Word problems notoriously cause students stress and anxiety on the SAT. Since the test makers know this, you should plan to see them frequently, especially in questions involving percentages. But there are a couple of strategies to help you conquer your fears and attack percentage problems successfully.
The best solution strategy for word problems is translation. To use translation, first convert words to math symbols. Then break down the question phrase by phrase.
Let’s consider an example:
If 10 is 2% of z, what is 50% of z ?
Start with the first part of the question—if 10 is 2% of z—and translate it into math symbols. Think back to what you know about the basics of translation:
of = multiply
is = equals
Every time you see the word “of” in your problem, use a multiplication sign (X).
Every time you see the word “is” use an equals sign (=).
if 10 is 2% of z
10 = 0.02 x z
You now have a mathematical sentence, and can solve for z:
10 = 0.02 X z
10/0.02 = (0.02 x z)/0.02
500 = z
Some students stop here and select answer choice (D). Wrong answer! Remember, we have only translated the first half of the question.
Now you must attack the second part—what is 50% of z? Another basic translation code is the word what. If there is no x variable in the problem, you can make what = x. But if x is already used, then you must give what another symbol. We recommend using a question mark to avoid confusion. For example:
what is 50% of z
? = 0.50 X z
In the first part of the question, we found that z = 500. Using this information, solve for the question mark:
? = 0.50 X 500
? = 250
The correct answer is (C), 250.
Most percentage problems like this one are considered Easy difficulty level. However, the test makers can boost the difficulty by changing what to what percent in a word problem. Whereas what = ?, what percent = . If you can remember this simple translation, you can easily score points on more difficult questions.
Let’s examine a Hard level question using what percent:
If s is 2% of t, what percent of t is 100 in terms of s ?
Don’t let the expression in terms of s throw you; this simply means that s will appear in the answer choices. We recommend that you cross this phrase out so that you are left with what percent of t is 100.
As with the previous problem, let’s start with the first half of the question:
s is 2% of t
s = 0.02 X t
Since we are solving in terms of s, find t:
Now move to the second half of the question. Remember to use when translating what percent.
And now solve for the question mark:
The correct answer is (E).
Translation is a good solution strategy for students who find percentage word problems confusing or worrisome. Remember to use a multiplication sign for of and for what percent.
Need more help? Check out the other seven PowerScore Solution Strategies in the SAT Math Bible.
PowerScore Practice Prep:
Can you solve the following math questions?