Sample PSAT Questions---Math3--Grid-ins

kmngUID: 46975

question 6 of 7

The sum of r and p is equal to twice s, and p is 36 less than twice the sum of r and s. What is the value of r ?
(from the October 12, 1999 test)

kmngUID: 46975

Correct Answer: 12
Explanation: The phrase "the sum of r and p is equal to twice s" can be written as r + p = 2s. The phrase "p is 36 less than twice the sum of r and s" can be written as p = 2(r + s) - 36. From the first equation, p = 2s - r. Substituting this expression for p into the second equation yields

2s - r = 2(r + s) - 36

2s - r = 2r + 2s - 36

-r = 2r - 36

-3r = -36

r = 12

The value of r is 12.

kmngUID: 46975

question 7 of 7

RESULTS OF AN ELECTION  Candidate   Number of Votes  
X 7,400
Y 2,375
Z 5,250

The results for three candidates in an election are shown in the table above. If each voter voted for exactly one candidate, what is the fewest number of voters who would have had to vote differently in order for Candidate Z to have received more votes than Candidate X?

(from the October 16, 1999 test)

kmngUID: 46975

Correct Answer: 1076
Explanation: For this question, let k be the number of voters who changed their vote. Since you want to make k as small as possible, the k voters should come from those who voted for Candidate X. To determine an answer to the problem, you would need to solve the inequality 5,250 + k > 7,400 - k. Solving this inequality yields 2k > 2150 or k > 1075. Therefore, 1,076 voters who had voted for Candidate X would have to change their vote and vote for Candidate Z in order for Candidate Z to receive more votes than Candidate X. The correct answer to this question is 1076.

kmngUID: 46975

Grid-ins (student-produced response questions) require you to solve the problem and enter your answer by marking the ovals in the special grid.