Problem Solving

[email protected] wrote:Jane decided to measure a length of fence but discovered that the first x inches of her 50-foot tape measure had broken off. According to the tape measure, the fence measured 10 feet 3 inches. What was the true length of the fence, in feet?

I'm assuming that that this is a "Variables in the Answer Choices" question in which the answer choices consist of variable expressions. If so, it would be useful if you posted the answer choices, since one approach to these questions is testing the answer choices.

Also, as Rahul mentioned, the GMAT won't assume that students know that 12 inches = 1 foot.

That said, let's go ahead and answer the question.

Since part of the tape measure is missing x inches, it will begin at a measurement of x inches. If the tape measure starts at x inches, any measurement will be x inches longer than the true length.

So, the true length = (the tape measure length) - (x inches)
Since our goal is to find the true length in feet, we'll need to convert 10 feet 3 inches and x inches into feet.

Since there are 12 inches in a foot, 10 feet 3 inches = 10 3/12 feet = 10.25 feet

Similarly, x inches = x/12 feet

So, true length = 10.25 feet - x/12 feet
= [spoiler]10.25 - x/12[/spoiler]

IMPORTANT: it's quite possible that the correct answer choice will look different since there are many ways to express 10.25 - x/12 (this is why it's important to post the answer choices)

For example, 10.25 - x/12 = 10 3/12 - x/12
= 123/12 - x/12
= [spoiler](123 - x)/12[/spoiler]
This is another possible answer.

Cheers,
Brent