A man can complete a piece of work in 36days working alone. Can a boy

Question

A man can complete a piece of work in 36days working alone. Can a boy complete the work in 54 days?

(1) The work done by a woman in 3 days is equal to the work done by a man in 2 days.
(2) The work done by a woman in a day exceeds twice the work done by a boy in a day.

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Shwarma · Answer

Option C
 
1. Rate(women)- 1/54 - not sufficient
2. Rate (women)> 2*rate(boy) - not sufficient

1&2
1/54>2*rate of boy
1/108>rate of boy

so sufficient

Purnank · Answer

Given - A man can complete a piece of work in 36days working alone. 
Assuming efficiency of men 'm', Therefore total work = 36m.
To check Can a boy complete the work in 54 days lets check given conditions.

1st - The work done by a woman in 3 days is equal to the work done by a man in 2 days.
assuming 'w' efficiency of women. Therefore, 3w=2m
Total work = 36m = 18*(2m) = 18*(3w) = 54*w-- Eq1
means women will 54 days working alone.
But nothing about boy so not sufficient.

2nd - The work done by a woman in a day exceeds twice the work done by a boy in a day.
assuming 'b' efficiency of boy. Therefore, w>2*b --- (Eq2) but dont have anything that we can compare with efficiency of men hence not sufficient.

Now combining both, comparing equation 2 with 1 confirms that if women taking 54 days to complete same job then boy will take definitely more than twice the days that women took.
Hence Answer C.

Legenddary1234 · Answer

To solve whether the boy can complete the work in 54 days, we need to analyze the information provided and use it to determine the boy's rate of work completion. We'll use the concept of work rates, where the rate is defined as the portion of work done in one day.

Let's denote:

The man's rate as ( M )
The woman's rate as ( W )
The boy's rate as ( B )
From the problem statement:

The man completes the work in 36 days, so his rate ( M = \frac{1}{36} ) of the work per day.
Statement (1): "The work done by a woman in 3 days is equal to the work done by a man in 2 days."

This can be mathematically expressed as ( 3W = 2M ).
Substituting ( M = \frac{1}{36} ), we get ( 3W = 2 \times \frac{1}{36} ) which simplifies to ( 3W = \frac{1}{18} ).
Solving for ( W ), we get ( W = \frac{1}{54} ) of the work per day.
Statement (2): "The work done by a woman in a day exceeds twice the work done by a boy in a day."

This can be mathematically expressed as ( W > 2B ).
We know ( W = \frac{1}{54} ), so ( \frac{1}{54} > 2B ).
Solving for ( B ), we get ( B < \frac{1}{108} ) of the work per day.
Now, we evaluate if the boy can complete the work in 54 days:

If ( B = \frac{1}{108} ), then it would take the boy 108 days to complete the work alone (since ( \frac{1}{B} = 108 )).
Given that ( B < \frac{1}{108} ), it will take the boy more than 108 days to complete the work.
Thus, using both statements, we can conclude that the boy cannot complete the work in 54 days, as his rate of work is less than ( \frac{1}{108} ) of the work per day, which is insufficient to complete the work in 54 days.

A man can complete a piece of work in 36days working alone. Can a boy

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GMAT Data Sufficiency (DS) Questions

A man can complete a piece of work in 36days working alone. Can a boy

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