The GRE is unlikely to give you a simple algebraic equation to solve like:
3a
2
=
10?
The GRE never asks questions that are simple and straightforward. Instead, expect questions that require you to convert complex written statements into variables:
If you tripled Adam's age, he would be double Frank's age. Frank is currently 10 years old.
This question translates into:
3a
2
=
10
You have to painstakingly convert the written language into your own algebraic equation. It is easy to make errors here, just be sure to double check yourself by Plugging In your solution or Backsolving from the answer choices.
Word Problems with Undefined Variables
These questions typically ask for increases or decreases in a given amount without any specificity.
800score Tip Many algebra word problems contain several variables and it is helpful on these questions to track the variables by using names that correspond to the items in the question.
For example, if the question is about John, use the variable "j " so that you don't get confused.
How to translate GRESpeak into equations:
Example
Word
What to do?
As equation
The sum of John's age and Steven's is 19.
sum
Addition
j + s = 19
The difference between Todd, the older brother, and Sandra, the younger sister, is 5 years.
difference
Subtraction. Note that Todd is older, so it is Todd minus Sandra.
t - s = 5
The product of my age and 12 is 144.
product
Multiplication
a × 12 = 144
The difference between Todd's age and Sandra's age is 5 years.
difference
Subtraction & absolute value (you don't know who is older).
|t - s| = 5
Six less than my age is 22.
less than
Subtraction
a - 6 = 22
The total of my pocket change and 10 dollars is $11.33.
total
Addition
c + 10 = 11.43
10 more than my age equals 23.
more than
Addition
10 + y = 23
Four times my age is 48.
times
Multiplication
4 × y = 48
Much of the challenge in this word problem translation process is not injecting errors. Plug In(picking numbers) and Backsolving are integral to most algebra problems of this sort. These techniques allow you to check your conversion to make sure it is valid.
Example (easy)
Steven is 12 years older than Mary. 3 years ago, Steven was 5 times as old as Mary.
How old is Mary?
Solution
Mary's age = m
Steven's age = s
Translate the GRESpeak
Translation
Statement
s = 12 + m
Steven is 12 years older than Mary
s - 3 = 5(m - 3) s - 3 = 5m - 15
s = 5m - 12
3 years ago, Steven was 5 times as old as Mary.
12 + m = 5m - 12
m = 5m - 24
-4m = -24
m = 6
Now we have two equations, simply solve:
Substitute s = 12 + m for s in the equation s = 5m - 12
Mary is 6 years old
Example (medium)
Ethan is as much older than Harry as Harry is older than Candice. Five years ago Ethan's age was double what the age difference between what his and Harry's will be 15 years from now. How old is Candice?
Solution
Ethan's age = e
Harry's age = h Candice's age = c
Translate the GRESpeak
Translation
Statement
e - h = h - c
First Statement: Ethan is as much older than Harry as Harry is older than Candice
e - 5 = 2[(e +15) - (h +15)]
Second Statement: Five years ago Ethan's age was double what the age difference between what his (Ethan) and Harry's will be 15 years from now.
e - 5 = 2[(e +15) - (h +15)] e - 5 = 2[(e +15 - h -15)]
Now we have two equations, simply solve.
e - 5 = 2(e - h)
The +15 and -15 cancel each other out.
e - 5 = 2e - 2h
Distribute 2(e - h)
-e = -2h + 5
subtract 2e to both sides and +5 to isolate e
e = 2h - 5
multiply both sides by -1
e - h = h - c
e = 2h - c
Set the first statement equal to e by adding h to each side.
