Overview of GRE Math
Translating word problems into basic equations in GRE math
Many times on the GRE you will be asked to transfer lines of text into basic equations. This is one of the most fundamental algebra skills.
Look at the following question from the Economist’s question bank:
In a research and development department, 14 workers have a PhD, and 30 workers don't have a PhD degree. In the department, the number of women that do not have a PhD degree is 10 greater than the number of women who do have a PhD. If a third of the men working in the department have a PhD degree, then how many women work in the department?
This is a sets problem and a table will make things easier.
Let x = the number of women who have a PhD.
Let y = the total number of men who work in the department.
The table thus becomes:
The box marked with the red question mark is the one we want to fill in with our answer.
The table is an addition table, so you can add horizontally and vertically. Set up two simultaneous equations:
1) x + x + 10 = 44 – y
→ 2x + 10 = 44 – y
→ 2x + y = 34
2) x + y/3 = 14
→ 3x + y = 42
Put these two equations together and solve them simultaneously:
(1) 2x + y = 34
(2) 3x + y = 42
Subtract equation (1) from equation (2)
x = 8
x represents the number of women with a PhD. The number without a PhD is x + 10 = 18. The total number of women in the department is therefore 8 + 18 = 26. Therefore, answer choice C is correct.
Here we see the value of being able to transfer lines of text into equations. Solving simultaneous equations is an important part of GRE math.