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On a wedding catering service, An experienced chef can

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On a wedding catering service, An experienced chef can

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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

OA D

Source: Economist GMAT

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BTGmoderatorDC 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
Source: Economist GMAT
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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Lets say, preparing 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.

Regards!

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BTGmoderatorDC 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 combined rate of one experienced chef and one novice chef is 1/8 + 1/12 = 3/24 + 2/24 = 5/24.

Now let x = the number of chefs of each kind need to prepare the wedding service in 1 hour and 36 minutes or (60 + 36)/60 = 96/60 = 8/5 hours, we have:

x * 5/24 * 8/5 = 1

x * 1/3 = 1

x = 3

Since 3 experienced chefs and 3 novice chefs are needed, a total of 6 chefs are needed for the wedding service.

Answer: D

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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: D

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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BTGmoderatorDC 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
Let service = 24 units.
Rate for each experienced chef = w/t = 24/8 = 3 units per hour.
Rate for each novice chef = w/t = 24/12 = 2 units per hour.
Combined rate for 1 experienced chef and 1 novice chef working together = 3+2 = 5 units per hour.
To produce 24 units in 1.6 hours, rate = w/t = 24/1.6 = 15 units per hour.
Since each pair of chefs produces 5 units per hour, number of pairs needed = 15/5 = 3.
Total number of chefs in 3 pairs = 2*3 = 6.

The correct answer is D.

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