1994 AMC 12 Problem 5

Attempt Problem 5 of the 1994 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 1994 AMC 12 solutions, or check the answer key.

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

Pat intended to multiply a number by

6

but instead divided by

6.

Pat then meant to add

14

but instead subtracted

14.

After these mistakes, the result was

16.

If the correct operations had been used, the value produced would have been

less than

400

between

400

and

600

between

600

and

800

between

800

and

1000

greater than

1000

Undo the mistaken subtraction and division to recover the starting number

Apply

6x+14

to that starting number

If the starting number is

x,

the mistaken calculation gives

\frac{x}{6}-14=16,

x=180.

The intended calculation would produce

6(180)+14=1094,

which is greater than

1000.

Thus the correct answer is E.

Problem 5 in other years