1990 AMC 12 Problem 11

Attempt Problem 11 of the 1990 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 1990 AMC 12 solutions, or check the answer key.

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11.

How many positive integers less than

50

have an odd number of positive integer divisors?

3

5

7

9

11

Divisors normally pair as

d

and

\frac{n}{d}

An unpaired divisor occurs exactly for a perfect square

A positive integer has an odd number of divisors exactly when it is a perfect square. The squares below

50

are

1,4,9,16,25,36,49,

so there are

7.

Thus the correct answer is C.

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