov 2011, 23:30
It takes 3 secretaries 30mins to type 36 pages at a ratio of 4:3:2 pages per secretary, e.g. the fastest types 16 pages in 30 mins, the middle one types 12 pages in 30mins, and the slowest one types 8 pages in 30mins, or she will take 3.75mins per page.
So, 3.75min/page x 52 pages = 195mins or 3hrs 15mins.
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Re: PS: 3 secretaries (m21-02) [#permalink]
09 Jan 2012, 11:21
I did the question as most others did and got to D within a minute to a minute and a half. Personally I do not feel that this is a 700 level question, however, seeing as they make the test and define its difficultly they would be the final authority on this topic. 700+ it is. Posted from my mobile device 
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Re: PS: 3 secretaries (m21-02) [#permalink]
10 Jan 2013, 04:26
answer D
3 secretary working together types 36 pages in 30 mins
3 secretary working together will type 72 pages in 60 mins
ratio of typing speed 4:3:2 , so assuming x is the no. of pages then 4x+3x+2X = 72 pages/hr
9x=72page/hr
X=8page/hr, slowest person types 2x times so 16 pages/hr or 4page/15mins
so 52 pages will be 52/4= 13(15mins) which equals 3 hour and 15mins
alternately 52 pages will be types in 16/hr*3 = 48page/3hours + 4page /15mins = 52 page in 3hr & 15mins
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Re: PS: 3 secretaries (m21-02)
[#permalink]
10 Jan 2013, 04:26
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