1970 AMC 12 Problem 25

Question

For every real number

x,

let

\lfloor x\rfloor

be the greatest integer which is less than or equal to

x.

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

W

ounces is always:

6W

6\lfloor W\rfloor

6(\lfloor W\rfloor-1)

6(\lfloor W\rfloor+1)

-6\lfloor-W\rfloor

Answer: E

Concepts:floor and ceiling functions money function

Difficulty rating: 1850

Small hint:

The number of charged ounces is the least integer at least

W

Big hint:

Use the identity

\lceil W\rceil=-\lfloor-W\rfloor

Solution:

Charging for every ounce or portion thereof means the number of charged ounces is

\lceil W\rceil.

The floor and ceiling functions satisfy

\lceil W\rceil=-\lfloor-W\rfloor.

Thus the cost is

6\lceil W\rceil=-6\lfloor-W\rfloor.

Therefore, the correct answer is E.