PSAT Math Grid-Ins Practice Test 5

1. A certain box has a width that is 2 inches more than its length and a height that is 5 inches less than its length. If each of the two smallest faces of the box has an area of 36 square inches, what is the volume of the box?

2. 5x - 3y = 7

2x + y = 5

If (x, y) is the solution to the system of equations above, what is the value of y?

3. In a certain marathon, 45 percent of the runners were men and the rest were women. The official timekeeper determined that 64 percent of the men and 68 percent of the women completed the marathon in under four hours.

What percent of the runners who completed the marathon in under four hours were women? (Ignore the percent symbol when entering your answer. For example, if the answer is 35.2%, enter 35.2.)

4. In a certain marathon, 45 percent of the runners were men and the rest were women. The official timekeeper determined that 64 percent of the men and 68 percent of the women completed the marathon in under four hours.

What percent of the runners completed the marathon in under four hours? (Ignore the percent symbol when entering your answer. For example, if the answer is 35.2%, enter 35.2.)

5. y = x + 8

y = x² - x - 7

If (x, y) is a solution to the equations above, what is one possible value for the sum of x and y?

6.

A jewelry supply store sells boxes of sheet metal for gold and platinum at the weights and prices listed in the table above. A jeweler wants to purchase at least 90 ounces of metal and plans to spend at least $170,000. If she has already ordered 10 boxes of gold, what is the minimum number of boxes of platinum she can order to satisfy the requirements?

7.

The graph above shows the amount of time, in hours, that Robert spends jogging in each month through a particular year. The information for the month of December is not included in the graph.

In November, Robert jogged at an average pace of 8 miles per hour. In December, Robert ran for h hours at an average pace of 7 miles per hour. If the total distance that Robert jogged each of the two months was the same, what is the value of h?

8.

The graph above shows the amount of time, in hours, that Robert spends jogging in each month through a particular year. The information for the month of December is not included in the graph.

In June, Robert ran at a pace of 5 miles per hour at the beginning of the month before he increased in pace to 6 miles per hour toward the end of the month. If he spent 70% of this jogging time at the slower pace, and the rest at the faster pace, what is the total distance, in miles that Robert jogged during the month of June?