Track / Stage 3 / 253 of 260 #253 of 1964

Problem 253

AMC 10/12, early questions

Algebra Difficulty 3.9 Find the answer South African Mathematics Olympiad · South Africa

The sums of three out of four numbers (omitting each of the four numbers in turn) are $20$ , $22$ , $24$ and $27$ , respectively. What is the sum of the four numbers?

Your answer

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

Since each of the given sums involves exactly three of the numbers, it follows that the sum of the four sums is three times the sum of the four numbers. Thus the required sum is equal to $(20 + 22 + 24 + 27)/3 = 93/3 = 31$ .

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