Each problem is a variation of the following equation:
(number)(average) = sum.
Q1: (number of units sold)(average price per unit) = revenue.
Q2: (number of hours)(average miles per hour) = distance.
In each case, the goal is to keep the product CONSTANT.
Thus, if one factor on the left is multiplied by x/y, the other factor on the left must be multiplied by y/x, so that the product doesn't change.
Q1. If price decreases by 25%, by what % should consumption increase so that the expenditure does not
increase?
a. 20%
b. 25%
c. 33.33%
d. 40%
e. 75%
To decrease the price by 1/4 is to multiply the price by 3/4.
Thus, to keep the product constant, the number of sales must be multiplied by 4/3 -- an increase of 1/3 = 33.33%.
The correct answer is
C.
Q2. If speed increases by 33.33%, what is the percent reduction in the time taken to travel the same
distance?
a. 20%
b. 25%
c. 33.33%
d. 66.66%
e. 75%
To increase the speed by 1/3 is to multiply the speed by 4/3.
Thus, to keep the product constant, the time must be multiplied by 3/4 -- a decrease of 1/4 = 25%.
The correct answer is
B.
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