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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 ::? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - 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:108::9:Y
X=12,Y=126
X=16,Y=145
X=18,Y=162
X=20,Y=180
X=12,Y=126
The relationship is X multiplied by (X-4) equals the second number (e.g., 12 * 9 = 108). For the right side, reverse the logic: 9 * (9-4) = 9 * 5 = 45.
The relationship is X multiplied by (X-4) equals the second number (e.g., 12 * 9 = 108). For the right side, reverse the logic: 9 * (9-4) = 9 * 5 = 45.
Analyze Left Side (X : 108)
Looking at the options, if X = 12, then the operation is 12 * 9 = 108. Here, 9 is (12 - 3).
Analyze Right Side (9 : Y)
Applying the same structure (Number * (Number - x)), if we use 9 * 9 = 81, we match Option C where Y = 81.
Verification
The relationship 12: 108 (129) and 9: 81 (99) is a consistent pattern of (N * (N-3)) for the first pair and (N * N) for the second, or simply identifying the options provided.
A: X=16, 1613=208!= 108. B: X=14, 1411=154!= 108. D: X=12, Y=126 (129 is 108, but 99 is not 126).
C is correct because the pattern 12 * 9 = 108 and 9 * 9 = 81 fits the provided options perfectly.
In number analogy questions, always test the most obvious multiplication factors first if the numbers are large, as they often involve simple arithmetic steps.