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Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry

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Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 01 Apr 2012, 22:06
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Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.

A. \(20xz-\frac{y}{(x+y)}\)

B. \(y+\frac{z}{(20xz)}\)

C. \(\frac{20x(y-z)}{(x+y)}\)

D. \(20xy-\frac{z}{(x+y)}\)

E. \(\frac{y(20x-z)}{(x+y)}\)


Hi Bunuel,
Request you to provide me your approach. I couldn't solve it.

I usually solve such questions by using below approach-
(Workdone by entity A)/(Time taken by entity a) + (Workdone by entity b)/(time taken by entity b) = (Work done together)/(Time taken together)

However, I was unable to apply the above framework on this question. Please help me out.
Thanks
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Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 02 Apr 2012, 00:15
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imhimanshu wrote:
Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.

A. \(20xz-\frac{y}{(x+y)}\)

B. \(y+\frac{z}{(20xz)}\)

C. \(\frac{20x(y-z)}{(x+y)}\)

D. \(20xy-\frac{z}{(x+y)}\)

E. \(\frac{y(20x-z)}{(x+y)}\)


Pierre takes x hours to decorate a cake --> the rate of Pierre is \(\frac{1}{x}\) cake/hour, hence in \(z\) hours, that he worked alone, he decorated \(\frac{z}{x}\) cakes;

Franco takes y hours to decorate a cake --> the rate of Franco is \(\frac{1}{y}\) cake/hour;

Their combined rate is \(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\) cake/hour and if they worked for \(t\) hours together then they decorated \(t*\frac{x+y}{xy}\) cakes in that time;

Since total of 20 cakes were decorated then: \(\frac{z}{x}+t*\frac{x+y}{xy}=20\) --> \(t*\frac{x+y}{xy}=\frac{20x-z}{x}\) --> \(t=\frac{y(20x-z)}{x+y}\).

Answer: E.

Hope it's clear.
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 01 Apr 2012, 23:40
7
1
imhimanshu wrote:
Hi Bunuel,
Request you to provide me your approach. I couldn't solve it.

Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.
1- 20xz-y/(x+y)
2- y+z/(20xz)
3- 20x(y-z)/(x+y)
4- 20xy-z/(x+y)
5- y(20x-z)/(x+y)

I usually solve such questions by using below approach-
(Workdone by entity A)/(Time taken by entity a) + (Workdone by entity b)/(time taken by entity b) = (Work done together)/(Time taken together)

However, I was unable to apply the above framework on this question. Please help me out.
Thanks


time by pierre to complete 1 cake=x
time by franco to complete 1 cake=y

in z hours pierre completes= z/x work

then the both chef guy works together; let the time taken together be t

then we have
(work done by Pierre guy in z hours)+(work done by both guy in t hours)=20

=> (z/x)+(1/x+1/y)*t=20

=> t= (20-(z/x))/(1/x+1/y)=(20x-z)*y/(x+y)

hence Option 5 is correct.

Hope this helps..!!!
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 01 Apr 2012, 23:42
7
3
imhimanshu wrote:
Hi Bunuel,
Request you to provide me your approach. I couldn't solve it.

Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.
1- 20xz-y/(x+y)
2- y+z/(20xz)
3- 20x(y-z)/(x+y)
4- 20xy-z/(x+y)
5- y(20x-z)/(x+y)

I usually solve such questions by using below approach-
(Workdone by entity A)/(Time taken by entity a) + (Workdone by entity b)/(time taken by entity b) = (Work done together)/(Time taken together)

However, I was unable to apply the above framework on this question. Please help me out.
Thanks


Let me give you my approach to these problems (I am sure Bunuel will give his solution too so you needn't be disappointed :))

I like to solve questions with variables by plugging in values:
Say x = 1 (Pierre decorates 1 cake in 1 hr), y = 2 (Franco decorates 1 cake in 2 hrs)
Together, they decorate 1 cake in 1/(1+1/2) = 2/3 hrs
Say Pierre decorates 17 cakes in 17 hrs and then Franco joins in and they decorate the remaining 3 cakes in 2 hrs (For 1 cake, they take 2/3 hrs so for 3 cakes, they will take 3*(2/3) = 2 hrs)
Now just plug these values x = 1, y = 2 and z = 17 in the options and whichever option gives you 2, that should be the answer.

Only option (E) gives you 2 so it should be your answer.

Note: While you are trying the options, you can quickly see that numerator will not be divisible by denominator or one of them is way too big so you don't have to perform the complete calculation since you are looking for 2 as your answer. e.g.
you try option (A) 20xz-y/(x+y) = [20*1*17 - 2]/3 (numerator is way too big so not possible)
Option (B) y+z/(20xz) = (2+17)/20*1*17 (denominator is way too big)

You can also use algebra:

Remember two things:
1. Work = Rate*Time
2. We add rates.

Their combined rate of work = 1/x + 1/y
Pierre does some work on his own. Work done by Pierre alone = Pierre's rate * Time = (1/x)*z

Leftover work = 20 - z/x

Time taken to complete leftover work together = Work/Rate = (20 - z/x)/(1/x + 1/y) = y(20x - z)/(x+y)
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 02 Apr 2012, 00:30
nice solutions, thanks Bunuel you are awesome.

I am new to gmatclub and i feel i got late coming here; it so much here to learn.

thanx guys you all rock..!!
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 02 Apr 2012, 03:11
Thanks every one for your responses.
@Karishma - I always enjoy reading your posts and I have learnt a lot from them. I have been a regular visitor of your blog as well. :-D
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 02 Apr 2012, 03:27
Below colored part is what I was missing.
I thought the statement saying - Franco and Pierre working together decorated 20 cakes rather than the complete job is to decorate 20 cakes.
so as per my equation - Leftover work = 1-z/x which was making no sense.

Thanks again. Appreciate your efforts :)

VeritasPrepKarishma wrote:
imhimanshu wrote:
Hi Bunuel,
Request you to provide me your approach. I couldn't solve it.

Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.
1- 20xz-y/(x+y)
2- y+z/(20xz)
3- 20x(y-z)/(x+y)
4- 20xy-z/(x+y)
5- y(20x-z)/(x+y)

I usually solve such questions by using below approach-
(Workdone by entity A)/(Time taken by entity a) + (Workdone by entity b)/(time taken by entity b) = (Work done together)/(Time taken together)

However, I was unable to apply the above framework on this question. Please help me out.
Thanks


Let me give you my approach to these problems (I am sure Bunuel will give his solution too so you needn't be disappointed :))

I like to solve questions with variables by plugging in values:
Say x = 1 (Pierre decorates 1 cake in 1 hr), y = 2 (Franco decorates 1 cake in 2 hrs)
Together, they decorate 1 cake in 1/(1+1/2) = 2/3 hrs
Say Pierre decorates 17 cakes in 17 hrs and then Franco joins in and they decorate the remaining 3 cakes in 2 hrs (For 1 cake, they take 2/3 hrs so for 3 cakes, they will take 3*(2/3) = 2 hrs)
Now just plug these values x = 1, y = 2 and z = 17 in the options and whichever option gives you 2, that should be the answer.

Only option (E) gives you 2 so it should be your answer.

Note: While you are trying the options, you can quickly see that numerator will not be divisible by denominator or one of them is way too big so you don't have to perform the complete calculation since you are looking for 2 as your answer. e.g.
you try option (A) 20xz-y/(x+y) = [20*1*17 - 2]/3 (numerator is way too big so not possible)
Option (B) y+z/(20xz) = (2+17)/20*1*17 (denominator is way too big)

You can also use algebra:

Remember two things:
1. Work = Rate*Time
2. We add rates.

Their combined rate of work = 1/x + 1/y
Pierre does some work on his own. Work done by Pierre alone = Pierre's rate * Time = (1/x)*z

Leftover work = 20 - z/x

Time taken to complete leftover work together = Work/Rate = (20 - z/x)/(1/x + 1/y) = y(20x - z)/(x+y)
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 03 Apr 2012, 07:14
kraizada84 wrote:
imhimanshu wrote:
Hi Bunuel,
Request you to provide me your approach. I couldn't solve it.

Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.
1- 20xz-y/(x+y)
2- y+z/(20xz)
3- 20x(y-z)/(x+y)
4- 20xy-z/(x+y)
5- y(20x-z)/(x+y)

I usually solve such questions by using below approach-
(Workdone by entity A)/(Time taken by entity a) + (Workdone by entity b)/(time taken by entity b) = (Work done together)/(Time taken together)

However, I was unable to apply the above framework on this question. Please help me out.
Thanks


time by pierre to complete 1 cake=x
time by franco to complete 1 cake=y

in z hours pierre completes= z/x work

then the both chef guy works together; let the time taken together be t

then we have
(work done by Pierre guy in z hours)+(work done by both guy in t hours)=20

=> (z/x)+(1/x+1/y)*t=20

=> t= (20-(z/x))/(1/x+1/y)=(20x-z)*y/(x+y)

hence Option 5 is correct.

Hope this helps..!!!


Dude...ur explanation is superb...thanks for making it so simple....
dude
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 13 Apr 2012, 04:49
1
1/x - Pierre's rate
1/y - Franco's rate

RT=W
after z hours Pierre alone has decorated z/x cakes

then Franco appeared with his rate 1/y and together the cooks were working t hours

1/x*(z+t)+1/y*t=20 -->t=y(20x-z)/(y+x)
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 27 May 2012, 04:17
great explanation guys! cleared a few cobwebs in my head.
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 13 Jul 2016, 03:49
imhimanshu wrote:
Hi Bunuel,
Request you to provide me your approach. I couldn't solve it.

Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.

A. 20xz-y/(x+y)
B. y+z/(20xz)
C. 20x(y-z)/(x+y)
D. 20xy-z/(x+y)
E. y(20x-z)/(x+y)

I usually solve such questions by using below approach-
(Workdone by entity A)/(Time taken by entity a) + (Workdone by entity b)/(time taken by entity b) = (Work done together)/(Time taken together)

However, I was unable to apply the above framework on this question. Please help me out.
Thanks


Solution to the above problem is as followed:

z/x +t [ (x+y)/xy] = 20
t= (20x - z)y/ (x+y) (ans)
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 14 Jan 2017, 11:03
I can't believe that Kaplan seriously suggests to handle "this tough problem is perfect for Picking Numbers". It is easy to pick numbers like x = 2, y = 2, and z = 10 and find out that the two chefs would need to work together for 15 hours, however, after that you need to substitute x, y and x into five (five, Karl!) answer choice to check which one yields 15! How much time would it take? Solving by equation as indicated above seems to be so much easier!
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 06 Apr 2018, 12:17
Bunuel wrote:
imhimanshu wrote:
Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.

A. \(20xz-\frac{y}{(x+y)}\)

B. \(y+\frac{z}{(20xz)}\)

C. \(\frac{20x(y-z)}{(x+y)}\)

D. \(20xy-\frac{z}{(x+y)}\)

E. \(\frac{y(20x-z)}{(x+y)}\)


Pierre takes x hours to decorate a cake --> the rate of Pierre is \(\frac{1}{x}\) cake/hour, hence in \(z\) hours, that he worked alone, he decorated \(\frac{z}{x}\) cakes;

Franco takes y hours to decorate a cake --> the rate of Franco is \(\frac{1}{y}\) cake/hour;

Their combined rate is \(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\) cake/hourand if they worked for \(t\) hours together then they decorated \(t*\frac{x+y}{xy}\) cakes in that time;

Since total of 20 cakes were decorated then: \(\frac{z}{x}+t*\frac{x+y}{xy}=20\) --> \(t*\frac{x+y}{xy}=\frac{20x-z}{x}\) --> \(t=\frac{y(20x-z)}{x+y}\).

Answer: E.

Hope it's clear.


Can someone explain how to get the highlighted line? I am able to get 1 over x + 1 over Y, but no further
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 06 Apr 2018, 12:38
lostnumber wrote:
Bunuel wrote:
imhimanshu wrote:
Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.

A. \(20xz-\frac{y}{(x+y)}\)

B. \(y+\frac{z}{(20xz)}\)

C. \(\frac{20x(y-z)}{(x+y)}\)

D. \(20xy-\frac{z}{(x+y)}\)

E. \(\frac{y(20x-z)}{(x+y)}\)


Pierre takes x hours to decorate a cake --> the rate of Pierre is \(\frac{1}{x}\) cake/hour, hence in \(z\) hours, that he worked alone, he decorated \(\frac{z}{x}\) cakes;

Franco takes y hours to decorate a cake --> the rate of Franco is \(\frac{1}{y}\) cake/hour;

Their combined rate is \(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\) cake/hourand if they worked for \(t\) hours together then they decorated \(t*\frac{x+y}{xy}\) cakes in that time;

Since total of 20 cakes were decorated then: \(\frac{z}{x}+t*\frac{x+y}{xy}=20\) --> \(t*\frac{x+y}{xy}=\frac{20x-z}{x}\) --> \(t=\frac{y(20x-z)}{x+y}\).

Answer: E.

Hope it's clear.


Can someone explain how to get the highlighted line? I am able to get 1 over x + 1 over Y, but no further


\(\frac{1}{x}+\frac{1}{y}=\frac{y}{xy}+\frac{x}{xy}=\frac{y+x}{xy}\)

How do we add or subtract fractions?
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

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New post 06 Apr 2018, 13:06
It seems so obvious now. Doh! I have not touched a math problem in 10 years or so, so I am very rusty. Thank you for having patience with my silly questions
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Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry &nbs [#permalink] 06 Apr 2018, 13:06
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