Percents

Link of the Day

One of the best ways to improve your SAT essay score is to begin looking for links between ideas.  Even though you don’t know what the SAT essay will be about, it will be broad enough to relate to news articles and books that you are reading now.  Practice looking for themes in this article about Iranian hostages who were just recently released.  You should be able to list the themes: family, politics, government, individuals, beliefs, and many more.  As soon as you see an essay question relating to any of these themes, you can use the facts from this article as an excellent example in support of your thesis.  If you choose to use this as one of your 5 prepared current events, make a list of all the facts you can use.

Arithmetic: Percents

Read the following SAT test question and then select the correct answer. 

Always read math questions carefully so that you can absorb all the information and avoid mistakes.  Identify the bottom line, what the question is asking you to find, and assess your options for reaching that bottom line.  Choose the most efficient method to attack the problem.  When you have an answer, loop back to verify that the answer matches the bottom line and you have finished all the steps in the problem.

If p percent of 75 is greater than 75, which of the following must be true?

Bottom Line: p = ?

Assess your Options:  It is often tempting to look down at the answer choices before you need them, but they could mislead you since most of them are wrong!.  You could take numbers that fit each answer choice and see if they give you a number greater than 75.  However, by applying what you know about percents, you can solve the problem much faster than you can by trying out 5 different numbers.

Attack the Problem:  There are a number of ways to think about percentages: as percents, decimals, numbers out of a hundred, parts of wholes….  The list continues.  Here is one of the fastest ways to think about the problem:

If you have one hundred percent of something, you have all of it.  So 100% of 75 is going to be 75.  If you want a result that is greater than 75, you are going to need more than 100% of 75.  Therefore, p must be bigger than 100.

Or, if you normally think about percents in terms of decimals, you know that 50% of something is .5.  In order to get a decimal from a percent, you had to move the decimal twice to the left.  So with 100%: 75 × 1.00 = 75.  Try writing an inequality to find the decimal that you would need in order to get a number bigger than 75: 75p > 75.  The p represents the unknown percent of 75 (remember, "of" means multiplication in math).  If you solve the inequality, you get p > 1.  Then you have to move the decimal back in order to get a percent: p > 100.  Your percent must be bigger than 100%.  This method takes much longer than the first one, but it proves that the first method is correct.  The testers realize that students are not used to working with percentages greater than 100, so it is a good idea to review how these work before the test!

Loop back:  You know what p must be greater than, so look down at your answer choices.

(A) p > 100

(B) p < 75

(C) p = 75

(D) p < 25

(E) p = 25

The correct answer is (A).

On sat.collegeboard.org, 71% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!