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On a wedding catering service, An experienced chef can prepare a servi

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On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post Updated on: 15 Nov 2014, 04:06
1
5
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A
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D
E

Difficulty:

  95% (hard)

Question Stats:

43% (02:08) correct 57% (02:14) wrong based on 274 sessions

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On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.

If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 8

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Please give Kudos if you find this post useful.


Originally posted by aimtoteach on 15 Nov 2014, 00:57.
Last edited by Bunuel on 15 Nov 2014, 04:06, edited 1 time in total.
Renamed the topic and edited the question.
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 15 Nov 2014, 01:39
aimtoteach wrote:
On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.

If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?


(1)2
(2)3
(3)4
(4)6
(5)8

Explain this question


let the work be 24 units. therefore each experience chef will do 24/8= 3 units per hour, and each novice chef will do 24/12= 2 units per hour.

since, catering service employs same number of novice and experienced chefs. thus total number of chefs will be even. option E) states that total number of chefs=8. i.e. experienced chefs=4 and novice chefs = 4 .
thus 4 experience chefs will do 3*4=12 units per hour and 4 novice chefs will do 2*4=8 units per hour
thus total time taken to complete the task will be 24/(12+8)=24/20= 1 hour 12 minutes. thus option e is out

lets try option D
no. of experience chefs=3 and novice chefs=3
thus 3 experience chefs will do 3*3=9 units per hour and 3 novice chefs will do 3*2=6 units per hour
thus total time token to complete the task will be 24/(9+6)=24/15 = 1 hour 36 minutes . thus D
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 15 Nov 2014, 20:12
2
aimtoteach wrote:
On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.

If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 8


Experienced chefs work = 1 wedding/8 hours
Novice chefs work = 1 wedding/12 hours

Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equal "x"

1hr and 36mins = 8/5 an hour

x/8 + x/12 = 1 wedding / (8/5)
x/8 + x/12 = 5/8
3x/24+2x/24 = 5/8
5x/24 = 5/8
x=3

So there are 3 novice chefs and 3 experienced chefs. In total there are 6. The answer is D.
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 07 Dec 2014, 11:01
2
Here's my approach.

Experienced chef - in 1 hour = 1/8 work
Novice chef - in 1 hour = 1/12 work.

In 1 hour total work =1/8+1/12 = 5/24 work.

Means 1 work (1 wedding) = 24/5 = 4.8 hours.

Means 2 chefs(1 experienced and 1 novice) complete 1 wedding in 4.8 hours.

We're asked for 1 hour and 36 min.

1 hour 36 min = 1.6 hours (convert).

That is 1/3 of 4.8 or in words, If 2 chefs complete 1 wedding in 4.8 hours, now it will take how many chefs to do it in one-third time...
TRIPLE !!!

1.6*3=4.8... So 3 pairs of chefs(experienced and novice) = 3*2 = 6 chefs
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 24 Aug 2015, 13:55
lets say, preapring a service for wedding is equivalent to 120units of work. (common multiple of 8 &12)

Experienced chef will do = 15 units/hour
Novice chef will do = 10 units/hour
So, in one hour both will perform = 25units of work. If both of them work together then they will finish it in = 120/25 --> 4.8 hours, which is equivalent to 4 hours 48 minutes.

1E:1N= 4 hours 48 minutes
3E:3N= 1hour 36 minutes.

Therefore, total chefs required 6.

Cheers,
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 24 Aug 2015, 15:26
8/5 hrs x 5/24 combined hourly rate of 2 chefs (1E+1N)=1/3 service
3x2=6 total chefs
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 24 Aug 2015, 21:01
2
aimtoteach wrote:
On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.

If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 8



The important thing here is that equal number of experienced and novice chef are to be hired. So let's find the combined rate of 1 experienced + 1 novice chef:
Rate of experienced chef = (1/8)th of the wedding per hour
Rate of novice chef = (1/12)th of the wedding per hour
Together, their rate is 1/8 + 1/12 = 5/24 of the wedding per hour.

We want the chefs to take more than 1.5 hr but less than 2 hrs so their combined rate must be more than 1/2 but less than 2/3.

Looking at the options:
If we have 3 pairs of chefs, combined rate = 3*5/24 = 15/24 (more than 1/2 but less than 2/3)
If we have 4 pairs of chefs, combined rate = 4*5/24 = 20/24 (more than 2/3)

So answer must be 3 pairs or 6 total chefs.

Answer (D)
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 05 Aug 2016, 02:36
rate of experienced chef=1/8 per hour
rate of novice=1/12 per hour
combined rate=5/ 24 per hour

total time they will take together= 24/5 hours = 24*60/5 =288 min.

we need the work to be finished in 1hr 36 min ie 96 min.

2 chefs -----> 288 min
x chefs------> 96 min

i.e. 2*288 = x*96 (time and no of workers inversely proportional)
So, x = 2 * 288/96
So, x= 2 * 3 = 6
>>>>My answer D) 6 chefs
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 05 Aug 2016, 23:09
aimtoteach wrote:
On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.

If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 8


Combined rate for 1 experienced chef and 1 novice chef = 5/24

So, they do 5/24 of work in 1 hour
In 1 hour and 36 min or 1.6 hours they will do (5/24)*1.6 = 8/24 = 1/3
Therefore, for completing a job we will need 3 pairs ((1/3)*3) i.e. 6 chefs

Answer - D
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 09 Nov 2018, 05:42
aimtoteach wrote:
On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.

If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 8

Excellent opportunity for UNITS CONTROL, one of the most powerful tools of our method!

\(\left. \begin{gathered}
{\text{N}}\,\,{\text{pros}}:\,\,\frac{{\,1 \cdot N\,\,{\text{services}}\,}}{{8\,\,{\text{hours}}}} = \frac{{\,\frac{N}{2}\,\,{\text{services}}\,}}{{4\,\,{\text{hours}}}}\,\,\,\,\,\, \hfill \\
{\text{N}}\,\,{\text{novs}}:\,\,\frac{{\,1 \cdot N\,\,{\text{services}}\,}}{{12\,\,{\text{hours}}}} = \frac{{\,\frac{N}{3}\,\,{\text{services}}\,}}{{4\,\,{\text{hours}}}} \hfill \\
\end{gathered} \right\}\,\,\,1\,\,{\text{service}}\,\,{\text{together}}\,\,{\text{in}}\,\,\,1{\text{h}}36\min \,\,\,\,;\,\,\,\,\,? = 2N\)

\(\left( {1 + \frac{{36}}{{60}}} \right)\,\,{\text{hours}}\,\,\,\left[ {\,\frac{{\,\left( {\frac{N}{2} + \frac{N}{3}} \right)\,\,{\text{services}}\,}}{{4\,\,{\text{hours}}}}\,} \right]\,\,\,\,\,\, = \,\,\,1\,\,\,{\text{service}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{{96}}{{60 \cdot 4}}\,\,\left( {\frac{{N \cdot \boxed3}}{{2 \cdot \boxed3}} + \frac{{N \cdot \boxed2}}{{3 \cdot \boxed2}}} \right)\,\,\, = \,\,\,1\,\)

\(\Rightarrow \,\,\,\,\,\,\frac{{24}}{{\,60\,}}\,\,\left( {\frac{{N \cdot \boxed3}}{{2 \cdot \boxed3}} + \frac{{N \cdot \boxed2}}{{3 \cdot \boxed2}}} \right)\,\,\, = \,\,\,1\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\frac{{5N}}{6} = \frac{{60}}{{24}}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,N = \frac{6}{5}\left( {\frac{{60}}{{24}}} \right) = 3\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,? = 2N = 6\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: On a wedding catering service, An experienced chef can prepare a servi  [#permalink]

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New post 13 Nov 2018, 11:19
Hi All,

We're told that on a wedding catering service, an experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours. If the catering service employs the SAME number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes. This is an example of a Work Formula question and it can be solved in a couple of different ways. We can do a little math and take advantage of a 'rate shortcut' to save some calculation time.

Work = (A)(B)/(A+B) where A and B are the individual times it takes two entities to complete a task

IF.... we had just 1 experienced chef and just 1 novice chef, then the total time needed to prepare a service would be...
(8)(12)/(8+12) = 96/20 = 4 4/5 hours = 4 hours 48 minutes

IF... we DOUBLED the number of chefs, then the total time needed would be HALVED....
meaning that 2 experienced chefs and 2 novice chefs would need 2 hours 24 minutes. That's TOO SLOW though, so we need MORE chefs....

IF... we DOUBLED the number of chefs again, then the total time needed would be HALVED again....
meaning that 4 experienced chefs and 4 novice chefs would need 1 hour 12 minutes. That's TOO fast though, so we need LESS chefs...

There's only one answer between 4 chefs and 8 chefs....

Final Answer:

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Re: On a wedding catering service, An experienced chef can prepare a servi &nbs [#permalink] 13 Nov 2018, 11:19
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