New GRE Math Tips and Tricks

This is a fraction, not a word problem

The new GRE Quantitative section places a greater emphasis on word problems. Here are a couple of good examples of the types of word problems that will be more common on the new GRE.

Problem #1 –   This first problem is a numeric entry problem, one of the new problem types. For these problems, you will not be given multiple choices.  Here is the problem:

The best way to solve a problem like this is to form an equation.  When you’re forming an equation, first identify your unknown or unknowns. Here, the number of gallons is our unknown, so use the variable x to represent that number.

To get to the total bill, we first start with the fixed charge of $13.50.  The charge of $0.0075 is multiplied by the number of gallons, and this amount is added to the fixed charge.  This total will equal the total amount of the bill. As an equation, this looks like the following.

13.50 + 0.0075x = 40.50

To solve for x, first subtract 13.50 from both sides of the equation.

13.50 + 0.0075x – 13.50 = 40.50 – 13.50

0.0075x = 27

Now, divide both sides of the equation by 0.0075. Don’t be afraid to use your calculator for the arithmetic!

0.0075x / 0.0075 = 27 / 0.0075

x = 3600

It wouldn’t hurt to work backwards to quickly double check your answer. Multiply 3600 by 0.0075 and you get 27. (Again, use your calculator.) Add 27 to 13.50 and we have our total of 40.50.

The correct answer is 3600.

Problem #2 –

This next question is a little more difficult, and it demonstrates another of the new GRE question types. For this problem, you will select all of the answers that apply. Remember, you only receive credit for the question if your answer is exactly correct. You must select all of the correct answers and none of the incorrect answers to receive credit.

Again, let’s start by identifying our unknown. Here, the unknown is Kate’s gross income, so we’ll let x represent that income. She spent between 1/3 and 1/4 of her income on mortgage payments. In other words, her mortgage payments will be less than 1/3 of her income but more than 1/4 of her income.  We know the total amount of the mortgage payments was $13,470, so now we can form two inequalities.

13470 < 1/3 x (Mortgage payments are less than 1/3 of income)

13470 > 1/4 x    (Mortgage payments are more than 1/4 of income)

Look at each inequality separately and simplify both of them.

13470 < 1/3 x

Simplify this inequality by multiplying both sides by 3. This will eliminate the 1/3.

13470· 3 < 1/3 x · 3

40410< x

This means that $40,410 is less than the gross income. In other words, the gross income must be greater than $40,410. Now, simplify the second inequality. Here, you will multiply both sides by 4.

13470> 1/4 x

13470· 4 > 1/4 x · 4

53880 > x

This means that the gross income must be less than $53,880.

Since we know that the gross income must be between $40,410 and $53,880, select all of the answers that are between these two numbers. The answer is (B), (C), (D), and (E).