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If 12 men and 16 women can do a piece of work in

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by NandishSS » Mon Aug 29, 2016 6:42 am
If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days

SOURCE:GMATPrep

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by MartyMurray » Mon Aug 29, 2016 7:04 am
I find that the consistently easiest and most straightforward way to handle work questions is to boil everything down to rates. In this case we are looking at a piece per day rate.

Work Accomplished By One Man In One Day: M

Work Accomplished By One Woman In One Day: W

12 men and 16 women can do a piece of work in 5 days

Translate into a rate. 12M + 16W = 1/5 per day

13 men and 24 women can do it in 4 days

Translate into a rate. 13M + 24W = 1/4 per day

Now just solve algebraically.

Multiply the first by 1.5 and subtract the second from the first.

18M + 24W = 1.5/5 per day

13M + 24W = 1/4 per day

5M = 1.5/5 - 1/4 = 3/10 - 1/4 = 6/20 - 5/20 = 1/20 per day

M = 1/100 per day

Solve for W.

12/100 + 16W = 1/5

12/100 + 16W = 20/100

16W = 8/100

W = 1/200 per day

Now determine rate for 7 men and 10 women.

7(1/100) + 10(1/200) = 7/100 + 5/100 = 12/100 per day

So it will take 100/12 or about 8.3 days for them to do it.

The correct answer is C.
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by GMATGuruNY » Mon Aug 29, 2016 8:09 am
NandishSS wrote:If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days
Let M = the rate for each man and W = the rate for each woman.

The TIME RATIO for 12 men and 16 women to 13 men and 24 women is 5 days to 4 days.
Since time and rate are RECIPROCALS, the RATE RATIO for 12M+16W and 13M+24W is equal to the reciprocal of the time ratio:
(12M+16W)/(13M+24W) = 4/5
60M + 80W = 52M + 96W
8M = 16W
M = 2W.

Let W = 1 widget per day, implying that M = 2 widgets per day.

Work produced each day by 12 men and 16 women = (12*2) + (16*1) = 40 widgets per day.
Thus, the total work produced by 12 men and 16 women over 5 days = 40*5 = 200 widgets.

Work produced each day by 7 men and 10 women = (7*2) + (10*1) = 24 widgets per day.
Time for 7 men and 10 women to produce 200 widgets = 200/24 = 25/3 ⩳ 8.3 days.

The correct answer is C.

I doubt that this problem is contained in GMATPrep.
While the question stem asks for an exact time, the OA is an approximation.
The GMAT does not use the phrase "piece of work."
Also, it seems sexist for the men's rate to be twice the women's rate.
The GMAT strives to avoid this sort of bias.
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by DavidG@VeritasPrep » Mon Aug 29, 2016 9:35 am
NandishSS wrote:If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days

SOURCE:GMATPrep

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I'll second Mitch's opinion: there's no way this is a GMATPrep question. It's deeply problematic. That said, here's how I thought about the math:

12M + 16W = 1/5
13M + 24W = 1/4

Adding, we get

25M + 40W = 9/20

Divide by 4, to ball park:

6.25M + 10W = 9/80

If 6.25 men and 10 women have a rate of 9/80, the time for them to complete the job is 80/9, or 8 8/9. If we had 7 men, rather than 6.25, it would cut a bit off the time, so 8.3 looks reasonable.
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by NandishSS » Mon Aug 29, 2016 7:15 pm
GMATGuruNY wrote:
NandishSS wrote:If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days
Let M = the rate for each man and W = the rate for each woman.

The TIME RATIO for 12 men and 16 women to 13 men and 24 women is 5 days to 4 days.
Since time and rate are RECIPROCALS, the RATE RATIO for 12M+16W and 13M+24W is equal to the reciprocal of the time ratio:
(12M+16W)/(13M+24W) = 4/5
60M + 80W = 52M + 96W
8M = 16W
M = 2W.

Let W = 1 widget per day, implying that M = 2 widgets per day.

Work produced each day by 12 men and 16 women = (12*2) + (16*1) = 40 widgets per day.
Thus, the total work produced by 12 men and 16 women over 5 days = 40*5 = 200 widgets.

Work produced each day by 7 men and 10 women = (7*2) + (10*1) = 24 widgets per day.
Time for 7 men and 10 women to produce 200 widgets = 200/24 = 25/3 ⩳ 8.3 days.

The correct answer is C.

I doubt that this problem is contained in GMATPrep.
While the question stem asks for an exact time, the OA is an approximation.
The GMAT does not use the phrase "piece of work."
Also, it seems sexist for the men's rate to be twice the women's rate.
The GMAT strives to avoid this sort of bias.
Guru/DavidG/Marty,

Agree with you might not be GMATPrep problem ,found this challenging problem in GMATCLUB

How long I have to practice to think like you and answer :-)

You guys are just awesome :-)

Thanks And Regards
Nandish
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If 12 men and 16 women can do a piece of work in

by DavidG@VeritasPrep » Tue Aug 30, 2016 8:13 am
Check out the official version of a comparable question: https://www.beatthegmat.com/work-rates- ... 71522.html

(And note how much more elegant the arithmetic turns out to be)
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by Matt@VeritasPrep » Thu Sep 01, 2016 5:37 pm
We could look for a more elegant combination of the two equations, though. Let's assume that the men each work at rate m and the women each work at rate w. We know that

Work = (12m + 16w) * 5

Work = (13m + 24w) * 4

Work = (7m + 10w) * x

and we want to find x.

Using the first two equations, we have 60m + 80w = Work and 52m + 96w = Work, so 60m + 80w = 52m + 96w, or 8m = 16w, or m = 2w.

From there, replace m with 2w in each equation, and set the first equal to the third.

(12m + 16w) * 5 = (7m + 10w) * x

(24w + 16w) * 5 = (14w + 10w) * x

200w = 24w * x

x = 200/24 = 50/6 = 8.33...
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by Scott@TargetTestPrep » Fri Dec 15, 2017 6:46 am
NandishSS wrote:If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days
We can let the time it takes 1 man to finish the work = m, and thus the rate of 1 man = 1/m. Likewise, we can let the time it takes 1 woman to finish the work = w, and thus the rate of 1 woman = 1/w.

Thus, the combined rate of 12 men and 16 women is 12/m + 16/w. Since they can finish the work in 5 days, their combined rate is also equal to 1/5. Thus, we have:

12/m + 16/w = 1/5

Multiplying both sides of the equation by 5mw, we have:

60w + 80m = mw

Similarly, the combined rate of 13 men and 24 women is 13/m + 24/w. Since they can finish the work in 4 days, their combined rate is also equal to 1/4. Thus, we have:

13/m + 24/w = 1/4

Multiplying both sides of the equation by 4mw, we have:

52w + 96m = mw

So, we have 60w + 80m = 52w + 96m (since they both equal mw).

60w + 80m = 52w + 96m

8w = 16m

w = 2m

We can now substitute w = 2m into the first equation, 12/m + 16/w = 1/5, to solve for m:

12/m + 16/(2m) = 1/5

12/m + 8/m = 1/5

20/m = 1/5

m = 100

Since m = 100 days, w = 200 days. The rate of 1 man is 1/100 and the rate of 1 woman is 1/200. Thus, the rate of 7 men and 10 women is 7/100 + 10/200 = 7/100 + 5/100 = 12/100, and the time for them to finish the same work is 1/(12/100) = 100/12 = 8.3 days.

Answer: C

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