Car z travels 40 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?

30/(0.75), or 40 miles, How do I figure this out without a calculator?

It is always best to avoid using decimals when calculating. Most of the time, the calculations can be carried out with considerably more ease if we convert to fractions. In the latter case we have:

30/(0.75)

It should be obvious to you from your GMAT preparation that the decimal 0.75 is a fraction that should have been committed to memory, namely, 3/4


so we have 30 / (3/4). And, of course, from the rules of dividing fractions we have to multiply 30 by the reciprocal of 3/4, so we have:

30 / 1 x 4/3. Notice we can cancel out the 3 in the denominator of our second fraction and reduce our 30 to a 10, so we have 10/1 x 4/1 = 40.