1962 AMC 12 Problem 22

Attempt Problem 22 of the 1962 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 1962 AMC 12 solutions, or check the answer key.

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

22.

The number

121_b,

written in the integral base

b,

is the square of an integer, for:

b=10,

only

b=10

and

b=5,

only

2\le b\le10

b\gt2

no value of

b

Convert

121_b

to an expression in

b

Remember that the digit

2

requires

b\gt2

In ordinary notation,

121_b=b^2+2b+1=(b+1)^2.

This is a square for every allowable base. Since digit

2

occurs, precisely the integral bases

b\gt2

are allowable.

Thus, the correct answer is D.

Problem 22 in other years