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GMAT Tips – Sample Problem: Algebraic Translation

Today’s GMAT Tip comes to us from Kaplan. In this article, Kaplan GMAT instructor Bret Ruber provides helpful advice on how to turn word problems into equations:

As you may have noticed in prepping for the GMAT, in many cases the challenges you face in GMAT problems are less about the specific math skills, and more about translating word problems into mathematical equations in a fast and efficient way.   Figuring out quickly HOW to approach the problem is one of the key skills the GMAT is testing (and, incidentally, a key skill in the business world as well).  Try this typical word problem translation question, and be sure to practice GMAT-style word problems frequently, in addition to just practicing algebraic skills.

Problem:

Jacob is now 12 years younger than Michael.  If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?

(A) 3

(B) 7

(C) 15

(D) 21

(E) 25

Solution:

The first step to answering this question is translating the information in the problem into equations.  If Jacob is 12 years younger than Michael, we can say that J = M – 12, where J is Jacob’s age and M is Michael’s age.

The second equation is a bit trickier to determine.  You must keep in mind that it refers to the relationship between their ages in 9 years.  Thus, Jacob will be J + 9 years old and Michael will be M + 9 years old.  The equation we can then write if Michael will be twice as old as Jacob in 9 years is M + 9 = 2(J + 9).

Because the question wants us to solve for Jacob’s age in 4 years, we should next rewrite our first equation as M = J + 12.  This allows us to substitute J + 12 for M in the second equation, which becomes (J + 12) + 9 = 2(J + 9).  Then solve for J as follows:

J + 12 + 9 = 2(J + 9)

J + 21 = 2J + 18

3 = J.

However, you must remember that the question asks for Jacob’s age in 4 years.  Since Jacob is 3 years old today, we know that he will be 7 years old in 4 years.  Thus, the correct answer is choice (B).

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