Rate (m09q05)

Oldest

Best Reply

Author

Message

Manager

Status: Preparing myself to break the sound( 700 )-barrier!

Affiliations: IFC - Business Edge, Bangladesh Enterprise Institute

Joined: 15 Feb 2011

Posts: 211

Location: Dhaka, Bangladesh

Schools: Texas A&M - Mays; PennState - Smeal; Purdue - Krannert; JohnsHopkins - Carey; Vanderbilt - Owen; WakeForest - Babcock; UBC - Sauder

WE 1: Financial Analyst/Financial Management Trainer - BRAC Afghanistan - 13 months

WE 2: Business Proposal Coordinator - MiDS, Inc. (in Kabul, Afghanistan) - 4 Months (did quit the job bcoz of security concerns)

WE 3: Readers For Readers (A Social Impact Generating Organization) - Co-Founder

Followers: 5

Kudos [?]: 16 [0], given: 136

Re: Rate (m09q05) [#permalink]

27 Jan 2012, 00:06

IMO, plugging in the answer options is the best way to solve this problem. Seriously! :-)

Intern

Joined: 14 Sep 2010

Posts: 24

Followers: 0

Kudos [?]: 4 [0], given: 3

Re: Rate (m09q05) [#permalink]

28 Jan 2012, 19:13

It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type
25 pages in 3 hours.

1. Let t be Jack's time in hours for job (20pgs), write rate eq.

r1 + r2 = R

20/t + 20/(t - 2) = [5/4(20)]/3

1a. Factor out 20, and solve quadratic for t > 2.

1/x + 1/(x - 2) = 5/12

t = 6
t - 2 = 4

2. Plug in times for job in eq.1 to determine Jack's rate and Tom rate.

20pgs/6hrs = 3.333
20pgs/4hrs = 5

r1 + r2 = R = 8.333

3. Verify rate together, R, against given information "Jack and Tom can type 25 pages in 3 hours".

If R = 8.333, 25/R should equal 3.

25/8.333 = 3 hours

4. Use Jack's rate to determine how long it will take Jack to type 40 pages

40pages/3.333 = 12 hours

Intern

Joined: 27 Dec 2011

Posts: 7

Followers: 0

Kudos [?]: 0 [0], given: 4

Re: Rate (m09q05) [#permalink]

06 Sep 2012, 23:02

Jack does 1 page in : t+ 2 / 20
T does 1 page in : t / 20
together they do 25 pages in 3 hrs
there fore, 1 page in 3 /25

( t+2 / 20 ) + ( t/20 ) = 3 /25 -- > 1 page

solving t = 1/5 , 20 pages : 4 hr for T and 6 hrs for Jack.

for 40 pages : 8 hrs for T and 12 hrs for Jack..

Please let me know if this is the correct approach...

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11565

Followers: 1796

Kudos [?]: 9571 [0], given: 826

Re: Rate (m09q05) [#permalink]

07 Sep 2012, 02:16

sapna44 wrote:

Check this post for correct solutions: rate-m09q05-73633.html#p856920

Hope it helps.
_________________

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

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. NEW!!!

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. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Intern

Joined: 30 Aug 2012

Posts: 9

Concentration: General Management, Finance

Followers: 0

Kudos [?]: 7 [0], given: 3

Re: Rate (m09q05) [#permalink]

08 Sep 2012, 05:55

mandb wrote:

Is there an easier way to get the answer?
I can get the formula. But when I find the root it really takes too much time. How do i solve this in 2 min?
Should I back solve by dividing all the answers by 2?

Answer Choice is 12.

For Time and Work problems, If A takes x hrs to do a work and B takes y hours to do a work they combindly do the work in n hrs

Formula is => 1/x+1/y = 1/n

Here Tom takes x hrs to type 20 pages
So Jack takes (x+2) hrs to type 20 pages

So Tom takes 5x/4 to type 25 Pages => Jack takes 5(x+2)/4 hrs to type 25 pags

They both completed typing in 3 hrs, accoring to above formula (1/(5x/4)) +(1/(5(x+2)/4)) = 1/3

This leads to an equation 5x^2-14x-24 = 0 Since x cannot be less than zero x =4
x = Time taken by Tom to type 20 pages. So Jack takes 6 hrs to type 20 pages => Jack takes 12 hrs to type 40 pages.

Intern

Joined: 28 Jan 2011

Posts: 6

Followers: 0

Kudos [?]: 2 [0], given: 0

Re: Rate (m09q05) [#permalink]

15 Sep 2012, 03:26

If anybody wants it, here's a pure algebra solution (didn't take very long):

J can do 20 pages in J hours; let's call 20 pages "1 job". So J can do 1/j part of job in 1 hour.
T can do 20 pages in T+2 hours; T can do 1/(j - 2) part of job in 1 hour.

Together they can do 1/j + 1/(j - 2) = (2j - 2) / (j^2 - 2j) {common denominator} in 1 hour, so reciprocal:
it takes (j^2 - 2j) / (2j - 2) hours to do 1 job or 20 pages.

It must take 5/4 of this to do 25 pages, which is also stated to be 3 hours. So

5*(j^2 - 2j) / 4*(2j - 2) = 3

which means 5j^2 - 10j = 24j - 24, or 5j^2 - 34j + 24 = 0, or (5j - 4)(j - 6) = 0, {no need for quadratic formula}
so j must be 6 (can't be 5/4 because then no way to subtract 2 hours for Tom).

If j does 20 pages in 6 hours, must do 40 pages in 12 hours.

Senior Manager

Joined: 22 Nov 2010

Posts: 260

Location: India

Schools: LBS '14 (S), INSEAD Jan '14, Said (I), Judge (S)

GMAT 1: 670 Q49 V33

WE: Consulting (Telecommunications)

Followers: 5

Kudos [?]: 20 [0], given: 68

Re: Rate (m09q05) [#permalink]

24 Dec 2012, 02:10

Bunuel wrote:

This problem was also posted in PS subforum. Below is my solution from there.

It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5
B. 6
C. 8
D. 10
E. 12

Let the time needed for Jack to type 20 pages by j hours, then for Tom it would be j-2 hours. So the rate of Jack is rate=\frac{job}{time}=\frac{20}{j} pages per hour and the rate of Tom rate=\frac{job}{time}=\frac{20}{j-2} pages per hour.

Their combined rate would be \frac{20}{j}+\frac{20}{j-2} pages per hour and this equal to \frac{25}{3} pages per hour --> \frac{20}{j}+\frac{20}{j-2}=\frac{25}{3} --> \frac{60}{j}+\frac{60}{j-2}=25. At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type 40 pages, then the answer would be 2j (as j is the time needed to type 20 pages). Answer E works: 2j=12 --> j=6 --> \frac{60}{6}+\frac{60}{6-2}=10+15=25.

Answer: E.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
questions-from-gmat-prep-practice-exam-please-help-93632.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate
solution-required-100221.html?hilit=work%20rate%20done
work-problem-98599.html?hilit=work%20rate%20done

Hope it helps.

Hi

Can we solve this question logically, without making equations as mentioned in http://www.veritasprep.com/blog/2011/03 ... -problems/
_________________

YOU CAN, IF YOU THINK YOU CAN

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11565

Followers: 1796

Kudos [?]: 9571 [1] , given: 826

Re: Rate (m09q05) [#permalink]

24 Dec 2012, 02:13

This post received
KUDOS

greatps24 wrote:

Bunuel wrote:

Hi

Can we solve this question logically, without making equations as mentioned in http://www.veritasprep.com/blog/2011/03 ... -problems/

Check here: it-takes-jack-2-more-hours-than-tom-to-type-20-pages-if-102407.html#p1024552

Hope it helps.
_________________

Re: Rate (m09q05) [#permalink] 24 Dec 2012, 02:13

		Similar topics	Author	Replies	Last post
Similar Topics:	13	Rate (m09q05)	jackychamp	27	04 Dec 2008, 20:49
		M09 Q05	run4run	1	31 Mar 2010, 13:04
		Rates	naveenhv	5	06 May 2011, 10:11
		rate	siddhans	3	29 Sep 2011, 01:20
		Rate	BDSunDevil	1	15 Oct 2011, 12:47

Rate (m09q05)

Moderator: Bunuel

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

Rate (m09q05)

Rate (m09q05)

Main navigation

GMAT Resources

Partners

MBA Resources