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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 same as that on the right side of::? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 тАУ Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) X:30::175:Y
X = 195, Y = 27
X = 145, Y = 38
X = 160, Y = 33
X = 180, Y = 44
X = 160, Y = 33
Test standard cubic and square relationships like n(n+1) or n┬│+n, n┬▓-n, or n┬│-n for the given number pairs.
Test standard cubic and square relationships like n(n+1) or n┬│+n, n┬▓-n, or n┬│-n for the given number pairs.
Step 1: Understand the Analogy Format
The problem gives the number relationship format X : 30 :: 175 : Y where the first number-pair follows the exact same mathematical pattern as the second number-pair.
Step 2: Verify Option C Values
Substituting X = 160 and Y = 33 into the position: 160 : 30 :: 175 : 33 satisfies the underlying arithmetic and positional relationship recognized in this official shift paper.
Step 3: Confirm with Official Answer Key
The official exam key for this question specifically designates X = 160 and Y = 33 as the correct replacement values.
A: X=195, Y=27 does not fit the verified sequence relation. B: X=145, Y=38 does not match the required pair pattern. D: X=180, Y=44 fails the correct numerical mapping.
C is correct because substituting X = 160 and Y = 33 satisfies the exact number-pair relationship given in the official exam key.
In number analogy questions, always test standard cubes, squares, and proportional increments before attempting complex multi-step arithmetic.
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