Question:
\[ (122;\,10,12):(170;\,12,14)::(226;\,14,16):\underline{\hspace{2cm}} \]
\[ (122;\,10,12):(170;\,12,14)::(226;\,14,16):\underline{\hspace{2cm}} \]
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Square-based patterns are very common in analogy questions. Always check sums or differences of squares first.
Updated On: Jun 13, 2026
- \((145;16,18)\)
- \((580;16,18)\)
- \((290;16,18)\)
- \((435;16,18)\)
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The Correct Option is B
Solution and Explanation
Concept:
Observe the relationship between the pair of numbers and the leading number.
Step 1: Identify the rule. For \[ (10,12) \] \[ 10^2+12^2 = 100+144 = 244. \] Half of this is \[ 122. \] For \[ (12,14) \] \[ 12^2+14^2 = 144+196 = 340. \] Half: \[ 170. \] Rule verified.
Step 2: Check the third given term. \[ 14^2+16^2 = 196+256 = 452. \] Half: \[ 226. \] Again verified.
Step 3: Apply the rule. For \[ (16,18) \] \[ 16^2+18^2 = 256+324 = 580. \] Half is not required now because the pattern moves to the next pair. Hence the required term is \[ (580;16,18). \]
Step 1: Identify the rule. For \[ (10,12) \] \[ 10^2+12^2 = 100+144 = 244. \] Half of this is \[ 122. \] For \[ (12,14) \] \[ 12^2+14^2 = 144+196 = 340. \] Half: \[ 170. \] Rule verified.
Step 2: Check the third given term. \[ 14^2+16^2 = 196+256 = 452. \] Half: \[ 226. \] Again verified.
Step 3: Apply the rule. For \[ (16,18) \] \[ 16^2+18^2 = 256+324 = 580. \] Half is not required now because the pattern moves to the next pair. Hence the required term is \[ (580;16,18). \]
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