Problem 6 · 2022 Math Kangaroo
Medium
Algebra & Patterns
substitution
I am smaller than my half and bigger than my double. The sum of me and my square is 0. Which number am I?
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Answer: B — −1
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Hint 1 of 2
Turn 'sum of me and my square is 0' into an equation and factor.
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Hint 2 of 2
Then check the two roots against 'smaller than my half' and 'bigger than my double'.
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Approach: solve x + x^2 = 0 and test the conditions
- x + x^2 = 0 gives x(x+1) = 0, so x = 0 or x = -1.
- x = 0 fails 'smaller than my half' (0 is not less than 0).
- x = -1: half is -0.5 and double is -2, and -2 < -1 < -0.5 works.
- So the number is -1.
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