1951 AMC 12 Problem 7

Attempt Problem 7 of the 1951 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 1951 AMC 12 solutions, or check the answer key.

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

An error of

0.02''

is made in the measurement of a line

10''

long, while an error of only

0.2''

is made in a measurement of a line

100''

long. In comparison with the relative error of the first measurement, the relative error of the second measurement is:

Greater by

0.18

The same

Less

10

times as great

Correctly described by both

(A)

and

(D)

Relative error is the absolute error divided by the measured length

Compare

\frac{0.02}{10}

with

\frac{0.2}{100}

The two relative errors are

\frac{0.02}{10}=0.002

and

\frac{0.2}{100}=0.002.

They are equal.

Thus, the correct answer is B.

Problem 7 in other years