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sarthak1701
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GMAT Focus 1: 575 Q77 V81 DI78
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If 12 men and 16 women can do a piece of work in 5 days and 13 men and 15 Sep 2024, 04:21
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PareshGmat
Let a man do \(\frac{1}{x}\) work per day and

each woman do \(\frac{1}{y}\) work per day

\(\frac{12}{x} + \frac{16}{y} = \frac{1}{5}............\)(1)
\(\frac{13}{x} +\frac{24}{y} = \frac{1}{4}\) ............ (2)

Multiply (1) by 3 & (2) by 2

\(\frac{36}{x} + \frac{48}{y} = \frac{3}{5}\) ....... (3)

\(\frac{26}{x} + \frac{48}{y} = \frac{1}{2}\) ........ (4)

Equation (3) - (4)

\(\frac{10}{x} = \frac{1}{10}\)

x = 100

y = 200

We require to find z; substituting the values

\(\frac{7}{x}+\frac{10}{y}= \frac{1}{z}\)

\(\frac{7}{100}+ \frac{10}{200} = \frac{1}{z}\)

\(\frac{7}{100}+ \frac{5}{100} = \frac{1}{z}\)

\(\frac{12}{100} = \frac{1}{z}\)

\(z = \frac{100}{12} = 8.33 = Answer\)
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This is the most straightforward way and it is what I did but it is way too time-consuming, it is better to check the choices first and see if they are far apart, if they are, it is better to solve it with shortcut methods mentioned by others.
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Fardin024
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If 12 men and 16 women can do a piece of work in 5 days and 13 men and 14 Nov 2024, 06:07
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SigEpUCI
If you solve the two equations:

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

and then plug M and W into

7M + 10W = X,

X should be the amount of days.

Thats too much math for me, and the numbers don't look too clean either.
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Shouldn’t it be 12M+16W=1/5?
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Bunuel
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If 12 men and 16 women can do a piece of work in 5 days and 13 men and 14 Nov 2024, 07:44
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Fardin024
SigEpUCI
If you solve the two equations:

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

and then plug M and W into

7M + 10W = X,

X should be the amount of days.

Thats too much math for me, and the numbers don't look too clean either.
Shouldn’t it be 12M+16W=1/5?
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If M and W denote the rates, then yes, it should be 12M + 16W = 1/5 and 13M + 24W = 1/4.
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If 12 men and 16 women can do a piece of work in 5 days and 13 men and 18 Nov 2025, 09:39
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