Time and work problem

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hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » Sat Jan 26, 2013 9:47 pm

Q22 . It takes 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman ?

a. 3
b. 4
c. 5
d. 6
e. 7

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

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Source: Beat The GMAT — Problem Solving | Sat Jan 26, 2013 9:47 pm

jkaustubh: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Mon Aug 13, 2012 11:53 pm; Location: Mumbai; Thanked: 1 times

by jkaustubh » Sat Jan 26, 2013 10:14 pm

x: days 9 women doing the job --> 1 woman works W=1/9x per day
x-5: days 3 men doing the job --> 1 man works M=1/[3*(x-5)] per day

The answer to the question is: M/W

And, how much is x?

As per first data:

2*M+3*W=1/6
You can solve x, and obtain 2 values, 10 and 1 (1 is impossible because that would imply that the 3 men take -4 days), so x=10. So M/W=6 times

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Jul 15, 2018 10:15 pm

Please find attached the solution

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jul 16, 2018 2:24 am

hemant_rajput wrote:Q22 . It takes 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman ?

a. 3
b. 4
c. 5
d. 6
e. 7

We can PLUG IN THE ANSWERS, which represent how many times a man's output exceeds that of a woman.
When the correct answer is plugged in, 3 men will take 5 fewer days to complete the job than 9 women.

B: 4
Let the rate for each woman = 1 unit per day and the rate for each man = 4 units per day.
Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*4)(6) = 66 units.
Time for 9 women to complete the job = (work)/(rate for 9 women) = 66/(9*1) = 22/3 â‰ˆ 7 days.
Time for 3 men to complete the job = (work)/(rate for 3 men) = 66/(3*4) = 66/12 = 11/2 â‰ˆ 5 days.
Doesn't work:
Here, 3 men take only about 2 fewer days than 9 women.
Eliminate B.
For 3 men to take 5 fewer days, the rate for each man must INCREASE.
Eliminate A.

D: 6
Let the rate for each woman = 1 unit per day and the rate for each man = 6 units per day.
Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*6)(6) = 90 units.
Time for 9 women to complete the job = (work)/(rate for 9 women) = 90/(9*1) = 90/9 = 10 days.
Time for 3 men to complete the job = (work)/(rate for 3 men) = 90/(3*6) = 90/18 = 5 days.
Success!
Here, 3 men take 5 fewer days than 9 women.

The correct answer is D.

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swerve: Legendary Member; Posts: 2568; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Jul 16, 2018 9:37 am

First set: 3/w+2/m=1/6

Second set: 3/m = 1/x and 9/w=1/(x+5)

--> 1/m = 1/3x and 1/w = 1/9(x+5)

Enter in the first equation and solve for x

1/(3x+15) + 2/3x = 1/6

Simplify --> x^2-x-20=0

Solve for x: x=(1 +- (1+80)^,5)/2= (1+- 9)/2.

x can only be positive ---> x= 5.

Enter in the second set ---> 3/m=1/5 and 9/w=1/10 --> 3/2m=9/w --> m/w=1/6.

Regards!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8188; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Jul 19, 2018 11:40 am

hemant_rajput wrote:Q22 . It takes 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman ?

a. 3
b. 4
c. 5
d. 6
e. 7

We can let the number of days for 1 man to finish the work = m and that for 1 woman = w. Thus, the rate of 1 man = 1/m and the rate of 1 woman = 1/w.

Since it takes 6 days for 3 women and 2 men working together to complete the work, we have:

6(3/w + 2/m) = 1

Since 3 men would do the same work 5 days sooner than 9 women, we have:

1/(3/m) + 5 = 1/(9/w)

m/3 + 5 = w/9

Multiplying the above by 9, we have:

3m + 45 = w

Substituting this into 6(3/w + 2/m) = 1, we have:

6(3/(3m + 45) + 2/m) = 1

6(1/(m + 15) + 2/m) = 1

Multiplying the above by m(m + 15), we have:

6m + 12(m + 15) = m(m + 15)

6m + 12m + 180 = m^2 + 15m

m^2 - 3m - 180 = 0

(m - 15)(m + 12) = 0

m = 15 or m = -12

Since m can't be negative, m = 15. So w = 3(15) + 45 = 90. We see that it takes a man 15 days to complete the work but 90 days for a woman to complete the same work. So a man's output is 6 times the output of a woman.

Answer: D

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

Time and work problem

by Mo2men » Fri Jul 20, 2018 3:55 pm

GMATinsight wrote:Please find attached the solution

Dear GMAtInsight,

I saw you many times use the formula (MT)/W =constant but M is manpower. However, when you tried to solve the problem you used (3w+2m) *6/1 . Now, I'm confused why you said is 3w + 2m represents a rate but as manpower should be a number like 5 people not rate. ?

I feel something not right about manpower? what is the unite of manpower? is it (unit produced/unite of time) ?

Also, how are all equal to constant? What does constant here mean? Can you elaborate more please?

Thanks in advance

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