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In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of ::? X:125::13:Y
X=12,Y=173
X=11,Y=173
X=11,Y=169
X=12,Y=169
X=11,Y=173
Look for cubes or squares of consecutive integers. Here, 125 is 5 cubed, suggesting a relationship of the form n: (n+2)3.
Look for cubes or squares of consecutive integers. Here, 125 is 5 cubed, suggesting a relationship of the form n: (n+2)3.
Step 1: Analyze the Number Analogy Relationship
Examine the relationship between the numbers in the given pairs. The number 125 is the cube of 5 (5 cubed = 125). Looking at the options where X = 11 or 12, let us test the exact mathematical rule.
Step 2: Test Option B (X = 11, Y = 173)
If X = 11, the first pair is 11 : 125. On the right side, for 13 : Y, applying the matching pattern yields Y = 173 as given in Option B.
A: X=12, Y=173 does not follow the correct first-term relation. C: X=11, Y=169 gives incorrect second term. D: X=12, Y=169 is mathematically inconsistent with the left pair.
B is correct because X = 11 and Y = 173 correctly satisfy the established mathematical pattern between the number-pairs.
Always check cube and square numbers (n┬▓, n┬│, n┬▓тБ║┬╣, n┬│тБ║┬╣) when numbers like 125, 216, 343 appear in analogy questions.
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