Problem: Of the following statements, the only one that is incorrect is:
Answer Choices:
A. An inequality will remain true after each side is increased, decreased, multiplied or divided (zero excluded) by the same positive quantity.
B. The arithmetic mean of two unequal positive quantities is greater than their geometric mean.
C. If the sum of two positive quantities is given, their product is largest when they are equal.
D. If and are positive and unequal, is greater than .
E. If the product of two positive quantities is given, their sum is greatest when they are equal.
Solution:
(E) is incorrect because, when the product of two positive quantities is given, their sum is least when they are equal. To prove this, let one of the numbers be ; then the other number can be written ( may be negative). Then if ,
which has its least value when .