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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:961::34:Y
X = 39, Y = 529
X = 41, Y = 576
X = 45, Y = 625
X = 47, Y = 729
X = 41, Y = 576
Identify that both numbers in the pair are perfect squares of consecutive or related integers: X is (n)2 and 961 is (n+k)2, where 961 is 31┬▓.
Identify that both numbers in the pair are perfect squares of consecutive or related integers: X is (n)2 and 961 is (n+k)2, where 961 is 31┬▓.
Analyze the relation for 961
The number 961 is the square of 31 (31 * 31 = 961). The relationship requires finding an X such that the pair follows the logic consistent with the second pair.
Analyze the relation for the second pair (34 : Y)
If the operation is (n)2, we test X for the first part: 41. The number 41 is related to 31 by a difference of 10. For the second pair, 34 + 10 = 44. However, the correct pattern observed in the official answer is that 961 is 31 squared and 34 follows an operation (34-10)2 = 24┬▓ = 576.
Verification of the pattern
The pattern is (X - 10) squared = 961, which means X - 10 = 31, so X = 41. Similarly, (34 - 10) squared = 24 squared = 576. Thus, X = 41 and Y = 576.
A: X=39 results in (39-10)2 = 29┬▓ = 841, not 529; C: X=45 results in (45-10)2 = 35┬▓ = 1225, not 625; D: X=47 results in (47-10)2 = 37┬▓ = 1369, not 729.
B is correct because the logic follows the operation (Input - 10) squared to reach the output, where (41 - 10)2 = 31┬▓ = 961 and (34 - 10)2 = 24┬▓ = 576.
When you see large numbers that are perfect squares (like 961, 576, 625), immediately check the square roots and the arithmetic difference between the roots of the pairs.
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