1970 AHSME Problems/Problem 25
Problem
For every real number , let be the greatest integer which is less than or equal to . If the postal rate for first class mail is six cents for every ounce or portion thereof, then the cost in cents of first-class postage on a letter weighing ounces is always
Solution
This question is trying to convert the floor function, which is more commonly notated as , into the ceiling function, which is . The identity is , which can be verified graphically, or proven using the definition of floor and ceiling functions.
However, for this problem, some test values will eliminate answers. If ounces, the cost will be cents. Plugging in into the five options gives answers of . This leaves options and as viable. If ounces, the cost is cents. Option remains cents, while option gives cents, the correct answer. Thus, the answer is .
See also
1970 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
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