Arithmetic: Translating Percentage Problems

Percentage questions on the GRE often use words and phrases in place of mathematical operators and expressions. To find the answers, just translate the relevant English into the required math. Call this solution strategy translation.

To translate a percentage question, break it down phrase by phrase and swap out words for operators. For instance, replace “is” with an equals sign and “of” with a multiplication sign. Here’s an example problem.

Start with the first part of the question—”if 10 is 2% of z”

is ⇒ =
of ⇒ ×

• If 10 is 2% of z
• If 10 = 0.02 × z
• If 500 = z

You may feel tempted to stop and select (D). Don’t do it! You still need to translate the second part of the question—”what is 50% of z”. You know how to translate “is” and “of”. The word “what” signifies an unknown, so it can be replaced with a variable, such as x. If the problem already uses x, replace “what” with a question. You can also use a question mark even if x isn’t in the problem.

what ⇒ ?

• what is 50% of z
• ? = 0.5 × z

Now, put all the parts together and solve for the unknown.

• ? = 0.5 × z
• z = 500
• ? = 0.5 × 500
• ? = 250
• Thus, (C) is correct.

Some of the more difficult percentage problems will require you to translate the phrase “what percent.” This pair of words points to an unknown percentage, so you’ll translate it into a fraction with a denominator of 100 and an unknown numerator—that is,x100 or ?100. Take a look at this tough question.

The phrase “in terms of s” means you need to set t equal to an expression that includes s. You’ll be able to do so right after you translate the first part of the question—”if s is 2% of t”

• If s is 2% of t
• if s = 0.02 × t

Now solve for t.

• s = 0.02 × t
• s0.02 = t

Next, translate the second part of the question—”what percent of t is 100 in terms of s”

what percent ⇒ ?100

• what percent of t is 100
• ?100 × t = 100

Finally, replace t with its equivalent in terms of s and then solve for the question mark.

• ?100 × s0.02 = 100
• ? × s2 = 100
• ? × s = 200
• ? = 200s
• Thus, (E) is correct

To review, you learned four English-to-Math translations you can use in wordy percentage problems. Here they are again.

1. is ⇒ = (equals)
2. of ⇒ × (times)
3. what ⇒ x or ?
4. what percent ⇒ x100 or ?100

Want more math tips like these? Check out the GRE Quantitative Reasoning Bible! In the meantime, try a few more practice problems.

Answers: 1. C  2. B  3. B