Problem 4 · 1995 AJHSME
Medium
Arithmetic & Operations
two-step-process
A teacher tells the class: "Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer." Ben thinks of 6 and gives his answer to Sue. What should Sue's answer be?
Show answer
Answer: C — 26.
Show hints
Hint 1 of 2
This is a 'machine' problem: a number goes in, gets transformed, and the OUTPUT becomes the input to the next machine. Don't skip ahead — feed Ben's result straight into Sue.
Still stuck? Show hint 2 →
Hint 2 of 2
Each person runs the same kind of step: take a number, add or subtract 1, then double. Do Ben's whole step, get his answer, then start Sue fresh with it.
Show solution
Approach: follow the output of one stage into the next
- Treat each person as a little machine. Ben's machine: (number + 1) then double. With 6: (6 + 1) × 2 = 14. That 14 is what Sue receives — Ben's number 6 is gone.
- Sue's machine starts fresh with 14: (14 − 1) × 2 = 26.
- The trap this catches: kids often re-use 6 in Sue's step. The rule is to pass forward only the answer, not the original number — that's how chained operations work.
Mark:
· log in to save