Problem 11 · 2022 Math Kangaroo
Medium
Arithmetic & Operations
sum-constraintwork-backward
There are five gaps in the calculation shown. Adriana wants to write a “+” in four of the gaps and a “−” in one of them so that the equation is correct. Where must the “−” go?
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Answer: D — between 15 and 18
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Hint 1 of 2
If all gaps were plus signs, what would the total be, and how does one minus change it?
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Hint 2 of 2
Changing a + to a - in front of a value drops the sum by twice that value; find which drop hits 45.
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Approach: compare the all-plus total to 45
- With all plus signs, 6+9+12+15+18+21 = 81.
- Turning the sign before a number n into minus lowers the total by 2n; we need to lose 81-45 = 36, so 2n = 36 and n = 18.
- The minus goes before 18, i.e. between 15 and 18, so the answer is D.
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