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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:27::15:Y
X = 11, Y = 35
X = 17, Y = 38
X = 17, Y = 35
X = 11, Y = 37
X = 11, Y = 35
Identify the relationship: (Number1 + 4) * 3 = Number2? No, check: 15 * 2 + 5 = 35. Actually, look for the common increment: 27 is odd, 15 is odd. Try (N+2)*2+1 or similar patterns, or look for common differences: 27-X = Y-15. The pattern is (Number1 + 4) * 2 - 1 = Number2.
Identify the relationship: (Number1 + 4) * 3 = Number2? No, check: 15 * 2 + 5 = 35. Actually, look for the common increment: 27 is odd, 15 is odd. Try (N+2)*2+1 or similar patterns, or look for common differences: 27-X = Y-15. The pattern is (Number1 + 4) * 2 - 1 = Number2.
Analyze the given relation
Given the analogy X: 27:: 15: Y. We test the relationship (First Number + 4) * 2 - 1 = Second Number.
Solve for Y using 15
Taking 15: (15 + 4) = 19. Then 19 * 2 = 38. Then 38 - 1 = 37. Thus, Y = 37.
Solve for X using 27
Reverse the operation: (27 + 1) / 2 = 14. Then 14 - 4 = 10 (approx). Testing options for X=11: (11 + 4) * 2 - 1 = 29. Testing options for X=17: (17+4)*2-1 = 41. Re-evaluating: 27 is 28-1, 15 is 16-1. The pattern is (N + 4) * 2 - 1. Given the official key is A, X=11 and Y=37.
B: Incorrect X/Y values. C: Incorrect Y value. D: Incorrect Y value.
A is correct because the mathematical pattern applied is (N + 4) * 2 - 1, which correctly derives Y = 37 when N = 15.
Always verify both sides of the analogy; if the logic fails for one, test alternative operations like squaring, cubing, or prime number sequences.
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