In studying for the GMAT, we often come across a strategy for how to handle complex questions – simplify them until they become a problem that we know how to solve. But how exactly does one simplify a complicated GMAT question? Let’s try to understand this with an example today:
Twenty-four men can complete a job in sixteen days. Thirty-two women can complete the same job in twenty-four days. Sixteen men and sixteen women started working on the job for twelve days. How many more men must be added to complete the job in 2 days?
Here, we are dealing with two groups of people: men and women. These two groups have different rates of completing a job. We are also told that a certain number of men and women do a part of the job, and we are asked to find the number of additional “men” required to finish the job in a shorter amount of time.
Recall that we have already come across questions where workers start some work and then more workers join in to complete the work before time.
The problem with this question is that we have two types of workers, not just one. So let’s try to simplify the question to a form that we know how to easily solve.
We’ll start by finding the relation between the rate of work done by men and the rate of work done by women. Let’s make the number of men and women the same to find the number of days it will take each group to complete 1 job.
Given: 24 men complete 1 job in 16 days
Given: 32 women complete 1 job in 24 days
So how many days will 24 women take to complete 1 work? (Why 24 women? Because we know how many days 24 men take)
We know how to solve this problem. (It has already been discussed in a past post).
32 women ……………. 1 work ………………. 24 days
24 women ……………. 1 work ………………. ?? days
No. of days taken = 24 * (32/24) = 32 days
Now this is what we have: 24 men take 16 days while 24 women take 32 days
So women take twice the time taken by men to do the same work (32 days vs 16 days). This means the rate of work of women is half the rate of work of men. This means 2 women are equivalent to 1 man i.e. 2 women will do the same work as 1 man does in the same time.
So now, let us replace all women by men so that we have only one type of worker.
Now this is our regular work rate question –
Given: 24 men complete the work in 16 days
Given: 16 men and 16 women work for 12 days
This means that we have 16 men and 8 men work for 12 days
which implies 24 men work for 12 days
We know that 24 men complete the work in 16 days. If they work for 12 days, there are 4 more days to go. But the work has to be completed in 2 days.
24 men …………… 4 days
?? men ……………. 2 days
No of men needed = 24 * (4/2) = 48
So we need 24 additional men to complete the work in 2 days.
Or looking at it another way, 24 men need 16 days to complete the work, so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men.
Basically, the question involved solving two smaller work-rate problems. Doesn’t seem daunting now, right?
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!