For those of you who didn’t know, the GRE does not allow a calculator. So, if you haven’t done math by hand for a while, you may have forgotten how to do many simple calculations. Here are some tips that will help you do math by hand quickly and accurately. While these tips will help you on the entire test, you’ll get the most out of them on the quantitative comparison section.
1. Cross-multiply two fractions to compare them.
The numerator with the larger product will belong to the larger fraction:
Example 1: 4 / 5 vs. 8 / 11
Which fraction is bigger? I could change both to decimals, but let’s try the cross-multiply method, which is much faster.
(4)(11)= 44 and (8)(5)= 40
44 is the larger product. Since the product involved 4, which is the numerator of 4/5, 4/5 is the bigger fraction.
2. Squaring a fraction or decimal between 0 and 1 will make the number smaller.
Example 2: (1/3)² = 1/9
While this tip is very simple to prove, it’s crucial that you keep it in mind during the quantitative comparison section so that you can avoid unnecessary calculation.
3. Taking the square root of a fraction or decimal between 0 and 1 will make the number larger.
Example 3: √(¼) = ½
4. Memorize these two formulas for dealing with division:
a) (1/x) / y = 1 / xy
b) 1 / (x/y) = y / x
Students often fumble the calculations when presented with multiple layers of division or fractions. These simple formulas should keep you on track.
Example 4a: 1/2 / 3 = (½)(1/3)=1/6
Example 4b: 1 / 2/3 = 3/2
5. In order to find a percentage increase, find the difference between the original number and the increased (or decreased) number and divide that by the original number.
Example 5: A pair of pants was selling for $20 last week, but now is selling for $27 this week. By what percent did the price of the pants increase?
27 – 20 = 7
7 / 20 = 35 / 100 = 35 percent
The GRE will often provide you with a simple method for solving a problem that will not be obvious. The challenge lies in finding the simplest method. Notice how the above problem was solved a lot faster by subtracting the equation than by solving for the variables.
Example 6: if 4x+2y=23 and 3x+3y=22, then x- y =
Set up the equations like you see below, and see if adding or subtracting will help you arrive at the answer more quickly. In this case, subtraction will do the trick.
4x + 2y = 23
– (3x+ 3y = 22)
x- y = 1.