There are 5,280 Feet in 1 Mile and 12 Inches in One Foot 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?

1. 5,280 - 12
2. 5,280/12
3. 12(5,280)
4. 12^2(5,280)
5. 12/5,280

‘There are 5,280 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?' - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”.
To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1

 it is asked How many inches are in a mile?
We are asked to start with one mile and convert it to inches using the two conversion factors provided.
Miles are first converted to feet:
Miles are first converted to feet:
The 1 mile we started with is therefore 5,280 feet long.
We need to put up a conversion ratio in order to convert from feet to inches.
Since 12 in = 1 ft, (12 in)/(1 ft) = 1.
Likewise, (1 ft)/(12 in) = 1
since 1ft = 12in.
In order to ensure that the units cancel out appropriately, multiply the 5,280 ft that we have in a mile by the proper factor of one:
5,280ft * (12in/1ft) = 5,280(12) in
5,280ft * (1ft/12in) = 5,280*1 ft2/in
The units we need are produced by the initial computation.
The answer is C, which is 12 * 5,280.

Correct Answer: C

Approach Solution 2

There is another approach to answering this question which is easier
if there are 12 inches in 1 foot and 5280 foot in 1 mile, this means:

12 inch = 1 foot
5280 feet = 1 mile

When we substitute the values

5280 [12 inches] = 1 mile
5280*12 = 1 mile
The answer is C, which is 12 * 5,280.

Correct Answer: C

Approach Solution 3

The value of 2.5miles expressed to inches is 158,400inches

Given the following conversion factor: 12 inches = 1 foot and 5280 feet = 1 mile

We are to convert 2.5 miles to inches

Case 1, we need to convert to feet

5280 feet = 1 mile

that implies x = 2.5 miles
that implies x = 5280 * 2..5
that implies x = 13200 feet

Case 2, converting 13200feet to inches

Since 12 inches = 1 foot

that implies x = 13200 feet
that implies x = 12 * 13200
that implies x = 158,400 inches

Hence 2.5miles expressed to inches is 158,400inches.
Correct Answer: C

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