Problem 2 · 2010 Math Kangaroo
Medium
Arithmetic & Operations
sum-constraintarithmetic-series
Which number goes in the cell with the question mark if the sum of the numbers in both rows is equal?
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 2010 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | ? |
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Answer: C — 1910
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Hint 1 of 2
Add up the top row, including the 2010, then make the bottom row match.
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Hint 2 of 2
The bottom row is 11 through 20 plus the mystery cell.
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Approach: set the two row sums equal
- Top row: 1+2+...+10 = 55, plus 2010 gives 2065.
- Bottom row: 11+12+...+20 = 155, plus the unknown cell.
- Set them equal: 155 + ? = 2065, so ? = 1910.
Mark:
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