IF 1+2+5=15, 4+1+4=20 then 2+7+6=?

In this type of number-relationship puzzle, each worked example encodes one hidden arithmetic rule connecting the three numbers on the left to the value on the right. The task is to find an operation that fits EVERY given example exactly, then apply that same operation to the new set of numbers -- testing the rule against more than one example is what confirms it, rather than guessing from a single case.

1. Test simple addition on the first example: 1 + 2 + 5 = 8, but the equation shows 15, so plain addition is ruled out.

2. Try adding the first two figures and multiplying by the third: (1 + 2) x 5 = 3 x 5 = 15, which matches the first example.

3. Check the SAME rule on the second example: (4 + 1) x 4 = 5 x 4 = 20, which also matches -- the rule (first + second) x third is confirmed across both examples.

4. Apply the confirmed rule to the target equation: (2 + 7) x 6 = 9 x 6 = 54.

Since the rule (first + second) x third correctly reproduces BOTH given equations -- not just one -- it is the reliable rule to extend to the new case, giving 54.