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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 : 35 :: 8 : Y
X = 10 , Y = 20
X = 7 , Y = 48
X = 3 , Y = 74
X = 6 , Y = 68
X = 7 , Y = 48
Look for a consistent algebraic relationship between the pairs, specifically the form n┬▓ - 1 or n┬▓ + something constant applied to both sides.
Look for a consistent algebraic relationship between the pairs, specifically the form n┬▓ - 1 or n┬▓ + something constant applied to both sides.
Analyze the pattern
In the pair 8: Y, we observe the pattern: 8┬▓ - 1 = 64 - 1 = 63. However, looking at the options, we test X: 35. If the pattern is n┬▓ - 1, then for X: 35, we have X┬▓ - 1 = 35, implying X┬▓ = 36, so X = 6. But 6 is not in the correct pair option.
Re-evaluating the pattern
Testing Option B (X=7, Y=48): For 7: 35, the relationship is 7 * 5 = 35. For 8: 48, the relationship is 8 * 6 = 48. Both follow the pattern of multiplying the first number by (n-2) or simply (n * (n-2)). Specifically: 7 * (7-2) = 7 * 5 = 35 and 8 * (8-2) = 8 * 6 = 48.
A: 108=80 not 35, C: 31=3 not 35, D: 6*4=24 not 35.
B is correct because the logic applied is (n * (n-2)), where 7 * (7-2) = 35 and 8 * (8-2) = 48.
When number pairs don't fit simple square/cube logic, check if the multiplier is tied to the first number itself via simple subtraction.
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