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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:346::9:Y
X = 8, Y = 756
X = 5, Y = 612
X = 7, Y = 732
X = 6, Y = 729
X = 7, Y = 732
Look for a cube or square relationship between the numbers. Here, the relation is n cubed plus 1 (n┬│ + 1).
Look for a cube or square relationship between the numbers. Here, the relation is n cubed plus 1 (n┬│ + 1).
Step 1: Analyze the Right Pair (9 : Y)
We are given the number 9 on the right side. Following Option C, Y = 732. Let's check the relation between 9 and 732: 9 cubed is 729, and adding 3 gives 729 + 3 = 732 (n┬│ + 3 pattern).
Step 2: Apply the Pattern to the Left Pair (X : 346)
Using the same pattern (n┬│ + 3) for the first number X, we get X┬│ + 3 = 346. Therefore, X┬│ = 346 - 3 = 343. Since 7 cubed (7┬│) is 343, X = 7.
Step 3: Confirm Option C
With X = 7 and Y = 732, both pairs satisfy the exact mathematical operation n┬│ + 3.
A: X = 8, Y = 756 does not follow the n┬│ + 3 pattern. B: X = 5, Y = 612 does not yield 346 for X = 5. D: X = 6, Y = 729 does not match the required output.
C is correct because both number pairs follow the rule n cubed plus 3 (n┬│ + 3), giving X = 7 (7┬│ + 3 = 346) and Y = 732 (9┬│ + 3 = 732).
Always check for cube and square series plus or minus a constant when dealing with numbers around 300 to 800 in reasoning tests.