AlgebraHardGreatest difference of two bounded integers
Algebra practice question
The integers x and y satisfy 2 < x < 7 and 1 < y < 3. What is the greatest possible value of x − y?
Answer: 4
The largest integer x is 6 and the smallest integer y is 2, so x − y is at most 6 − 2 = 4.
Common wrong answers
- If you answered 3
- 3 uses y = 3, which is excluded.
- If you answered 5
- 5 uses x = 7 or y = 1, one of which is excluded.
- If you answered 6
- 6 uses x = 7 and y = 1, but both bounds are strict.
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