ISEE Mathematics Achievement Question 323: Answer and Explanation

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Question: 323

7. If 70x + 33y = 4,233, and x and y are positive integers, x could be which of the following values?

  • A. 42
  • B. 47
  • C. 55
  • D. 60

Correct Answer: D

Explanation:

D 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 a possible value of x. So, Plug In for x and see if there is an integer that would work to make the rest of the equation balance. Start with one of the middle choices. Try (C): if x = 55, then 70(55) = 3,850. Solve the rest of the equation: 3,850 + 33y = 4,233 to see if y is an integer. Subtract 3,850 from both sides to find that 33y = 383. You can try dividing, but you could also ballpark. 33 × 11 = 363 and 33 × 12 = 396, so 383 is not divisible by 33. Therefore, eliminate (C) and try another choice. Try (D): 70(60) + 33y = 4,233 simplifies to 4,200 + 33y = 4,233. Subtract 4,200 from both sides to find that 33y = 33. Divide each side by 33 to find that y = 1. 1 is an integer, so this satisfies the question. The correct answer is (D).

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