Based on the analogy given, find the missing pair from the given options.
32 : 13 :: ---- : ----
Analogy Logic Identification
The question presents a number analogy: 32 : 13 :: ---- : ----. We need to identify the relationship between the digits of the first number (32) and the second number (13).
Let the first number be $N_1 = 32$. Its digits are 3 and 2.
Let the second number be $N_2 = 13$.
The relationship is found by squaring the digits of $N_1$ and summing them:
Calculation: ${3}^2 + {2}^2 = 9 + 4 = 13$.
Since ${3}^2 + {2}^2 = 13$, the rule is confirmed: The second number equals the sum of the squares of the digits of the first number.
Option Pair Verification
Now, we apply this rule to the given options:
- Option 1: 51 : 36 Digits of 51 are 5, 1. ${5}^2 + {1}^2 = 25 + 1 = 26 \neq 36$.
- Option 2: 83 : 121 Digits of 83 are 8, 3. ${8}^2 + {3}^2 = 64 + 9 = 73 \neq 121$.
- Option 3: 71 : 81 Digits of 71 are 7, 1. ${7}^2 + {1}^2 = 49 + 1 = 50 \neq 81$.
- Option 4: 47 : 65 Digits of 47 are 4, 7. ${4}^2 + {7}^2 = 16 + 49 = 65 = 65$.
Conclusion
Option 4 (47 : 65) is the correct missing pair because it follows the analogy rule.
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