GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 04:20 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 07 Sep 2010
Posts: 249
Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

8
18 00:00

Difficulty:   55% (hard)

Question Stats: 71% (03:00) correct 29% (03:13) wrong based on 277 sessions

HideShow timer Statistics

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
Math Expert V
Joined: 02 Sep 2009
Posts: 58327
Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

13
8
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: $$\frac{z}{x}+t*\frac{x+y}{xy}=20$$ --> $$t*\frac{x+y}{xy}=\frac{20x-z}{x}$$ --> $$t=\frac{y(20x-z)}{x+y}$$.

Hope it's clear.
_________________
Manager  B
Joined: 13 Mar 2012
Posts: 202
Concentration: Operations, Strategy
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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..!!!
_________________
Practice Practice and practice...!!

If there's a loophole in my analysis--> suggest measures to make it airtight.
General Discussion
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

8
4
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)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  Joined: 01 Apr 2012
Posts: 6
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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..!!
Manager  Joined: 07 Sep 2010
Posts: 249
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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. Manager  Joined: 07 Sep 2010
Posts: 249
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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)
Manager  Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 162
Schools: Johnson '15
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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
_________________
Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat Satyameva Jayate - Truth alone triumphs
Manager  B
Joined: 16 Jan 2011
Posts: 89
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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)
Senior Manager  Joined: 28 Dec 2010
Posts: 262
Location: India
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

great explanation guys! cleared a few cobwebs in my head.
Intern  Joined: 23 Dec 2015
Posts: 21
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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)
Manager  B
Joined: 12 Nov 2016
Posts: 130
Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39 GMAT 2: 650 Q47 V33 Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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!
Intern  B
Joined: 28 Mar 2018
Posts: 45
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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: $$\frac{z}{x}+t*\frac{x+y}{xy}=20$$ --> $$t*\frac{x+y}{xy}=\frac{20x-z}{x}$$ --> $$t=\frac{y(20x-z)}{x+y}$$.

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
Math Expert V
Joined: 02 Sep 2009
Posts: 58327
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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: $$\frac{z}{x}+t*\frac{x+y}{xy}=20$$ --> $$t*\frac{x+y}{xy}=\frac{20x-z}{x}$$ --> $$t=\frac{y(20x-z)}{x+y}$$.

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?
_________________
Intern  B
Joined: 28 Mar 2018
Posts: 45
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

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
Non-Human User Joined: 09 Sep 2013
Posts: 13154
Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry   [#permalink] 17 May 2019, 20:26
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  