Practice GMAT Problem Solving Question

There are 5,280 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?

Correct Answer: C

We are given two conversion factors and are asked to start with 1 mile and convert it to inches.
The first conversion relates miles to feet: 1 mile = 5,280 ft. Thus, the 1 mile we began with is equivalent to 5,280 feet.
In order to convert from feet to inches, we must set up a conversion ratio. Since 12 in = 1 ft, (12 in)/(1 ft) = 1. Likewise, (1 ft)/(12 in) = 1 since 1ft = 12in.
Taking the 5,280 ft that we have in 1 mile, multiply it by the correct factor of 1, making sure the units cancel correctly:
5,280ft * (12in/1ft) = 5,280(12) in
The equation below aligns the units wrong. Do not make this mistake:
5,280ft * (1ft/12in) = 5,280*1 ft²/in
The first calculation yields the units we are looking for. Thus, the answer is C, 12*5,280.
Another way to think of this problem is to realize that if there are 12 inches in 1 foot and 5280 foot in 1 mile, then:
12 inch = 1 foot
5280 feet = 1 mile
Via substitution:
5280 [12 inches] = 1 mile
5280*12 = 1 mile