Difficulty: Medium
Correct Answer: 2
Explanation:
Introduction / Context:
This puzzle introduces a custom binary operation *, which does not mean normal multiplication. We are shown three example values of a * b and must infer the rule that produces 3, -2, and 8 from the given pairs. Then we apply the same rule to find 14*10.
Given Data / Assumptions:
Concept / Approach:
The results are relatively small and can be positive or negative. A natural idea is to relate them to the difference between the two numbers, perhaps scaled or halved. We test whether 8*2 and 18*2 can both be generated from a simple function of (a − b).
Step-by-Step Solution:
Step 1: Test the rule f(a, b) = (a − b) / 2.
For 8*2: (8 − 2) / 2 = 6 / 2 = 3, which matches.
For 18*2: (18 − 2) / 2 = 16 / 2 = 8, which also matches.
Step 2: Check this rule on the third example.
For 14*18: (14 − 18) / 2 = −4 / 2 = −2, matching the given value.
Step 3: The pattern is confirmed: a * b = (a − b) / 2.
Step 4: Apply this rule to 14*10.
14*10 = (14 − 10) / 2.
Compute the difference: 14 − 10 = 4.
Now divide by 2: 4 / 2 = 2.
Verification / Alternative check:
Any alternative rule must produce the three given results exactly. It is very unlikely that a more complicated expression will match all three examples so neatly. The simple halved difference rule works perfectly, making it the intended operation.
Why Other Options Are Wrong:
Values like -5, -2, and 6 result from misapplying the rule or using the wrong sign. For instance, using (b − a)/2 would give negative values where the operation is known to be positive. Only 2 remains consistent with all examples.
Common Pitfalls:
Learners often try literal multiplication a × b or average (a + b)/2, which immediately fails for at least one of the given pairs. Forgetting to divide by 2, or mixing up the order (b − a instead of a − b), also leads to incorrect answers.
Final Answer:
According to the defined operation, the value of 14*10 is 2.
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