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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 09 Jan 2016 Posts: 110 GPA: 3.4 WE: General Management (Human Resources) 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 16 Apr 2017, 05:20 3 19 00:00 Difficulty: 55% (hard) Question Stats: 69% (03:01) correct 31% (02:49) wrong based on 186 sessions ### HideShow timer Statistics 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work? A. 15 B. 18 C. 12.5 D. 10 E. 16 ##### Most Helpful Expert Reply e-GMAT Representative Joined: 04 Jan 2015 Posts: 2313 Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 16 Apr 2017, 20:49 5 4 Chemerical71 wrote: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work? A. 15 B. 18 C. 12.5 D. 10 E. 16 • 2 men and 3 boys can do a piece of work in 10 days. o Thus, 20 men and 30 boys can do a piece of work in 1 day......(i) • 3 men and 2 boys can do the same work in 8 days. o Thus, 24 men and 16 boys can do the same work in 1 day....(ii) • Equating (i) and (ii) we get - o 20 men + 30 boys = 24 men + 16 boys o 4 men = 14 boys o 2 men = 7 boys • Substituting this in equation (i) we get o 10 boys can do a piece of work in 10 days. o But we need to find out in how many days 2 men and 1 boy can do the work, which is equivalent to 8 boys.  8 boys can do the same work in (10*10/8) = 12.5 days. Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts _________________ Register for free sessions Number Properties | Algebra |Quant Workshop Success Stories Guillermo's Success Story | Carrie's Success Story Ace GMAT quant Articles and Question to reach Q51 | Question of the week Must Read Articles Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2 Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2 Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry Algebra- Wavy line | Inequalities Practice Questions Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com ##### General Discussion Math Expert Joined: 02 Aug 2009 Posts: 7108 Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 16 Apr 2017, 08:53 1 1 Chemerical71 wrote: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work? A. 15 B. 18 C. 12.5 D. 10 E. 16 Two points before coming to the solution.. 1) under no circumstances, it is sub-600 level. 2) the choices are always in ascending order, so may not be a very authentic source although the Q is ok. Let m men can complete the job on their own and B boys can complete the work. So $$\frac{2}{m}+\frac{3}{b}=\frac{1}{10}$$.. $$\frac{2*3}{m}+\frac{3*3}{b}=\frac{3}{10}$$..(i) $$\frac{3}{m}+\frac{2}{b}=\frac{1}{8}$$... $$\frac{2*3}{m}+\frac{2*2}{b}=\frac{2}{8}$$...(ii) Subtract i from ii.. $$\frac{9}{b}-\frac{4}{b}=\frac{3}{10}-\frac{2}{8}$$.. $$\frac{5}{b}=\frac{1}{20}$$... Or b=20*5=100.. Substitute in i to get value of m.. $$\frac{2}{m}+\frac{3}{100}=\frac{1}{10}$$.. $$\frac{2}{m}=\frac{1}{10}-\frac{3}{100}$$.. $$\frac{2}{m}=\frac{7}{100}$$.. We are looking for $$\frac{2}{m}+\frac{1}{b}=7/100+1/100=8/100$$.. So time taken=100/8=12.5.. _________________ 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 Current Student Joined: 09 Mar 2017 Posts: 91 Location: Netherlands Concentration: General Management, Finance GMAT 1: 690 Q45 V40 Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 16 Apr 2017, 11:45 Let x be men and y boys (2y+3x)/xy=1/10 (3y+2x)/xy=1/8 Through elimination you will get X=2/7y Therefore 10/y=1/10 Y rate=1/100 X rate=3.5/100 So rate of 2x+y=8/100 or 1/12.5 per day. Therefore it will be completed in 12.5 day Sent from my SM-G935F using GMAT Club Forum mobile app VP Joined: 07 Dec 2014 Posts: 1129 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 16 Apr 2017, 13:10 1 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work? A. 15 B. 18 C. 12.5 D. 10 E. 16 let m and b=rates for 1 man and 1 boy respectively multiplying, 6m+9b=3/10 and 6m+4b=1/4 subtracting, b=1/100 m=3.5/100 let d=days d(7/100+1/100)=1 d=12.5 days C Manager Joined: 09 Jan 2016 Posts: 110 GPA: 3.4 WE: General Management (Human Resources) Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 16 Apr 2017, 22:58 chetan2u wrote: Chemerical71 wrote: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work? A. 15 B. 18 C. 12.5 D. 10 E. 16 Two points before coming to the solution.. 1) under no circumstances, it is sub-600 level. 2) the choices are always in ascending order, so may not be a very authentic source although the Q is ok. Let m men can complete the job on their own and B boys can complete the work. So $$\frac{2}{m}+\frac{3}{b}=\frac{1}{10}$$.. $$\frac{2*3}{m}+\frac{3*3}{b}=\frac{3}{10}$$..(i) $$\frac{3}{m}+\frac{2}{b}=\frac{1}{8}$$... $$\frac{2*3}{m}+\frac{2*2}{b}=\frac{2}{8}$$...(ii) Subtract i from ii.. $$\frac{9}{b}-\frac{4}{b}=\frac{3}{10}-\frac{2}{8}$$.. $$\frac{5}{b}=\frac{1}{20}$$... Or b=20*5=100.. Substitute in i to get value of m.. $$\frac{2}{m}+\frac{3}{100}=\frac{1}{10}$$.. $$\frac{2}{m}=\frac{1}{10}-\frac{3}{100}$$.. $$\frac{2}{m}=\frac{7}{100}$$.. We are looking for $$\frac{2}{m}+\frac{1}{b}=7/100+1/100=8/100$$.. So time taken=100/8=12.5.. thank you for reply..I have been preparing for gmat since few months.For quant, i am doing manhattan, veritas and some gmat club solution mainly you , Bunnel after completing official sources.. I think this problem is consistent with gmat quant that's why i have posted. Manager Joined: 20 Jun 2016 Posts: 61 Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 11 Sep 2018, 06:52 10*(2M+3B)=8*(2M+16B) we get 2M=7B. We have to find 2M+1B= 7B+1B putting this in the first equation we get-- replacing 2M by 7B 10B takes 10 days Therefore 1B takes 100 days . hence 8B takes 100/8 = 12.5 days _________________ Life is a challenge face it. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4295 Location: United States (CA) Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 14 Sep 2018, 16:47 Chemerical71 wrote: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work? A. 15 B. 18 C. 12.5 D. 10 E. 16 Let m = the rate of 1 man and b = the rate of 1 boy. We can create the equations: 2m + 3b = 1/10 and 3m + 2b = 1/8 Multiplying the first equation by -2 and the second by 3, we have: -4m - 6b = -2/10 and 9m + 6b = 3/8 Adding the equations together, we have: 5m = 3/8 - 2/10 5m = 3/8 - 1/5 5m = 15/40 - 8/40 5m = 7/40 m = 7/200 Substitute m = 7/200 into 2m + 3b = 1/10, we have 2(7/200) + 3b = 1/10 7/100 + 3b = 1/10 3b = 10/100 - 7/100 3b = 3/100 b = 1/100 Letting x = the number of days needed to complete the work by 2 men and 1 boy, we have: x(2(7/200) + 1/100) = 1 x(8/100) = 1 x = 100/8 = 12.5 Answer: C _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions SVP Joined: 26 Mar 2013 Posts: 1917 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 24 Sep 2018, 03:05 Chemerical71 wrote: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work? A. 15 B. 18 C. 12.5 D. 10 E. 16 Dear EMPOWERgmatRichC I tried to use same concept that you used in the following but ended up choosing wrong answer: https://gmatclub.com/forum/if-12-men-an ... l#p2137361 3 men and 2 boys would take a total of 8 days to complete a task. If we HALVE the number of workers again, we would again DOUBLE the amount of time needed to complete the task: 1.5 men and 1 boys would take a total of 16 days to complete a task. The question ask for 2 men and 1 boy. With using extra 0.5 man , it should take little less than 16, which is 15 in answer choices. It is the close number to 16. However, the answer is (12.5) Can you help please? Thanks EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13095 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 [#permalink] ### Show Tags 24 Sep 2018, 10:25 1 Hi Mo2men, You CAN use that same logic here, but you have to be a bit more focused on the 'impact' that each man has on the overall calculation/rate. The prompt gives us two pieces of data to work with: 2 men and 3 boys can do a piece of work in 10 days 3 men and 2 boys can do the same work in 8 days Consider the second piece of information relative to the first piece. We remove 1 boy from the job, so we LOSE that boy's work output. Adding 1 extra man 'makes up' for that loss AND then cuts the total down from 10 days to 8 days. Thus, that 1 man clearly has a big impact on the total time; by himself, he clearly represents MORE than a 2 day decrease in time needed to complete the job (again, he's also making up for the lost productivity from losing that 1 boy). Thus, 1/2 of a man would account for MORE than a 1 day decrease in time needed to complete the job. You are absolutely correct that it would take 1.5 men and 1 boy a total of 16 days to complete the task. Adding that extra 1/2 of a man would decrease that total by MORE than 1 day though, so the correct answer CANNOT be 15 days (it has to be something less than that). Logically, 12.5 days makes far more sense. 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: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

### Show Tags

24 Sep 2018, 11:33
Chemerical71 wrote:
2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work?

A. 15
B. 18
C. 12.5
D. 10
E. 16

Let´s repeat EXACTLY the same approach we used here: https://gmatclub.com/forum/if-12-men-an ... 11-20.html

$$\begin{array}{*{20}{c}} {\left( {\text{I}} \right)} \\ {\left( {{\text{II}}} \right)} \end{array}\,\,\begin{array}{*{20}{c}} {\left[ {2\,\,{\text{men}}\,\,\, \cup \,\,\,{\text{3}}\,\,{\text{boys}}} \right]\,\,\, - \,\,{\text{1}}\,\,{\text{work}}\,\,\, - \,\,\,10\,\,\,{\text{days}}} \\ {\left[ {3\,\,{\text{men}}\,\,\, \cup \,\,\,{\text{2}}\,\,{\text{boys}}} \right]\,\,\, - \,\,{\text{1}}\,\,{\text{work}}\,\,\, - \,\,\,8\,\,\,{\text{days}}} \end{array}$$

$${\text{?}}\,\,\,{\text{:}}\,\,\,\left[ {2\,\,{\text{men}}\,\,\, \cup \,\,\,1\,\,{\text{boy}}} \right]\,\,\, - \,\,{\text{1}}\,\,{\text{work}}\,\,\, - \,\,\,?\,\,{\text{days}}$$

Let "task" be the fraction of this work that one man can do in 1 day, hence:

$$1\,{\text{man}}\,\,\, - \,\,\,1\,\,{\text{day}}\,\,\, - \,\,\,1\,\,\,{\text{task}}$$

Let k (k>0) be the fraction of the "task" defined above that one boy can do in 1 day (where k may be between 0 and 1, or equal to 1, or greater), hence:

$$1\,{\text{boy}}\,\,\, - \,\,\,1\,\,{\text{day}}\,\,\, - \,\,\,k\,\,\,{\text{task}}$$

Now the long-lasting benefit of this "structure": everything else becomes easy and "automatic":

$$\left( {\text{I}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left[ {2\,\,{\text{men}}\,\,\, \cup \,\,\,{\text{3}}\,\,{\text{boys}}} \right]\,\, - \,\,{\text{10}}\,\,{\text{days}}\,\,\, - \,\,\,2 \cdot 10 \cdot 1 + 3 \cdot 10 \cdot k\,\,\,{\text{tasks}}\,\, = \,\,\,1\,\,{\text{work}}\,$$

$$\left( {{\text{II}}} \right)\,\,\, \Rightarrow \,\,\,\,\left[ {3\,\,{\text{men}}\,\,\, \cup \,\,\,{\text{2}}\,\,{\text{boys}}} \right]\,\, - \,\,{\text{8}}\,\,{\text{days}}\,\,\, - \,\,3 \cdot 8 \cdot 1 + 2 \cdot 8 \cdot k\,\,\,{\text{tasks}}\,\, = \,\,\,1\,\,{\text{work}}$$

Therefore: $$20 + 30 \cdot k = 24 + 16 \cdot k\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,k = \frac{2}{7}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,1\,{\text{work}}\,\,{\text{ = }}\,\,\,{\text{28}}\frac{4}{7}\,\,\,{\text{tasks}}$$

$$?\,\,\,\,:\,\,\,\,\left[ {2\,\,{\text{men}}\,\,\, \cup \,\,\,1\,\,{\text{boy}}} \right]\,\,\,\, - \,\,\,{\text{1}}\,\,{\text{day}}\,\,\, - \,\,\,2 \cdot 1 + 1 \cdot \frac{2}{7} = 2\frac{2}{7}\,\,{\text{tasks}}$$

And we finish in "high style", using UNITS CONTROL, one of the most powerful tools of our method:

$$?\,\,\, = \,\,\,28\frac{4}{7}\,\,\,{\text{tasks}}\,\,\,\left( {\frac{{1\,\,{\text{day}}}}{{2\frac{2}{7}\,\,{\text{tasks}}}}\begin{array}{*{20}{c}} \nearrow \\ \nearrow \end{array}} \right)\,\,\,\, = \,\,\,\,\frac{{7 \cdot 28 + 4}}{{2 \cdot 7 + 2}} = \frac{{200}}{{16}} = \frac{{80 + 16 + 4}}{8} = 12\frac{1}{2}\,\,\,\,\,\left[ {{\text{days}}} \right]$$
Obs.: arrows indicate licit converter.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

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Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 &nbs [#permalink] 24 Sep 2018, 11:33
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