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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 = 825, Y = 718
X = 812, Y = 756
X = 834, Y = 704
X = 898, Y = 649
X = 825, Y = 718
Look for the arithmetic relationship between the first and second numbers in the given pair: 679 and 864. Notice that 679 + 185 = 864. Test this same addition of 185 to the other number pairs.
Look for the arithmetic relationship between the first and second numbers in the given pair: 679 and 864. Notice that 679 + 185 = 864. Test this same addition of 185 to the other number pairs.
Step 1: Analyze the Given Pair Relationship
Examine the relationship between numbers on the left and right sides. For X : 679 :: 864 : Y, test the constant difference between the first and second terms in each proportional pair.
Step 2: Test Option A Values
Substitute X = 825 and Y = 718. The difference between 825 and 679 is 146 (825 - 679 = 146). Similarly, the difference between 864 and 718 is 146 (864 - 718 = 146).
Step 3: Confirm the Pattern Consistency
Both pairs follow the exact same mathematical subtraction of 146, confirming that Option A is the correct solution.
B: 812 and 756 do not maintain a uniform difference with 679 and 864. C: 834 and 704 yield inconsistent differences. D: 898 and 649 fail to satisfy the equal difference pattern.
A is correct because substituting X = 825 and Y = 718 gives a consistent difference of 146 across both proportional number pairs (825 - 679 = 146 and 864 - 718 = 146).
In number analogy questions with large three-digit numbers, always test subtraction (difference) first before checking squares, cubes, or digit sums.
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