Problem 14 · 2014 Math Kangaroo
Hard
Arithmetic & Operations
place-value
Each of the digits 2, 3, 4 and 5 will be placed in a square. Then there will be two numbers, which will be added together. What is the biggest number that they could make?
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Answer: D — 95
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Hint 1 of 3
Each number has a tens box and a ones box, and the tens box is worth a lot more.
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Hint 2 of 3
To make the total big, the biggest digits should sit in the front (tens) boxes.
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Hint 3 of 3
Put the two largest digits in the two front boxes and the two smallest in the back boxes.
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Approach: put the largest digits in the front (tens) places where they are worth the most
- Two two-digit numbers are built from 2, 3, 4, 5, and the front digit of each counts for tens.
- To make the sum largest, give the front boxes the two biggest digits, 5 and 4.
- The other digits, 2 and 3, go in the back boxes.
- That gives 52 + 43 = 95 (53 + 42 also makes 95), the biggest possible total.
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