Problem 2 · 2019 Math Kangaroo
Medium
Arithmetic & Operations
sum-constraintcasework
The numbers 1, 2, 3 and 4 are placed in different cells of the 2×2 table shown. Then the sum of the numbers in each row and in each column is found. Two of these sums are 4 and 5. What are the two remaining sums?
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Answer: E — 5 and 6
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Hint 1 of 2
The four entries 1,2,3,4 add to 10, so the two row sums add to 10 and the two column sums add to 10.
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Hint 2 of 2
If one given sum is a row and the other a column, find each partner from the total 10.
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Approach: use that all four numbers total 10
- The numbers 1+2+3+4 = 10.
- The two row sums add to 10; the two column sums also add to 10.
- Given sums 4 and 5: the partner of a 4-sum is 6, and the partner of a 5-sum is 5.
- So the two remaining sums are 5 and 6 — answer (E).
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