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Difficulty: EasyAnalogy and Classification

In the given numerical analogy, the second number is related to the first number following a specific mathematical rule. Which number replaces the question mark (?) to complete the analogy?

7:50::9:?7 : 50 :: 9 : ?
  1. 8282Answer
  2. B
    8181
  3. C
    8080
  4. D
    6363

Answer

The number that completes the analogy is 8282.
The relationship in the first pair is established by squaring the first number and adding 11, since 72+1=49+1=507^2 + 1 = 49 + 1 = 50. Following the exact same mathematical rule for the second pair, squaring 99 and adding 11 gives 92+1=81+1=829^2 + 1 = 81 + 1 = 82. Therefore, 8282 is the correct completing number.

Step-by-Step Solution

1
Analyze the rule relating the first pair 7:507 : 50
Observe that 72=497^2 = 49, and 49+1=5049 + 1 = 50. The pattern is n:n2+1n : n^2 + 1.
Identify the multi-step mathematical transformation mapping the input to the output.
2
Apply the identified rule (n:n2+1n : n^2 + 1) to the third number 99
Calculate 92+1=81+1=829^2 + 1 = 81 + 1 = 82.
Complete the analogy by executing the identical operation on the third term.

Key Concept

Numerical Analogy with Square and Increment Pattern (n:n2+1n : n^2 + 1)
Estimated Time:45s
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Topics

Analogy and Classification

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