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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # A husband and wife can complete a certain task in 1 and 2 hours  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 13 Oct 2013 Posts: 133 Concentration: Strategy, Entrepreneurship A husband and wife can complete a certain task in 1 and 2 hours [#permalink] ### Show Tags 03 Jul 2015, 21:59 1 3 00:00 Difficulty: 5% (low) Question Stats: 91% (01:38) correct 9% (01:16) wrong based on 209 sessions ### HideShow timer Statistics A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task? a)15:46 b)3:10 c)12:23 d)5:18 e)10:3 _________________ --------------------------------------------------------------------------------------------- Kindly press +1 Kudos if my post helped you in any way Math Expert Joined: 02 Aug 2009 Posts: 7030 Re: A husband and wife can complete a certain task in 1 and 2 hours [#permalink] ### Show Tags 03 Jul 2015, 22:14 sunita123 wrote: A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task? 15:46 3:10 12:23 5:18 10:3 Hi.. couples one hour work=1/1+1/2=3/2 so total time=2/3.. now, kids one hour work=1/4+1/6=5/12 so total time=12/5.. ratio=2/3:12/5=5:18 ans D _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Manager Joined: 13 Oct 2013 Posts: 133 Concentration: Strategy, Entrepreneurship Re: A husband and wife can complete a certain task in 1 and 2 hours [#permalink] ### Show Tags 03 Jul 2015, 22:34 Thank you, may be my concept is wrong here. i did not understand this part couples one hour work=1/1+1/2=3/2 my understanding was , we take work always as 1. here 3/2 means more than one job i.e 1.5 jobs? chetan2u wrote: sunita123 wrote: A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task? 15:46 3:10 12:23 5:18 10:3 Hi.. couples one hour work=1/1+1/2=3/2 so total time=2/3.. now, kids one hour work=1/4+1/6=5/12 so total time=12/5.. ratio=2/3:12/5=5:18 ans D _________________ --------------------------------------------------------------------------------------------- Kindly press +1 Kudos if my post helped you in any way Math Expert Joined: 02 Aug 2009 Posts: 7030 Re: A husband and wife can complete a certain task in 1 and 2 hours [#permalink] ### Show Tags 03 Jul 2015, 22:50 sunita123 wrote: Thank you, may be my concept is wrong here. i did not understand this part couples one hour work=1/1+1/2=3/2 my understanding was , we take work always as 1. here 3/2 means more than one job i.e 1.5 jobs? hi sunita123, you are absolutely correct in that front.. i mean by couples one hour work=1/1+1/2=3/2 that the couple can finish 3/2 times of work in one hour .. so they can finish the work in 2/3 hrs _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Intern Joined: 04 Apr 2015 Posts: 16 Concentration: Human Resources, Healthcare GMAT Date: 08-06-2015 GPA: 3.83 WE: Editorial and Writing (Journalism and Publishing) Re: A husband and wife can complete a certain task in 1 and 2 hours [#permalink] ### Show Tags 03 Jul 2015, 23:34 sunita123 ---------------------------------------------------------------------------------------------------------------------------------------------- Here's how you can solve the doubt you've: Work-Rate problems are inverse proportion type situations ie More men - Less time required (Hence, inversely proportional) Man and Wife do work together - in 1 hour how much can both do? So in 1 hr man can finish the whole job and wife can finish half the job right? Look at this in terms of efficiency i.e. Man has 100% efficiency in 1 hour and wife has efficiency of 50% in 1 hour. -> Combined their efficieny becomes 150% More efficiency -> more work done -> less time taken Note: Relating efficiency to 1 unit of time and work: if a man takes 'n' hours or 'n' days to finish his task, then his efficiency must be measured in terms of each of the individual hours of 'n' hours or each of the days counted in 'n' days. For eg: woman takes 2 hours to complete task implies her efficiency in 1 hour is 50% giving efficiency in 2 hrs to be 100%; in mathematial form: W takes 2 hours > in 1 hour she does 1/2 of work > efficiency 1/2 X 100 = 50% > in two hours 2 X (1/2) X 100 > giving us 2 hrs (100% efficiency) > basically the inverse of 1/n (here 1/2) gives how much time she takes to do the full job > 2 hrs. So now going back to problem: M and W's total efficiency is 150% - 150/100 > inverse > 100/150 = 2/3 (why inverse? because they dont have to finish 1.5 amount of job. They've to finish 1W not 1.5W so unitary method approach applied here ) For kids > 1/4+1/6 = 5/12 > inverse = 12/5 Ratio > (2/3)/(12/5) = 5:18 Hope this helps CEO Joined: 20 Mar 2014 Posts: 2635 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) A husband and wife can complete a certain task in 1 and 2 hours [#permalink] ### Show Tags 04 Jul 2015, 03:35 sunita123 wrote: Thank you, may be my concept is wrong here. i did not understand this part couples one hour work=1/1+1/2=3/2 my understanding was , we take work always as 1. here 3/2 means more than one job i.e 1.5 jobs? chetan2u wrote: sunita123 wrote: A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task? 15:46 3:10 12:23 5:18 10:3 Hi.. couples one hour work=1/1+1/2=3/2 so total time=2/3.. now, kids one hour work=1/4+1/6=5/12 so total time=12/5.. ratio=2/3:12/5=5:18 ans D Work-rate problems can also be looked at in the same form as the Distance = Speed X time, where we replace Distance by Work and Speed by rate. For example, in this problem, Work = Rate X Time, where Work = 1 unit, Rate of Husband = $$R_H$$=1/1 (as Work is 1 unit and time husband takes = 1 hour). Similarly, Rates of Wife, Rae and Herman are : $$R_W$$=1/2, $$R_R$$=1/4 and $$R_{He}$$=1/6 Now, for combined rates, $$R_H$$+$$R_W$$=1+1/2 = 3/2 (we are adding the rates here as the more efficient or high the rates are the sooner will be work be finished. It is very similar to if the speed is higher, you will take less time to cover the same distance!) and $$R_R$$+$$R_He$$ = 1/4+1/6 = 10/24 Thus, time taken by Husband and Wife to do 1 unit of work, 1 = 3/2*$$t_1$$ >> $$t_1$$=2/3 hours Time taken by Rae and Herman to do 1 unit of work , 1 = 10/24*$$t_2$$ >> $$t_2$$= 24/10 hours Finally, $$\frac{t_1}{t_2}$$ = (2/3)/(24/10)= $$\frac{5}{18}$$ Manager Joined: 13 Oct 2013 Posts: 133 Concentration: Strategy, Entrepreneurship Re: A husband and wife can complete a certain task in 1 and 2 hours [#permalink] ### Show Tags 04 Jul 2015, 08:52 Thank you everyone for the explanation:). this certainly helps. _________________ --------------------------------------------------------------------------------------------- Kindly press +1 Kudos if my post helped you in any way EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12856 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A husband and wife can complete a certain task in 1 and 2 hours [#permalink] ### Show Tags 04 Jul 2015, 21:48 Hi All, This prompt can also be solved by using the Work Formula: Work = (A)(B)/(A+B) where A and B are the individual times that it takes to complete the 'job' We're told that a husband and wife can complete a task in 1 hour and 2 hours, respectively. Working together, it would take them... (1)(2)/(1+2) = 2/3 hours to complete the task Next, we're told that the two children can complete the task in 4 hours and 6 hours, respectively. Working together, it would take them... (4)(6)/(4+6) = 24/10 hours to complete the task We're asked for the RATIO of the couple's time to the children's time.... (2/3) / (24/10) = (2/3)(10/24) = 20/72 = 5/18 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: A husband and wife can complete a certain task in 1 and 2 hours  [#permalink]

### Show Tags

08 Jul 2017, 23:49
sunita123 wrote:
A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?

a)15:46

b)3:10

c)12:23

d)5:18

e)10:3

We know work done together:

$$\frac{ab}{a + b}$$

For Husband and Wife we can write:

$$\frac{1}{1} + \frac{1}{2} = 2 * \frac{1}{2} + 1 = \frac{2}{3}$$

For Rae and Herman we can write:

$$\frac{1}{4} + \frac{1}{6} = \frac{24}{10} = \frac{12}{5}$$

So, ratio of couple and children working together:

$$= \frac{2/3}{12/5}$$

$$= \frac{2}{3} * \frac{5}{12}$$

$$= \frac{5}{18}$$

$$= 5:18$$

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Joined: 30 Apr 2013
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Re: A husband and wife can complete a certain task in 1 and 2 hours  [#permalink]

### Show Tags

15 Dec 2017, 06:04
EMPOWERgmatRichC wrote:
Hi All,

This prompt can also be solved by using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual times that it takes to complete the 'job'

We're told that a husband and wife can complete a task in 1 hour and 2 hours, respectively. Working together, it would take them...

(1)(2)/(1+2) = 2/3 hours to complete the task

Next, we're told that the two children can complete the task in 4 hours and 6 hours, respectively. Working together, it would take them...

(4)(6)/(4+6) = 24/10 hours to complete the task

We're asked for the RATIO of the couple's time to the children's time....

(2/3) / (24/10) =
(2/3)(10/24) =
20/72 =
5/18

GMAT assassins aren't born, they're made,
Rich

Hello Rich,

Thanks for the explaination. How could we solve this problem by assuming values for work?
Re: A husband and wife can complete a certain task in 1 and 2 hours &nbs [#permalink] 15 Dec 2017, 06:04
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