ISEE Mathematics Achievement Question 321: Answer and Explanation

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Question: 321

5. Victor, Jonathan, and Russell buy a home theater system. Victor pays twice as much as Jonathan, and Victor pays half as much Russell. If the home theater system costs $560, how much does Jonathan pay?

  • A. $60
  • B. $80
  • C. $100
  • D. $120

Correct Answer: B

Explanation:

B The question is asking for a specific value and there are real numbers in the choices, so use PITA to solve. The question asks for how much Jonathan paid, so label the choices as such and create 2 additional columns next to it, one labeled as Victor and the other as Russell. Now, test the choices and follow instructions from the question stem, starting with (C). Choice (C) means that Jonathan paid $100. The question states that Victor paid twice as much as Jonathan, so Victor paid 100 × 2 = 200. The question then states that Victor paid half as much as Russell, so Russell paid twice as much as Victor: 200 × 2 = 400. Find the total: $100 + $200 + $400 = $700, which is too much, so eliminate (C) and (D). Try (B): if Jonathan paid $80, then Victor paid 80 × 2 = 160, and Russell paid 160 × 2 = 320. Find the total: $80 + $160 + $320 = $560, which is the amount stated in the question. The correct answer is (B).

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