When a question offers multiple bits of information, starting with the last piece can often be a way of dramatically simplifying the problem.
Take the following problem:
Mary’s income is 60 percent more than Tim’s income, and Tim’s income is 40% less than Juan’s income. What percent of Juan’s income is Mary’s income?
A) 124%
B) 120%
C) 96%
D) 80%
E) 64%
The last person mentioned here is Juan, so let’s call Juan’s income $100. She then knocked out the remaining calculations in about 30 seconds. If Juan’s income is $100, and Tim’s income is 40% less than Juan’s, than Tim’s income would be $60. And if Tim’s income is $60, and Mary’s income is 60% more than Tim’s, Mary’s income would be 60 + 60% of 60 = 60 + 36 = 96. (Or 1.6 * 60 = 96.) If Mary’s income is $96 and Juan’s is $100, then clearly, Mary’s income is 96% of Juan’s, and the answer is C.
Let’s try it again on another question:
In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. (mypatraining.com) If 5000 have been vaccinated against both, how many have been vaccinated only against rubella?
A) 2500
B) 7500
C) 10000
D) 15000
E) 17500
First, note that this is a classic overlapping sets questions, so let’s set up a simple matrix:
But now, let’s start by inserting the last piece of information we’re given. 5000 have been vaccinated against both, so that goes in the Mumps/Rubella Vaccine cell. Now we’ve got:
Next, we’ll work backwards. We’re told that the number that have been vaccinated against both (5000) is twice the number that have been vaccinated against only mumps. So the number that have been vaccinated against only mumps must be 2500. Now our table looks like this:
Now we know that 7500 people have been vaccinated against Mumps. Last, we’re told that the number vaccinated against Rubella is twice the number that have been vaccinated against Mumps, which means that 15,000 people have been vaccinated against Rubella. If 15,000 total have been vaccinated against Rubella, and 5000 of those have been vaccinated against both, then, according to our table, 10,000 have been vaccinated against only Rubella. So C is our answer.
Takeaway: The question writer is going to provide information to you in a very strategic way. If the most useful piece of info comes at the end of a lengthier question, the question will be harder if you start at the beginning. It may ruin the suspense, but as a consolation, you’re more likely to get the question right.
