1992 AMC 12 Problem 4

Attempt Problem 4 of the 1992 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 1992 AMC 12 solutions, or check the answer key.

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

a,

b,

and

c

are positive integers and

a

and

b

are odd, then

3^a+(b-1)^2c

odd for all choices of

c

even for all choices of

c

odd if

c

is even; even if

c

is odd

odd if

c

is odd; even if

c

is even

odd if

c

is not a multiple of

3

; even if

c

is a multiple of

3

Determine the parity of each of the two terms

Because

b

is odd,

b-1

is even

The power

3^a

is odd. Since

b-1

is even,

(b-1)^2c

is even for every positive integer

c.

The sum of an odd integer and an even integer is always odd.

Thus the correct answer is A.

Problem 4 in other years