Maths Olympiad Prep

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Algebra Difficulty 2.4 Junior Find the answer

Consider the following flowchart: INPUT →\rightarrow Subtract 8→□→8 \rightarrow \square \rightarrow Divide by 2→□2 \rightarrow \square Add 16→16 \rightarrow OUTPUT. If the OUTPUT is 32, what was the INPUT?

A number or a short expression. Spacing and $ signs are ignored.

Solution

We start from the OUTPUT and work back to the INPUT. Since the OUTPUT 32 is obtained from adding 16 to the previous number, then the previous number is 32−16=1632 - 16 = 16. Since 16 is obtained by dividing the previous number by 2, then the previous number is 2×162 \times 16 or 32. Since 32 is obtained by subtracting 8 from the INPUT, then the INPUT must have been 32+8=4032 + 8 = 40.

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