Difficult Work/Rate Problem

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mattocks: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Mar 07, 2010 1:17 pm

by mattocks » Sun Mar 28, 2010 11:23 am

Can someone explain the best way to solve this problem?

13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

a) 42
b) 54
c) 21
d) 63
e) 24

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Source: Beat The GMAT — Problem Solving | Sun Mar 28, 2010 11:23 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sun Mar 28, 2010 8:47 pm

mattocks wrote:Can someone explain the best way to solve this problem?

13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

a) 42
b) 54
c) 21
d) 63
e) 24

IMO A

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Mon Mar 29, 2010 2:50 am

mattocks wrote:Can someone explain the best way to solve this problem?

13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

a) 42
b) 54
c) 21
d) 63
e) 24

13M + 7B = 1/7 (per day work of 13 men and 7 boys)
13W + 6B = 1/6 (per day work of 13 women and 6 boys)
------------------------------
13M+13W+13B = 13/42

per day work of (M+W+B) = 1/42. Hence, number of days required for 1 man, 1 woman, and 1 boy = 42 days.

Regards,
Harsha

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pops: Master | Next Rank: 500 Posts; Posts: 148; Joined: Tue Jun 09, 2009 11:06 pm; Thanked: 7 times

by pops » Mon Mar 29, 2010 6:42 am

mattocks wrote:Can someone explain the best way to solve this problem?

13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

a) 42
b) 54
c) 21
d) 63
e) 24

Hi,
Trick here would be to notice the pattern of numbers : 13, 7, 6 ....
now make an equation as per given condition:
13 * 1/m + 7 * 1/b = 1/7
13 * 1/w + 6 * 1/b = 1/6

[quickly realise that 7/b + 6/b =13/b and we are asked to know 1/m+1/w+1/b]
so, add above 2:
13 * (1/m+1/w+1/b) = 1/7 + 1/6 = 13/42
hence, the answer = 42

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eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » Mon Mar 29, 2010 1:47 pm

Using information given form the equations

13/x + 7/y = 1/7
6/y +13/z = 1/6

Here we have 3 variables and 2 equations which is unsolvable, that means theres some trick, so observing the equations, we realize their sum gives us the answer

Answer A

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Tue Mar 30, 2010 1:35 am

7(13M+7B) = 6(6B+13W) = k(M+B+W)

(13M+7B) = k(M+B+W)/7
(6B+13W) = k(M+B+W)/6
sum these two

13M+13B+13W = k(M+B+W)(1/7 + 1/6)

k = 42

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Tue Mar 30, 2010 8:31 am

pops wrote: Trick here would be to notice the pattern of numbers : 13, 7, 6 ....
now make an equation as per given condition:
13 * 1/m + 7 * 1/b = 1/7
13 * 1/w + 6 * 1/b = 1/6
[quickly realise that 7/b + 6/b =13/b and we are asked to know 1/m+1/w+1/b]
so, add above 2:
13 * (1/m+1/w+1/b) = 1/7 + 1/6 = 13/42
hence, the answer = 42

13 M + 7 B = 7 days ---1 and 6 B + 13 W = 6 days ----2
LCM of 7 and 6 = 42
13M+7B in 42 days can do 6 times the work ---1
......6B + 13 W in 42 days can do 7 times the work-------2 Adding 1 and 2
13M+13B+13W in 42 days can do 13 times the work so dividing by 13
M+B+W can in 42 days can do the the work once.

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