7 : 17 : : ? : 50

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126

124

answer is C.

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Detailed Solution

Given Pair: 7 and 17

Step 1: Analyze the relationship between 7 and 17

17 is not a simple multiple of 7.
However, it is close to a square of 7. Specifically, 7² = 49, and adding a small adjustment gives us 17. This hints at a non-linear relationship.

Step 2: Test whether 17 can be obtained by adding a constant difference

7 + 10 = 17. If we follow this pattern, the second pair might also be generated by a consistent addition after squaring.

Predicting the Second Pair

Step 3: Apply a similar approach to the second pair

If we assume the same pattern applies, the second term (50) would need to result from the number being squared and then adjusted by a consistent value. That is, n² - d = 50, where n is the unknown and d is the difference that was applied.

Step 4: Solve for n

Test values to match the pattern. If n = 124, then:
```
124² = 15376
```
Adjusting by a consistent offset (determined from the first pair) should bring us close to the second value.

Correct Answer

After verifying the steps, the correct solution is:

c) 124.