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# Twenty-four men can complete a work in sixteen days.Thirty-two women c

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Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 12:10
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Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days.Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 21:10
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Chemerical71 wrote:
Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

First find the relation of rate of work done by men vs women.

24 men complete the work in 16 days.
32 women can complete the same work in 24 days.
So 24 women will take 24 * (32/24) = 32 days to complete the work

Same number of women take twice the time (16 days vs 32 days) so their rate of work is half.
So 16 women are equivalent to 8 men work-wise.

So 16 + 8 = 24 men start working and work for 12 days. They complete the work in 16 days so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men.

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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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17 Mar 2017, 00:52
4
2
Chemerical71 wrote:
Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days.Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

let the work be z rate of doing work for man and woman be x and y respectively

According to question
24*16*x = z
32*24*y = z

therefore 24*16*x = 32*24*y or x = 2y

work done in 12 days = (16x +16y)12 = (32y + 16y) 12 = 48*12y = 24*24y

work left = 32*24y-24*24y = 8*24y

work left = (no of men added rate+ current workers rate)*2

or 8*24y = (N*x +16x+16y)*2

putting x = 2y

4*24y = 2Ny+48y
2Ny = 48y

or N = 24.

Option B
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 20:49
4
24 men ----------- 16 days ------------ 1 complete work
1 man ------------ 1 day ------------1/(24*16) portion work

32 women ----------- 24 days ------------ 1 complete work
1 woman ------------ 1 day ------------1/(32*24) portion work

Hence,
1 man &1 woman ------------ 1 day ------------{1/(32*24) + 1/(24*16)} portion work = 1(/24)*(1/16 + 1/32) = (1/24)*(3/32) = (1/8)*(1/32)
Now,
16 man & 16 woman ------------ 1 day ------------ 16* (1/8)*(1/32) portion work = 2*(1/32) = 1/16
16 man & 16 woman ------------ 12 day ------------ 12*(1/16) = 3/4
Remaining work - 1/4

Now, extra work in next 2 days: 1/4 - 2*(1/16) = 1/8
Then, extra men required in next 2 days: (24*16)/(2*8) = 24 .

This is not a SUB-600 level question.
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 20:54
saswata4s wrote:
24 men ----------- 16 days ------------ 1 complete work
1 man ------------ 1 day ------------1/(24*16) portion work

32 women ----------- 24 days ------------ 1 complete work
1 woman ------------ 1 day ------------1/(32*24) portion work

Hence,
1 man &1 woman ------------ 1 day ------------{1/(32*24) + 1/(24*16)} portion work = 1(/24)*(1/16 + 1/32) = (1/24)*(3/32) = (1/8)*(1/32)
Now,
16 man & 16 woman ------------ 1 day ------------ 16* (1/8)*(1/32) portion work = 2*(1/32) = 1/16
16 man & 16 woman ------------ 12 day ------------ 12*(1/16) = 3/4
Remaining work - 1/4

Now, extra work in next 2 days: 1/4 - 2*(1/16) = 1/8
Then, extra men required in next 2 days: (24*16)/(2*8) = 24 .

This is not a SUB-600 level question.
Then, extra men required in next 2 days: (24*16)/(2*8) = 24 . please explain this step again.
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 23:09
VeritasPrepKarishma wrote:
Chemerical71 wrote:
Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

First find the relation of rate of work done by men vs women.

24 men complete the work in 16 days.
32 women can complete the same work in 24 days.
So 24 women will take 24 * (32/24) = 32 days to complete the work

Same number of women take twice the time (16 days vs 32 days) so their rate of work is half.
So 16 women are equivalent to 8 men work-wise.

So 16 + 8 = 24 men start working and work for 12 days. They complete the work in 16 days so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men.

Dear VeritasPrepKarishma, Does the font highlighted in red reflecting the relationship is inversely proportional instead of directly proportional?

For example, 10 apples cost $20, 5 apples will cost (5*$20/10=$10). _________________ "Be challenged at EVERY MOMENT." “Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.” "Each stage of the journey is crucial to attaining new heights of knowledge." Rules for posting in verbal forum | Please DO NOT post short answer in your post! Advanced Search : https://gmatclub.com/forum/advanced-search/ Retired Moderator Joined: 04 Aug 2016 Posts: 515 Location: India Concentration: Leadership, Strategy GPA: 4 WE: Engineering (Telecommunications) Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 17 Mar 2017, 02:42 ziyuen wrote: VeritasPrepKarishma wrote: Chemerical71 wrote: Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days? A .16 B. 24 C. 36 D. 48 E. 54 First find the relation of rate of work done by men vs women. 24 men complete the work in 16 days. 32 women can complete the same work in 24 days. So 24 women will take 24 * (32/24) = 32 days to complete the work Same number of women take twice the time (16 days vs 32 days) so their rate of work is half. So 16 women are equivalent to 8 men work-wise. So 16 + 8 = 24 men start working and work for 12 days. They complete the work in 16 days so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men. Answer (B) Dear VeritasPrepKarishma, Does the font highlighted in red reflecting the relationship is inversely proportional instead of directly proportional? For example, 10 apples cost$20, 5 apples will cost (5*$20/10=$10).

Total Work completed = Rate of work of each man * total # of man * total time

Rate of work of each man = Total Work completed / (total # of man * total time) = 1/ (24*16)
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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18 Mar 2017, 11:58
2
1
ziyuen wrote:
VeritasPrepKarishma wrote:
Chemerical71 wrote:
Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

First find the relation of rate of work done by men vs women.

24 men complete the work in 16 days.
32 women can complete the same work in 24 days.
So 24 women will take 24 * (32/24) = 32 days to complete the work

Same number of women take twice the time (16 days vs 32 days) so their rate of work is half.
So 16 women are equivalent to 8 men work-wise.

So 16 + 8 = 24 men start working and work for 12 days. They complete the work in 16 days so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men.

Dear VeritasPrepKarishma, Does the font highlighted in red reflecting the relationship is inversely proportional instead of directly proportional?

For example, 10 apples cost $20, 5 apples will cost (5*$20/10=$10). The relation between no. of workers and no of days is inversely proportional. If there are fewer women, no of days taken will be more. No of women * No of days = Constant 32 women * 24 days = 24 women * ?? days ?? days = 24 days * (32 women/24 women) ?? days = 24 days For more on direct and inverse proportion, check: https://www.veritasprep.com/blog/2013/0 ... -directly/ https://www.veritasprep.com/blog/2013/0 ... inversely/ _________________ 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 > GMAT self-study has never been more personalized or more fun. Try ORION Free! Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 3911 Location: United States (CA) Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 21 Mar 2017, 06:20 4 2 Chemerical71 wrote: Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days.Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days? A .16 B. 24 C. 36 D. 48 E. 54 Since 24 men can complete a work in 16 days, the rate of 24 men is 1/16, and hence the rate of 1 man is (1/16)/24 = 1/384. Similarly, 32 women can complete the same work in 24 days, the rate of 32 women is 1/24, and hence the rate of 1 woman is (1/24)/32 = 1/768. Thus, the rate for 16 men and 16 women is 16 x (1/384) + 16 x (1/768) = 1/24 + 1/48 = 2/48 + 1/48 = 3/48 = 1/16. Since these 16 men and 16 women worked for 12 days, they completed (1/16) x 12 = 12/16 = 3/4 of the job. Thus, 1/4 of the job is left to be done. To find the number of additional men needed to complete the remaining work in 2 days, we can let n = the additional men needed and create the following equation (keep in mind that the rate of each man is 1/384 and the rate of the existing 16 men and 16 women is 1/16): n(1/384)(2) + (1/16)(2) = 1/4 n/192 + 1/8 = 1/4 n/192 = 1/8 8n = 192 n = 24 Answer: B _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions BSchool Forum Moderator Joined: 28 Mar 2017 Posts: 1172 Location: India GMAT 1: 730 Q49 V41 GPA: 4 Re: Twenty-four men can complete a job in sixteen days. Thirty-two women [#permalink] ### Show Tags 15 May 2017, 11:28 2 Bunuel wrote: Twenty-four men can complete a job in sixteen days. Thirty-two women can complete the same job in twenty-four days. Sixteen men and sixteen women started working on the job for twelve days. How many more men must be added to complete the job in 2 days? (A) 16 (B) 24 (C) 36 (D) 48 (E) 54 1M 1D work=1/(16*24) 1W 1D work=1/(24*32) 16M 1D work=1/24=2/48 16W 1D work=1/48 16M&W 1D work=3/48=1/16 16M&W 12D work=12/16 Hence remaining work=4/16=1/4 -------> this work should be completed by the additional men 1M 1D work=1/(16*24) 1M 2D work=1/(16*12) xM 2D work=x/(16*12), this must be equal to 1/4 x/(16*12)=1/4 => x=48 Answer: D _________________ Kudos if my post helps! Long And A Fruitful Journey - V21 to V41; If I can, So Can You!! Preparing for RC my way My study resources: 1. Useful Formulae, Concepts and Tricks-Quant 2. e-GMAT's ALL SC Compilation 3. LSAT RC compilation 4. Actual LSAT CR collection by Broal 5. QOTD RC (Carcass) 6. Challange OG RC 7. GMAT Prep Challenge RC Manager Joined: 27 Mar 2016 Posts: 51 Re: Twenty-four men can complete a job in sixteen days. Thirty-two women [#permalink] ### Show Tags 15 May 2017, 11:46 1 Lets take lcm of 16,24 and 32 i.e 96. So let the work job be 96. Now for men let their one day effort be x. So x*24*16= 96, hence x= 1/4 Similary for women let their one day effort per person be y . So y*32*24=96 Y= 1/8. Now (1/4+1/8)*16*12=72. So 24 units of work is left. Now let no of men be z 1/4*2*z= 24. Hence z =48 Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app Manager Joined: 09 Oct 2016 Posts: 89 Location: United States GMAT 1: 740 Q49 V42 GPA: 3.49 Twenty-four men can complete a job in sixteen days. Thirty-two women [#permalink] ### Show Tags 15 May 2017, 12:18 This one took a while to do simply bc of all the calculations (if there is a quick way please let me know) I ended up with 48, D. Men rate = 1/384 Women rate = 1/768 Combined and through 14 days = 336/384, 48 being the difference Edit: upon further review, I made a mistake and didn't account for the two days. It should be 24 additional men, making the total 48 on day 12. This would produce the additional 96 units needed Posted from my mobile device Current Student Joined: 12 Aug 2015 Posts: 2638 Schools: Boston U '20 (M) GRE 1: Q169 V154 Twenty-four men can complete a job in sixteen days. Thirty-two women [#permalink] ### Show Tags 15 May 2017, 16:55 1 Excellent question. 700 level for sure .. Here is what I did on this question----> Let us decode the statements ==> Let the complete work be designated by W. Twenty-four men can complete a job in sixteen day. Speed of each men => W/(16*24) per day Thirty-two women can complete the same job in twenty-four days. Speed of each women => W/(32*24) per day 16 men and 16 women stated working Combined speed of 16 men and 16 women => W/(16*24) * 16 + W/(32*24) *16 => W/24+W/48 => W/16 per day Now combining they work for 12 Days => Work done => 12*W/16 => 3W/4 Left over work => W-3W/4 => W/4 Now let more men =x Hence--> 2* [(x+16) W/(16*24) + 16*W/(32*24)] = W/4 Solving this we get => x=24 Hence B. SMASH THAT B. Looking forward to the OE. _________________ MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs! STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+) AVERAGE GRE Scores At The Top Business Schools! Current Student Joined: 12 Aug 2015 Posts: 2638 Schools: Boston U '20 (M) GRE 1: Q169 V154 Twenty-four men can complete a job in sixteen days. Thirty-two women [#permalink] ### Show Tags 16 May 2017, 00:53 3 gmatexam439 wrote: Bunuel wrote: Twenty-four men can complete a job in sixteen days. Thirty-two women can complete the same job in twenty-four days. Sixteen men and sixteen women started working on the job for twelve days. How many more men must be added to complete the job in 2 days? (A) 16 (B) 24 (C) 36 (D) 48 (E) 54 1M 1D work=1/(16*24) 1W 1D work=1/(24*32) 16M 1D work=1/24=2/48 16W 1D work=1/48 16M&W 1D work=3/48=1/16 16M&W 12D work=12/16 Hence remaining work=4/16=1/4 -------> this work should be completed by the additional men 1M 1D work=1/(16*24) 1M 2D work=1/(16*12) xM 2D work=x/(16*12), this must be equal to 1/4 x/(16*12)=1/4 => x=48 Answer: D You did all the hard work. But missed out just at the very end. The highlighted portion is incorrect. Here is the corrected version --> The work 1/4 would be done by both x men and 16 women. You forgot to take 16 women into account. NOTE -> You have taken the entire men's number as x. So work done by x men and 16 women in 2 days => 2[x/24*16 +16/24*32] =1/4 x=40 Hence additional men required => 40-16 => 24 Smash that B. _________________ MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs! STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+) AVERAGE GRE Scores At The Top Business Schools! Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4110 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 16 May 2017, 09:05 1 1 Chemerical71 wrote: Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days.Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days? A .16 B. 24 C. 36 D. 48 E. 54 Quote: Twenty-four men can complete a work in sixteen days. So, Total mandays = 24*16 => 384 Quote: Thirty-two women can complete the same work in twenty-four days. So, Total womandays = 32*24 => 768 Now, total work = LCM( 384,768 ) => 768 So, Efficiency of men = 2 & Efficiency of women = 1 Quote: Sixteen men and sixteen women started working for twelve days. Work completed = (16*2 + 16*1 )12 => 576 units , Work left = 768 - 576 => 192 Quote: How many more men are to be added to complete the work remaining work in 2 days? $${(16+m)*2 + 16*1 }*2 = 192$$ Or, $$(16+m)*2 + 16 = 96$$ Or, $$(16+m) = 40$$ Or, $$m = 24$$ Thus, we need to add , 24 more men workers, answer must be (B) 24 men... _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Intern Status: preparing Joined: 30 Dec 2013 Posts: 40 Location: United Arab Emirates Concentration: Technology, Entrepreneurship GMAT 1: 660 Q45 V35 GMAT 2: 640 Q49 V28 GMAT 3: 640 Q49 V28 GMAT 4: 640 Q49 V28 GMAT 5: 640 Q49 V28 GPA: 2.84 WE: General Management (Consumer Products) Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 17 May 2017, 04:08 1 the question is done in two parts: 1) work rate comparison bw men and women 24 men ---- 16 days 1 man ----- 24x16 16 man ----- 24 days 32 women ---- 24 days 16 women --- 48 days so men : women = 2 : 1 men will do double the work done by women 2) work remaining after 12 days, that needs to be done in 2 days men need 24 days to finish the work. so in 12 days they will do half the job m ---- 1/2 women need 48 days to finish the job, and in 12 days they will do 12/48 = 1/4 th of the work w----- 1/4 total work done in 12 days = m+w = 1/2 + 1/4 = 3/4 balance = 1/4 of work In other words 1/4 * 24 =6 days of work for 16 men and 16 women how many additional men required to finish in two days : 1/2 of work is done by 16 men so 1/4 of work will be done by 8 men total = 16+8= 24 men Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 3911 Location: United States (CA) Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 18 May 2017, 20:05 Chemerical71 wrote: Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days.Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days? A .16 B. 24 C. 36 D. 48 E. 54 We are given that the rate of 24 men is 1/16, so the rate of each man is (1/16)/24 = 1/(16 x 24). Similarly, we are given that the rate of 32 women is 1/24, so the rate of each woman is (1/24)/(32) = 1/(24 x 32). Now we can find the fraction of the job that is completed by 16 men and 16 women in one day. 16 x 1/(16 x 24) + 16 x 1/(24 x 32) 1/24 + 1/(24 x 2) 2/48 + 1/48 3/48 = 1/16 We see that 16 men and 16 women can complete 1/16 of the job in one day, so they can complete 12 x 1/16 = 12/16 = 3/4 of the job in 12 days. We can let m be the number of additional men who must be added to complete the job in two more days. Since we have 1 - 3/4 = 1/4 of the job left and it needs to be completed in two2 more days, each day they need to complete (1/4)/2 = 1/8 of the job. Thus, we can create the following equation to solve for m: (16 + m) x 1/(16 x 24) + 16 x 1/(24 x 32) = 1/8 1/24 + m/(16 x 24) + 1/48 = 1/8 Multiplying the above equation by 48, we have: 2 + m/8 + 1 = 6 m/8 = 3 m = 24 Answer: B _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions DS Forum Moderator Joined: 22 Aug 2013 Posts: 1348 Location: India Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 18 May 2017, 21:14 I will attempt this in a similar way as Ashudhall. In these kind of questions, its a good idea sometimes to take total units of work as the LCM of all the days and number of people given. Because we need a number which is divisible by all of those. Let me explain. LCM of 24, 16, 32 and 24 is 96. So lets assume total work to be done as 96 units. 24 men can do 96 units work in 16 days So 24 men can do in 1 day = 96/16 = 6 units of work. So 1 man can do in 1 day = 6/24 = 1/4 units of work Also, 32 women can do 96 units of work in 24 days So 32 women can do in 1 day = 96/24 = 4 units of work So 1 woman can do in 1 day = 4/32 = 1/8 units of work Thus, 16 men and 16 women can do in 1 day = 16*1/4 + 16*1/8 = 6 units of work As per the question, the work has to be completed in 14 total days In 14 days, these 16 men and 16 women would have completed = 14*6 = 84 units of work Remember that total units of work are 96. Remaining work units = 96-84 = 12 units If 'n' extra men are employed to finish off these 12 units in 2 days, it means these 'n' men finish 6 units in 1 day We know that 1 man does 1/4 units work in 1 day Therefore, no of men required 'n' = 6/(1/4) = 24 So 24 extra men are required. Answer is B Director Joined: 17 Dec 2012 Posts: 629 Location: India Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 06 Jun 2017, 01:03 Chemerical71 wrote: Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days.Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days? A .16 B. 24 C. 36 D. 48 E. 54 1. 1 man takes 384 days and 1 woman takes 768 days 2. (no.of days worked by men* no.of men)/(time taken for a man working alone) + (no.of days worked by additional men * no.of additional men )/(time taken for a man working alone)+ (no.of days worked by women* no.of women)/(time taken for a woman working alone) = 1 3. (14*16)/384 + (2*x)/384 + (14*16)/768=1 We get x=24 _________________ Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com Holistic and Systematic Approach EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12702 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 14 Jan 2018, 12:54 Hi All, Before we get into this question, you've been posting a variety of 'tougher' prompts lately - so unless you're already scoring above 700 in your practice Exams (or on the Official GMAT), then you might be focusing on the wrong things. In these types of 'rate' questions, it often helps to think in terms of the TOTAL work that must be done to complete the task. If a 24-man crew can complete the job in 16 days, then that means that (24)(16) = 384 man-days of effort are required to complete the job. If a 32-woman crew can complete the job in 24 days, then that means that (32)(24) = 768 woman-days of effort are required to complete the job. Before we do anything else, it's important to compare these numbers: 384 and 768. Since 384 is exactly HALF of 768, in this question that means that the work that a woman does in 1 day = 1/2 of the work that a man does in 1 day. We're told that 16 men and 16 women work for 12 days each. That means they complete.... (16 men)(12 days) = 192 man-days of work = 1/2 of the job gets done (16 women)(12 days) 192 woman-days of work = 1/4 of the job gets done 1/2 + 1/4 = 3/4... so after 12 days, 3/4 of the job is done - and 1/4 of the job remains We're going to add a certain number of men, so that the job is completed in 2 more days. First though, we have to figure out how much more of the job gets completed with the existing people during that time... (16 men)(2 days) = 32 man-days of work = 1/12 of the job gets done (16 women)(2 days) 32 woman-days of work = 1/24 of the job gets done During the next 2 days, the existing people will complete 1/12 + 1/24 = 3/24 of the job gets done That leaves us with 1/4 - 3/24 = 3/24 of the job remains. 3/24 of 384 man-days = 48 man-days of work. The extra men that will be added will work for 2 days each, so.... (X men)(2 days each) = 48 days of man-work X = 24 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: Twenty-four men can complete a work in sixteen days.Thirty-two women c &nbs [#permalink] 14 Jan 2018, 12:54

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