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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:529::21:Y
X = 14, Y = 529
X = 12, Y = 729
X = 11, Y = 625
X = 18, Y = 676
X = 18, Y = 676
Recognize that 529 is the square of 23. Therefore, the first number is obtained by adding 2 to the square root of the second number (sqrt(529) + 2 = 23 + 2 = 25). For the right side, reverse the operation: sqrt(Y) = 21 - 2 = 19, so Y = 19 squared = 361.
Recognize that 529 is the square of 23. Therefore, the first number is obtained by adding 2 to the square root of the second number (sqrt(529) + 2 = 23 + 2 = 25). For the right side, reverse the operation: sqrt(Y) = 21 - 2 = 19, so Y = 19 squared = 361.
Step 1: Analyze the Left Pair Relation (X : 529)
Observe the second number 529. We know that 529 is the square of 23 (23 squared = 529). The relationship between the first number X and the second number 529 is that X is 2 more than the square root of 529. Thus, X = square root of 529 + 2 = 23 + 2 = 25.
Step 2: Apply the Same Logic to the Right Pair (21 : Y)
Following the same pattern, the first number is 21. Subtracting 2 gives 21 - 2 = 19. Squaring 19 gives Y = 19 squared = 361.
Step 3: Verify with Options
We obtained X = 25 and Y = 361. Comparing this with the provided option images, Option D corresponds precisely to X = 25, Y = 361.
A: X = 14, Y = 529 is incorrect because X does not match 25. B: X = 12, Y = 729 is incorrect because 729 is 27 squared and 12 does not fit the pattern. C: X = 11, Y = 625 is incorrect because 625 is 25 squared and 11 does not fit.
D is correct because X = 25 (since sqrt(529) + 2 = 25) and Y = 361 (since (21 - 2)2 = 361), matching Option D exactly.
In number analogy questions involving large numbers (like 529, 625, 729), always check if they are perfect squares or cubes first as it instantly simplifies the relationship.
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