Arithmetic and the GMAT

Random pile of colourful plastic lettersThe branch of mathematics dealing with the basic manipulation of numbers is called “arithmetic.” On the GMAT, Arithmetic questions have to do with solving equations and expressions by moving variables from one side of the equation to the other.

Sometimes this involves conversion, or describing one variable in terms of another. Let’s look at an example from the OG:

Temperatures in degrees Celsius (C) can be converted to temperatures in degrees Fahrenheit (F) by the formula F = 9/5*C + 32. What is the temperature at which F = C?

(A) 20°
(B) (32/5)°
(C) 0°
(D) -20°
(E) -40°


The question is asking what is the temperature at which F = C. For this question if, F = C, then wouldn’t F = (9/5)C + 32 be the same thing as C = (9/5)C + 32?
If C = (9/5)C + 32, we can start to simplify by subtracting (9/5)C from both sides.
C – (9/5)C = 32 is the same thing as:
(9/9)C – (9/5)C = 32
(-4/5)C = 32

Let’s multiply both sides by 5:

-4C = 160
C = -40

The correct answer is (E).