1990 AMC 12 Problem 15

Attempt Problem 15 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.

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

15.

Four whole numbers, when added three at a time, give the sums

180,

197,

208,

and

222.

What is the largest of the four numbers?

77

83

89

95

cannot be determined from the given information

Add the four given triple-sums

Each original number appears in exactly three of those sums

T

is the sum of the four numbers, adding the four triple-sums gives

\begin{aligned} 3T&=180+197+208+222\\ &=807, \end{aligned}

T=269.

The omitted numbers are

269-180,

269-197,

269-208,

and

269-222,

whose largest is

89.

Thus the correct answer is C.

Problem 15 in other years