If 31 : 52 = 4836 and 18 : 4 = 216, then what is the value of 51 : 27?
4131
Each pair of numbers is linked to its result by a single arithmetic rule, which we first discover from the given examples.
Take the simpler pair \(18 : 4\). Their product is \(18 \times 4 = 72\), and \(72 \times 3 = 216\), which matches the stated result.
Check the rule on \(31 : 52\). The product is \(31 \times 52 = 1612\), and \(1612 \times 3 = 4836\), which matches again.
So the confirmed rule is: multiply the two numbers, then multiply that product by 3.
Apply it to \(51 : 27\). First the product: \(51 \times 27 = 1377\).
Then multiply by 3: \(1377 \times 3 = 4131\).
The key idea is to test a candidate operation on every given pair before trusting it, so the value is 4131.
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