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# PS: 3 secretaries (m21-02)

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Director
Joined: 09 Aug 2006
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21 Nov 2007, 11:30
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

[Reveal] Spoiler: OA
D

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Joined: 29 Mar 2007
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21 Nov 2007, 11:34
1
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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?

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.
Manager
Joined: 04 Nov 2007
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21 Nov 2007, 15:48
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
Manager
Joined: 03 Sep 2006
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21 Nov 2007, 20:59
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.
Intern
Joined: 17 Jun 2008
Posts: 2
Re: PS: 3 secretaries (m21-02) [#permalink]

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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
Intern
Joined: 09 Sep 2009
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29 Dec 2009, 06:46
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]

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29 Dec 2009, 19:50

This question is classified as GMAT hardest questions. Do we see these kind of questions at 700+ stage?
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Joined: 04 Dec 2009
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Re: PS: 3 secretaries (m21-02) [#permalink]

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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]

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05 Jan 2011, 07:05
3
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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
Intern
Joined: 12 Nov 2010
Posts: 22
Re: PS: 3 secretaries (m21-02) [#permalink]

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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]

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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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Senior Manager
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Re: PS: 3 secretaries (m21-02) [#permalink]

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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)
Manager
Joined: 01 Jan 2011
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Re: PS: 3 secretaries (m21-02) [#permalink]

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09 Jan 2011, 02:24
52/16=3.25hrs..ans is D
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Re: PS: 3 secretaries (m21-02) [#permalink]

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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]

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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
Intern
Joined: 30 Aug 2012
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Re: PS: 3 secretaries (m21-02) [#permalink]

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10 Jan 2013, 04:26
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
Manager
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Re: PS: 3 secretaries (m21-02) [#permalink]

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15 Jan 2013, 02:57
slowest secretary contributes 2/9th of the quantities in half an hour = 36X2/9 = 8 pgs in half hour or 16 pages in 1 hr. hence to produce 52 pages it will take 52/16 = 3 hrs and 15 mins.
Intern
Joined: 22 Dec 2013
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Re: PS: 3 secretaries (m21-02) [#permalink]

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03 Jan 2014, 19:42
1
KUDOS
Cheers everyone this is my first post and 1st day of GMAT prep..
+1 for D
-Total Time taken for 36 pages is 30 minutes I.e overall typing speed is 36/30=1.2 page/minute
-Now considering slowest typing speed ratio w.r.t total speed we get 2/9 (slowest speed/overall)
-To type 52 pages overall time will be 52(pages)/1.2(pages/minute)=43.4 minutes
Therfore multiplying the slowest time ratio of 9/2 to overall time will lead to slowest individual time taken I.e. 195 mintes
3hr 15 min

Posted from my mobile device
Intern
Joined: 03 Jan 2014
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Re: PS: 3 secretaries (m21-02) [#permalink]

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05 Jan 2014, 07:02
4x+3x+2x=9x=36 or 2x=8 or 8 pages in 30 min or 4 pages in 15 min hence 52 pages in 15x13 or 195 min or 3hr15 min ans D
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Re: PS: 3 secretaries (m21-02) [#permalink]

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20 Apr 2014, 02:46
Suppose the speed of slowest secretary is 2a -> total speed of 3 ppl = 9a = 36/0.5 = 72 => 2a = 16 => time to finish 52 pages = 52/16 = 3.25 hrs = 3hrs15mins
Re: PS: 3 secretaries (m21-02)   [#permalink] 20 Apr 2014, 02:46
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