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Sample PSAT Questions---Math3--Grid-ins [复制链接]

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Pisces双鱼座 荣誉版主

发表于 2002-10-4 20:41:59 |显示全部楼层
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)

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Pisces双鱼座 荣誉版主

发表于 2002-10-4 20:42:48 |显示全部楼层
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.

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Pisces双鱼座 荣誉版主

发表于 2002-10-4 20:43:37 |显示全部楼层
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)

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Pisces双鱼座 荣誉版主

发表于 2002-10-4 20:45:08 |显示全部楼层
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.

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Pisces双鱼座 荣誉版主

发表于 2002-10-4 20:46:06 |显示全部楼层

Directions:

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

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RE: Sample PSAT Questions---Math3--Grid-ins [修改]

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