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Working alone, Printers X, Y, and Z can do a certain printin

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Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post 05 Mar 2014, 01:16
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11
(B) 1/2
(C) 15/22
(D) 22/15
(E) 11/4

Problem Solving
Question: 130
Category: Arithmetic Operations on rational numbers
Page: 78
Difficulty: 600


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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post 05 Mar 2014, 01:17
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SOLUTION

Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11
(B) 1/2
(C) 15/22
(D) 22/15
(E) 11/4

The rate of Y and Z are 1/15 and 1/18 job/hour, respectively.

Their combined rate is 1/15 + 1/18 = 1/t. Thus the time it takes Printers Y and Z to do the job is t = 90/11.

Thus required ratio is 12/(90/11) = 22/15.

Answer: D.
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post 05 Mar 2014, 19:39
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Job rate of Printer Y = \frac{1}{15}

Job rate of Printer Z = \frac{1}{18}

Job rate for Y & Z = \frac{1}{15} + \frac{1}{18} = \frac{11}{90}

Time taken by Y & Z = \frac{90}{11}

Ratio of (Time taken by Printer X) to (Combined time taken by Y & Z)

= 12 * \frac{11}{90} = \frac{22}{15}

Answer = D
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Last edited by PareshGmat on 05 Mar 2014, 23:57, edited 3 times in total.
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post 05 Mar 2014, 22:35
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Y and Z can do the job in (15*18)/15+18 hours, that is (15*18)/33 hours.

X can do the job in 12 hours.

Ratio = 12/(15*18)/33 = 22/15

Answer (D).
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post 08 Mar 2014, 11:38
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SOLUTION

Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11
(B) 1/2
(C) 15/22
(D) 22/15
(E) 11/4

The rate of Y and Z are 1/15 and 1/18 job/hour, respectively.

Their combined rate is 1/15 + 1/18 = 1/t. Thus the time it takes Printers Y and Z to do the job is t = 90/11.

Thus required ratio is 12/(90/11) = 22/15.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post 18 Mar 2014, 03:14
Rate(X)=1/12
Rate(Y)=1/15
Rate(Z)=1/18

Time for X=12

Combined Rate of Y and Z= 1/15 + 1/18 = 33/(18*15)

Since Rate * Time = work

And work =1 then Time for combined Y and Z = (18*15)/33

Ratio of Time for X/Time for combined Y and Z

(12*33)/(18*15)=22/15
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post 15 Apr 2014, 20:10
Printer X can do Printing Job in 12 hrs.
So Printer X completes (1/12)th of the work in 1hr.

Printer Y can do Printing Job in 15 hrs.
So Printer Y completes (1/15)th of the work in 1hr.

Printer Z can do Printing Job in 18 hrs.
So Printer Z completes (1/18)th of the work in 1hr.

Printer's Y and Z combined rate(working for 1 hr) is 1/15+1/18 = 11/90;

ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates is (1/12)/(11/90) = 15/22;

so rate is 15/22; rate is inversly proportional to time.
Time is 22/15; Hence D
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post 28 Apr 2014, 01:34
Rate X: 1/12
Rate Y: 1/15
Rate Z: 1/18

Combined rate Y and Z ( let's call this ''c''): (1/15)+(1/18)=(6/90)+(5/90)=(11/90)

Rate x / Rate c = (1/12)/(11/90) = (1/12)*(90/11) = (90/132) = (15/22)

Answer D.
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Re: Working alone, Printers X, Y, and Z can do a certain printin   [#permalink] 28 Apr 2014, 01:34
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