Translating Words into Math on the GMAT

GMAT word problems often cause test-takers difficulty. The language usually doesn’t seem straightforward, and deciding how to begin answering the question can be challenging. Kaplan teaches students to think critically and to consider using a strategy such as Picking Numbers rather than always jumping into straight-up math to find the answers to Quantitative Reasoning questions.
Even before deciding whether to use a particular strategy, you need to recognize how to apply the strategy. And for most GMAT word problems, that means “translating” English to math.
 

This translation is often all you need to do to take the first step toward finding the right answer. Before you can begin translating any piece of text, you need to be fluent in both languages.
If a question includes the word equals, you can easily presume that that translates to the = symbol. But you are just as likely to see a question that uses the words “costs” or “weighs.” Identifying when these other words translate to equals will be key to writing a correct equation. Likewise, recognizing phrases that mean greater than or less than will allow you to craft a correct inequality.
Here is a list of common phrases you will encounter in word problems, paired with their mathematical equivalents.


*A good rule of thumb when translating is to choose letters for your variables that make sense in the context of the problem. A person named David could be represented by the variable D or d, and chocolate could be represented by the variable C or c.

Take the following example:
Sarah has five more books than Tina has.
We can begin by assigning the variable S to Sarah’s age and T to Tina’s age. (It wouldn’t be wrong to let Sarah’s age be represented by x and Tina’s by y, but it’s easier to keep them straight with letter-appropriate variables.)

Sarah has five more books than Tina has.

S = 5 + T

You would tackle a more complex, multi-part word problem the same way; just translate words into math piece-by-piece, from left to right, one statement at a time. Let’s look at a test-like example:
Michael is 4 years older than Sam. Jacob is 12 years younger than Michael. Sam is twice as old as Jacob. How old will Jacob be in 4 years?
We begin at the beginning, translating the first statement: Michael is 4 years older than Sam.

Michael is 4 years older than Sam.

M = 4 + S

An equation involving addition is easiest to translate words into math. When the situation involves subtraction, be sure to put the minus symbol before the value being subtracted. For this example, we have to move some items into a different order in the equation than they were given in English:

Jacob is 12 years younger than Michael.

J = M − 12

If we had translated directly, we would have gotten J = 12 − M, which would not be correct. Always check to be sure you have put terms in their proper position.
Let’s move to the third sentence in the word problem: Sam is twice as old as Jacob.

Sam is twice as old as Jacob.

S      =      2J

Translating a word problem into an equation not only allows you to solve algebraically, but also it gives you something with which to Pick Numbers or Backsolve. Here are our three equations:

M = 4 + S

J = M − 12

S = 2J

Now, let’s put the pieces together to solve this problem:
Jacob is 12 years younger than Michael. Michael is 4 years older than Sam. Sam is twice as old as Jacob. How old will Jacob be in 4 years?
A. 8
B. 10
C. 12
D. 14
E. 16
The task in this question is to solve for Jacob’s age in four years. So that is actually another equation we need to translate. The variable J represents Jacob’s age now, so we need to add 4 to it to find his age in 4 years:

How old will Jacob be in 4 years?

? = J + 4

We can set aside the task for the moment and focus on solving for J using the three equations we crafted from the question stem. Because S = 2J, we can use substitution to replace S in the first equation: M = 4 + (2J).
Now we only have two equations, and two variables, so we can either use combination or substitution to solve for J. Let’s substitute this new equation into the second: J = (4  + 2J) − 12.

Now just solve for J:

J = (4  + 2J) − 12

J − 2J = 4 − 12

–J = -8

J = 8

Answer choice A is 8, but remember that Step 4 of the Kaplan Method is to Confirm Your Answer. The question asks us to solve for J + 4, which is answer choice C, 12. Always confirm that you answered the question asked and didn’t translate the problem (and do all the algebra) in vain.