Question

A certain truck uses $\frac{1}{12}+k{v}^2$ gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses 152 gallon of fuel per mile?
(1) The value of k is $110,800$.
(2) When the truck travels at 30 miles per hour, it uses $\frac{1}{6}$ gallon of fuel per mile.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

This problem can be solved by determining the positive value of v so that .

1. This indicates the value of k and so the value of v can be determined by solving for v; Thus, sufficient.
2. This indicates that The value of k can be determined by solving this equation for k. Then that value of k can be substituted into,which can then be solved for the value of v; Thus, sufficient. The correct answer is D; each statement alone is sufficient.