1976 AMC 12 Problem 5

Attempt Problem 5 of the 1976 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1976 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

How many integers greater than ten and less than one hundred, written in base ten notation, are increased by nine when their digits are reversed?

0

1

8

9

10

Represent the tens and units digits by

t

and

u

The increase is

10u+t-(10t+u)=9(u-t)

The condition is

9(u-t)=9,

u=t+1.

The possibilities are

12,

23,

34,

45,

56,

67,

78,

and

89,

giving

8

integers.

Therefore, the correct answer is C.

Problem 5 in other years