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twice as many omelettes

by sanju09 » Thu Feb 19, 2015 4:04 am
Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo could prepare in 30 minutes. If both chefs working together for 10 minutes could prepare 11 omelettes, how many omelettes could Chef Karin prepare working alone for 25 minutes?
A. 12
B. 15
C. 18
D. 22
E. 25

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by regor60 » Thu Feb 19, 2015 10:20 am
sanju09 wrote:Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo could prepare in 30 minutes. If both chefs working together for 10 minutes could prepare 11 omelettes, how many omelettes could Chef Karin prepare working alone for 25 minutes?
A. 12
B. 15
C. 18
D. 22
E. 25

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by Brent@GMATPrepNow » Thu Feb 19, 2015 10:43 am
sanju09 wrote:Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo could prepare in 30 minutes. If both chefs working together for 10 minutes could prepare 11 omelettes, how many omelettes could Chef Karin prepare working alone for 25 minutes?

A. 12
B. 15
C. 18
D. 22
E. 25
Nice question, Sanju!

One approach is to determine the RELATIVE RATES of Karin and Zibo.

Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo could prepare in 30 minutes.
Let's arbitrarily say that Chef Zibo can prepare 1 omelette in 30 minutes
This means that Chef Karin can prepare 2 omelettes in 50 minutes
NOTE: Since we have different times (30 min and 50 min), it's hard to compare rates. So, let's find a NICE timeframe where we can compare both chefs.

The LEAST COMMON MULTIPLE of 30 and 50 is 150, so let's see how many omelettes each chef can make in 150 minutes
- If Chef Zibo can prepare 1 omelette in 30 minutes, then he/she can prepare 5 omelettes in 150 minutes
- If Chef Karin can prepare 2 omelette in 50 minutes, then he/she can prepare 6 omelettes in 150 minutes

So, within the same 150-minute timeframe, Chef Zibo can prepare 5 omelettes and Chef Karin can prepare 6 omelettes.
In other words, for EVERY 11 omelettes that get produced TOGETHER, Chef Zibo prepares 5 omelettes and Chef Karin prepares 6 omelettes.

...both chefs working together for 10 minutes could prepare 11 omelettes
PERFECT.
This means that, in 10 minutes, Chef Zibo prepares 5 omelettes and Chef Karin prepares 6 omelettes.
If Chef Karin can produce 6 omelettes in 10 minutes, he/she can produce 12 omelettes in 20 minutes, and 15 omelettes in 25 minutes.

Answer: B

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Fri Feb 20, 2015 6:53 am, edited 1 time in total.
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by sandipgumtya » Fri Feb 20, 2015 6:05 am
Brent,
I think it should be 15.Opt-B.
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by GMATGuruNY » Fri Feb 20, 2015 6:31 am
sanju09 wrote:Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo could prepare in 30 minutes. If both chefs working together for 10 minutes could prepare 11 omelettes, how many omelettes could Chef Karin prepare working alone for 25 minutes?
A. 12
B. 15
C. 18
D. 22
E. 25
Let K = Chef Karin and Z = Chef Zibo.

Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo could prepare in 30 minutes.
Let's say Z produces 1 omelet in 30 minutes, implying that K produces 2 omelets in 50 minutes.
At a rate of 1 omelet per 30 minutes, the number of omelets produced by Z in 150 minutes = 5.
At a rate of 2 omelets per 50 minutes, the number of omelets produced by K in 150 minutes = 6.
Thus, if Z and K work together for 150 minutes, the total number of omelets produced = 5+6 = 11.
Of these 11 omelets, K produces 6.
Implication:
When Z and K work together, K produces 6/11 of the work.

Both chefs working together for 10 minutes could prepare 11 omelettes.
Thus, the combined rate for Z and K working together = w/t = 11/10 omelets per minute.
Since K produces 6/11 of the work, K's rate alone - (6/11)(11/10) = 3/5 omelet per minute.

Result:
At a rate of 3/5 omelet per minute, the number of omelets produced by K in 25 minutes = r*t = (3/5)(25) = 15 omelets.

The correct answer is B.
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by Brent@GMATPrepNow » Fri Feb 20, 2015 6:54 am
sandipgumtya wrote:Brent,
I think it should be 15.Opt-B.
Good catch!
I edited my answer - thanks.

Cheers,
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by prachi18oct » Fri Feb 20, 2015 10:08 am
I did it in the below manner:-

Rate * time = work done

Z = Zibo's rate
K = karin's rate
x = omelettes by z

For Z=> Z * 30/60 = x => Z = 2x (1)
For K => K * 50/60 = 2x => K = 12/5x (2)

Now combine: (Z+K)*10/60 = 11 => Z+K = 66 (3)

Solve for x => x = 15

For K 's rate , put value of x in (2) => K = 36
Now K*25/60 =?
36*25/60 = 15 omelettes by K alone in 25 mins.
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by GMATGuruNY » Fri Feb 20, 2015 10:33 am
sanju09 wrote:Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo could prepare in 30 minutes. If both chefs working together for 10 minutes could prepare 11 omelettes, how many omelettes could Chef Karin prepare working alone for 25 minutes?
A. 12
B. 15
C. 18
D. 22
E. 25
An alternate approach is to apply the following formula:
(rate)(time)/work = (rate)(time)/work.

Let K = Chef Karin's rate and Z = Chef Zibo's rate.

Since K produces twice as many omelets in 50 minutes as Z produces in 30 minutes, we get:
(K)(50)/2w = (Z)(30)/w
25K = 30Z
Z = (25/30)K
Z = (5/6)K.

Thus, when K and Z work together, their combined rate = K + Z = K + (5/6)K = (11/6)K.
Since this combined rate takes 10 minutes to produce 11 omelets, we get:
(11/6)K * 10 = 11
K = 6/10
K = 3/5.

At a rate of 3/5 omelet per minute, the number of omelets produced by K in 25 minutes = rt = (3/5)(25) = 15.

The correct answer is B.
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by sanju09 » Mon Feb 23, 2015 11:16 pm
Great replies! Thanks Brent for the back-up.

Rates can best be compared if we set the work equal. In that case, ratio in individual rates is equal to the reciprocal of ratio in individual times taken.

To compare, we can say that if K prepares 2 omelettes in 50 minutes, then Z would prepare i omelette in 30 minutes; or if K prepares 1 omelette in 25 minutes, then Z would prepare i omelette in 30 minutes.

Hence, the ratio in their rates is, i.e. K to J is 30:25 or 6:5.

It means that in a given time, if K prepares 6, then Z prepares 5, together they could prepare 6 + 5 = 11 in the given time, which is given to be 10 minutes in the question. Using this we can say that K alone can prepare

6 omelettes in 10 minutes

6/10 omelettes in 1 minute

(6/10) × 25 = [spoiler]15 omelettes in 25 minutes.

It's (B) really. [/spoiler]
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by wings.ap » Fri Nov 13, 2015 10:58 pm
I did the question in the below method.

K makes 2x omelette in 50 mins then in 1 min = 2x/50
Z makes x omelette in 30 mins then in 1 min = x/30
combined they make 11 omelette in 10 mins so in 1 min = 1.1

We know 1.1 = 2x/50+x/30 = 110x/1500.

Cancelling out the constants gives us x = 15.

so 2x = 30 and 25mins is half of 50 mins so answers is 15 omelette in 25mins.
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by Zoser » Wed Feb 22, 2017 8:52 am
Brent!

Can you please explain why you took the individual rate of Karen of 6/150min and applied it to the combined rate to find Karin`s output in 25 min? Why you did not do the below

Karin prep 6 in 150
then she prep X in 25
150x=150
x=1

What did I do wrong here?
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by Brent@GMATPrepNow » Wed Feb 22, 2017 9:15 am
Zoser wrote:Brent!

Can you please explain why you took the individual rate of Karen of 6/150min and applied it to the combined rate to find Karin`s output in 25 min? Why you did not do the below

Karin prep 6 in 150
then she prep X in 25
150x=150
x=1

What did I do wrong here?
I think you may have misread the information that says "Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo"

I think you read it as "Chef Karin can prepare two omelettes in 50 minutes..."
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by [email protected] » Wed Feb 22, 2017 9:54 am
Hi All,

In these types of questions, it often helps to find a basis for comparison based on either "time" or "output." Here, we're given the output of each chef, but for different amounts of time. The LCM of 50 and 30 is 150, so let's see what happens when each chef works for 150 minutes...

Z = can prepare X omelets in 30 minutes
K = can prepare 2X omelets in 50 minutes

Z = can prepare 5X omelets in 150 minutes
K = can prepare 6X omelets in 150 minutes

So, in 150 minutes, the two chefs can prepare a TOTAL of 11X omelets. This is interesting since we're then told that the two chefs can create 11 omelets in 10 minutes (meaning that Z would prepare 5 of omelets while K would prepare 6 of the omelets)....

We're then asked how many omelets K could prepare in 25 minutes. Since K can prepare 6 omelets in 10 minutes, (s)he can prepare 6(2.5) = 15 omelets in 25 minutes.

Final Answer: B

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by Jeff@TargetTestPrep » Mon Feb 27, 2017 10:37 am
sanju09 wrote:Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo could prepare in 30 minutes. If both chefs working together for 10 minutes could prepare 11 omelettes, how many omelettes could Chef Karin prepare working alone for 25 minutes?
A. 12
B. 15
C. 18
D. 22
E. 25
We are given that Chef Karin can prepare twice as many omelettes in 50 minutes as Chef Zibo can prepare in 30 minutes. Thus, if we let the rate of Chef Karin = k and the rate of Chef Zibo = z, we can create the following equation:

50k = 2(30z)

50k = 60z

5k = 6z

5k/6 = z

We are also given that both chefs working together for 10 minutes could prepare 11 omelettes. Thus:

(k + z)10 = 11

Next we can substitute 5k/6 for z in the equation (k + z)10 = 11 and we have:

(k + 5k/6)10 = 11

10k + 50k/6 = 11

Multiplying the entire equation by 6, we have:

60k + 50k = 66

110k = 66

k = 66/110 = 6/10 = 3/5

Thus, Chef Karin can prepare (3/5) x 25 = 15 omelets in 25 minutes.

Answer: B

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