Problem Solving

Hi Sri,

I'm a big fan of TESTing VALUES, which is the approach that Mitch used to answer this question. There's another way to solve it though that just requires you to know some math concepts...

There are two "logic shortcuts" to this question that can help you to zero-in on the correct answer.

First, we're dealing with "square feet" of a stripe, which implies the area formula for a rectangle (L x W)....

In this case, we have a length of M MILES, so L = M(5280)
We have a width of T INCHES; since we're dealing in SQUARE FEET, we have to convert inches to feet: W = T/12

So, if we just focus on the area, we'll have 5280(M)(T) / 12. Eliminate B, D and E.

Second, we're told that 1 gallon of paint covers P SQUARE FEET. This is "ratio data", so to calculate the number of gallons.....whichever side of the fraction has the area....the other side has the P. This means that the P must be in the denominator. Eliminate C.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

gmattesttaker2 wrote:
A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of p square feet of highway, how many gallons of paint will be needed to paint a stripe t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)

A. (5,280 mt) / (12p)
B. (5,280 pt) / (12m)
C. (5,280 pmt) / 12
D. (5,280)(12m) / (pt)
E. (5,280)(12p) / (mt)

We are given that 1 gallon of paint covers p square feet of highway. Thus, thus the "coverage rate" is:

(p square feet)/(1 gallon)

We need to determine how many gallons are needed to cover a total area of:

(t inches)(m miles)

Converting inches to feet and miles to feet, we have:
(t/12 feet)(5,280m feet) = 5,280mt/12 square feet

Now we can determine how many gallons we need to cover the particular stretch of highway:

gallons needed = area/rate

[5,280mt/12 square feet]/[(p sqaure feet)/(1 gallon)]

5,280mt/12p gallons

Answer: A