ISEE Word Problems Question 178: Answer and Explanation

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Question: 178

9. The square of a positive number minus the number equals 72. What is the value of the number?

A. 8
B. 9
C. 10
D. 11

Correct Answer: B

Explanation:

The answer is B

Write the equation: x² - x = 72. Subtract 72 from both sides: x² - x - 72 = 0. Factor the left-hand side: (x + 8)(x - 9) = 0. Thus, x = 9 or -8. As the question indicated that x is a positive number, x = 9.

You may not have learned how to factor a quadratic yet. Even so, this question designed for older ISEE students is solvable if you test the answers. Start with choice (B) or (C). If you start with 10, you get 100 - 10 = 90, which is greater than 72. Eliminate choices (C) and (D). Now try 9: 81 - 9 = 72.

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