Problem 17 · 2010 Math Kangaroo
Stretch
Arithmetic & Operations
arithmetic-seriessum-constraint
Which number must replace the question mark if the total of the numbers in each row is the same?
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 199 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | ? |
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Answer: A — 99
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Hint 1 of 2
Add up the top row, then make the bottom row reach the same total.
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Hint 2 of 2
The top row is 1+2+…+10 plus 199.
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Approach: match the two row sums
- Top row: 1 + 2 + … + 10 = 55, plus 199 gives 254.
- Bottom row: 11 + 12 + … + 20 = 155.
- So the missing number is 254 − 155 = 99.
Mark:
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