PSAT Math Grid-Ins Practice Test 17

1. The table below shows the number of applications and the number of admissions to a particular college at the end of each calendar year.

During one year between 1980 and 2000, the college started to accept the Common Application and also began offering early decision to its applicants. The Common Application allows students to use the same application to apply to multiple schools, making applying easier. Early decision gives students the opportunity to apply early for admission. If accepted, though, students must commit to go to the school. The college made these two changes to encourage more students to apply and to enable the school to admit only students who were really committed to attending, thus helping the college's application yield (i.e., the number of students admitted who actually attend). These factors resulted in an overall increase in the selectivity of the college. In what year did the college most likely first implement these policies?

2. A certain cube has edges of length L inches, surface area of A square inches, and volume of B cubic inches. For what value of L would
A = B?

3. If (a, b) is a solution to the system of equations below, what is the value of a?

2a - b = 4

3a + b = 6

4. A currency conversion store at an airport in New York City posts the following conversion rate table.

The conversion store charges 1 percent of the amount converted plus a $2 flat fee for each total transaction (including multiple-currency exchanges as long as they take place in a single visit to the store). The flat fee is assessed in addition to the 1 percent conversion fee.

Suppose a customer wanted to see the conversion rate, before doing a transaction or paying any associated fees, of U.S. dollars to Australian dollars. What is the conversion rate of U.S. dollars to 1 Australian Dollar to the nearest hundredth?

5. A currency conversion store at an airport in New York City posts the following conversion rate table.

The conversion store charges 1 percent of the amount converted plus a $2 flat fee for each total transaction (including multiple-currency exchanges as long as they take place in a single visit to the store). The flat fee is assessed in addition to the 1 percent conversion fee.

Andrew has come back to the United States from a trip to Asia and wishes to convert 700 Japanese yen and 900 Indian rupees. If he converts them to U.S. dollars at the airport currency store, how many U.S. dollars will he have from this conversion after the store transaction is complete to the nearest tenth of a dollar? (Ignore the dollar sign when gridding in your answer.)

6. A high school is going to have its prom and is evaluating two different D.J.s—D.J. A and D.J. B. The first one, D.J. A, has a $300 rental fee and charges $150 per hour. The second one, D.J. B, has a $200 rental fee and charges $175 per hour. After how many hours of performing will the cost for both D.J.s be the same?

7. Marcus completely filled his truck's 14-gallon gas tank. The computer at the gas pump indicates that Marcus spent $34 in this transaction; the price per gallon was $3. How many gallons of gas did Marcus have in his tank before he started to fill it?

8. A lamp business uses the following equations to express supply and demand as a function of price and quantity for its lamps:

Supply: Price = 30 - Quantity

Demand: Price = 10 + 3 × Quantity

How many lamps does the business need to sell in order for the supply of lamps to equal the demand for lamps exactly, i.e., for the supply and demand to be at equilibrium?

9. What is the value of the smallest side in a right triangle with a hypotenuse of 8 and angles of 30 and 60 degrees?