Problem Solving

Vincen wrote:20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60

Given: 20 workmen can make 35 widgets in 5 days.

If we DOUBLE the number of workmen, then those workmen will make TWICE as many widgets in 5 days.
So, 40 workmen can make 75 widgets in 5 days.

Likewise, If we TRIPLE the number of workmen, then those workmen will make THREE TIMES as many widgets in 5 days.
So, 60 workmen can make 105 widgets in 5 days.

Answer: E

Cheers,
Brent

Hi Vincen,

When dealing with these types of 'work' questions, it can be helpful to think in terms of the total amount of work that needs to be done to complete the given task. We're told that it takes 20 workmen 5 days to complete the task. That's...

(20 men)(5 days each) = 100 work-days of effort to create 35 widgets.

Thus, there are a number of different ways to complete that work:
1 worker can work for 100 days
2 workers can work for 50 days each
4 workers can work for 25 days each
Etc.

The question asks us to create 105 widgets, which is 3 times the 35 in the above calculation. Those 105 widgets would take 3(100) = 300 work-days of effort. If we have to complete the job in 5 days, then we can set up the following equation:

(X men)(5 days each) = 300 work-days

X = 60 men

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Vincen wrote:20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60

We are given that the rate of 20 workmen is 35/5 = 7 widgets per day. We need to determine how many workmen are needed for a rate of 105/5 = 21 widgets per day. We can let x = the number of workman and create the following proportion:

20/7 = x/21

(20)(21) = 7x

(20)(3) = x

60 = x

E