Select the option that is related to the third term in the same way as the second term is related to the first term. 13 : 196 :: 9 : .......
100
Solving the Number Analogy: 13 : 196 :: 9 : ?
The problem requires finding the relationship between the first pair of numbers (13 and 196) and applying the same logic to the third number (9) to find the missing fourth number.
Identifying the Pattern
Let's examine the relationship between 13 and 196:
- Notice that 196 is a perfect square. Specifically, $196 = 14^2$.
- The number 14 is closely related to the first term, 13. It is one greater than 13: $14 = 13 + 1$.
- Therefore, the pattern is: $(\text{First Term} + 1)^2 = \text{Second Term}$.
Applying the Pattern to Find the Missing Number
Now, we apply this identified pattern to the number 9:
- Add 1 to the third term (9): $9 + 1 = 10$.
- Square the result: $10^2 = 100$.
Thus, the missing number is 100.
Conclusion
The analogy is $13 : 196$ ($ (13+1)^2 $) :: $9 : 100$ ($ (9+1)^2 $).
The option corresponding to 100 is Option A.
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