A lot of GMAT students have trouble with algebraic translation. This can be a huge detriment to someone’s score, because turning words into algebraic equations is a key component of many GMAT questions. However, it doesn’t have to be as difficult as it seems.
The key to algebraic translation is to break everything down into as simple of an equation as possible. A lot of people get tripped up, because they try to combine equations too soon and then they get confused. The key to algebraic translation is to take each piece and make it into its own equation, then work to put those equations together. If the pieces are written as algebraic equations, it’s much easier to see how they fit together.
Let’s look at an example:
There are three women in a certain book club: Vicky, Rosie and Ashley. Of the three, Vicky is the oldest. The difference between Vicky and Ashley’s ages is two times the difference between Vicky and Rosie’s ages. If Rosie is 27 years old, what is the average age of the women in the book club?
At first, this problem might seem unsolvable. How can we know the average of the three women if we only know one of their ages? However, let’s break it down sentence by sentence and see what we can find out.
The first sentence “There are three women in a certain book club: Vicky, Rosie and Ashley,” tells us there are three women in a book club. We can represent it like this:
Book Club= Vicky+Rosie+Ashley
Then, we learn that, “Of the three, Vicky is the oldest.” If we use V, R and A to represent their ages, we know that:
V>R and V>A
The third sentence is where it gets trickery, but we can translate “The difference between Vicky and Ashley’s ages is two times the difference between Vicky and Rosie’s ages,” into:
This is because we know that Vicky is the oldest. So if we subtract Ashley’s age from Vicky’s age, we will get twice the difference between Rosie’s age and Vicky’s age, which is represented as “V-R” because Vicky is the oldest.
We can then multiply out this equation to get:
We can actually isolate V by adding 2R to both sides and then subtracting V from both sides to get:
We then learn that Rosie’s age is 27, so the equation can also be:
This isn’t enough information to solve for the average yet, so let’s move on.
The final answer we want is the value of the average of the three ages, which can be represented algebraically as:
We can substitute 2R-A for V in that equation, which gives us:
Which simplifies to:
3R/3 or simply R
Thus, we know that Rosie’s age is equal to the average of the three ages. Thus the average age of the three women is 27.
If we tried to combine those equations in our head, before writing them down, then we would have had a lot of trouble. However, once we wrote the equations down, it was easy to see how they fit together and how we could use them to solve our problem.