Problem 22 · 2012 Math Kangaroo
Stretch
Algebra & Patterns
work-backward
Michael thought of a number. He multiplied this number by itself, added 1, multiplied the result by 10, added 3, and multiplied the total by 4. He arrived at 2012. Which number had Michael thought of to start with?
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Answer: D — 7
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Hint 1 of 2
Undo each step that led to 2012, working from the last operation back to the first.
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Hint 2 of 2
Divide by 4, subtract 3, divide by 10, subtract 1, then take the square root.
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Approach: reverse the operations
- He finished at 2012; undo 'x4' to get 2012 / 4 = 503.
- Undo '+3' to get 500, then undo 'x10' to get 50, then undo '+1' to get 49.
- 49 came from the number times itself, so the number is the square root: 7.
- He started with 7.
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