ISEE Word Problems Question 251: Answer and Explanation

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Question: 251

15. In the formula z = , x > 0, and y > 0. If one of the three variables does not change, which of the following is true?

  • A. as x decreases, z increases
  • B. as x increases, z decreases
  • C. as y decreases, z increases
  • D. as y increases, z increases

Correct Answer: C

Explanation:

The answer is C

To maintain balance when only two variables change: (1) as x increases, y must increase by the same factor or z must increase by the same factor, (2) as y increases, x must increase by the same factor or z must decrease by the same factor, or (3) as z increases, x must increase by the same factor or y must decrease by the same factor. Only choice (C) is consistent with these principles.

Plug in numbers for x, y, and z, making sure the equation balances, such as x = 12, y = 2, and z = 3. Now test each answer choice. For choice (A), if x is decreased to 6, z decreases. For choice (B), if x is increased to 18, z increases. For choice (C), if y is decreased to 1, z increases. For choice (D), if y is increased to 4, z decreases. Thus, choices (A), (B), and (D) fail

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