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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 ::? X:66::9:Y
X=9,Y=81
X=8,Y=83
X=8,Y=81
X=7,Y=80
X=8,Y=83
Look for a mathematical relationship between the first and second terms in the complete pair (9 : Y) or deduce the cube/square operation backwards. Here, 9 cubed plus 2 equals 729 + 2 = 731? Let's check: 8 cubed + 2 = 514? Let's test standard cubic/square patterns or simple multiplication.
Look for a mathematical relationship between the first and second terms in the complete pair (9 : Y) or deduce the cube/square operation backwards. Here, 9 cubed plus 2 equals 729 + 2 = 731? Let's check: 8 cubed + 2 = 514? Let's test standard cubic/square patterns or simple multiplication.
Analyze the Complete Pair (9 : Y)
In the right-hand pair 9 : Y, the second number is 81, which is the square of 9 (9 squared = 81). Alternatively, let's examine the left-hand pair X : 66.
Examine the Left-Hand Pair (X : 66)
If 66 is close to a square, 8 squared = 64, and 64 + 2 = 66. Testing this pattern: First number squared + 2 equals the second number.
Verify with Both Pairs
For X = 8: 8 squared + 2 = 64 + 2 = 66. For 9 : Y: 9 squared = 81 (or 9 squared + 2 = 83? Wait, let's check Option C: X = 8, Y = 81. Here 9 squared = 81, so Y = 81 directly matches Option C).
A: X=9, Y=81 is incorrect because X cannot be 9 as 9 squared + 2 = 83, not 66. B: X=8, Y=83 is incorrect because Y is 81 (9 squared). D: X=7, Y=80 does not fit 66.
C is correct because X = 8 (since 8 squared + 2 = 66) and Y = 81 (since 9 squared = 81).
Always test both square/cube operations and arithmetic offsets (like n squared + 2) when solving number analogy questions in SSC and RRB exams.
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