Bunuel wrote:

How many of the 400 students in the 11th grade will take calculus?

(1) 40 % of the students at the school take calculus.

(2) 80% of the 11th graders do not take calculus.

Kudos for a correct solution.

PRINCETON REVIEW OFFICIAL SOLUTION:So, what are we looking at here? What do we need to find out?

The key words in this question are “How many”? We are looking to determine an exact value. If we were looking to do this as a multiple-choice question we would be well on the way to figuring this out. Let’s see, 40% of the school takes calculus, but I don’t know the total. How can I get the total? I can’t. What other information do I have? You would be embarking on a trip that you don’t need to go on.

This question requires you to determine a value. It would be the number of students taking calculus. Therefore, you must ask yourself whether the information given to you will get you to a value. YOU DO NOT NEED TO FIND THE VALUE.

Let’s look at the question. You are given the information that there are 400 students in the 11th grade. From this you should be thinking that if you knew how many weren’t taking it, or a percent of 11th graders that were or weren’t taking it, then you could get to the answer.

Moving to the information in number (1), 40% of the students at the school take calculus. Unfortunately, the 40% figure deals with the entire school population and you do not know anything about the individual distribution within grades. Not enough information to resolve. For those of you familiar with the AD/BCE split technology, at this point you would exclude both A and D as answer choices because (1) will not be sufficient. If we knew that it was 40% of every grade, then that would be a different story.

Moving to number (2), we see that 80% do not take calculus. We’re done at this point, and (B) is the right answer. But wait, we didn’t get the answer! Don’t waste your time to figure out the number. However for the sake of completeness, we would therefore know that 20% of the 11th graders took calculus. So, 400 x 20% = 80. This is a real answer that satisfies our requirement to know how many students in the 11th grade take calculus.

A couple of other points – be careful when you move from eliminating (1) and going to (2). When you do that, you must remind yourself that the information in (1) is currently not available. The only time to use both pieces of information is when neither works individually. You need to be really careful. This is the point when you must use both pieces of information to resolve whether you have enough to answer the question.

What have we learned today? It is important to be aware of the type of question you are working on and be able to put on the right thinking cap. You will need to be able to effortlessly glide between the different types of question. Therefore, as you are moving to the next question, pause for just a second to get a sense of the question and then attack!

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