UP High Court RO / ARO 05 Jan 2022 Shift 2

Study the pattern carefully and select the number that can replace the question mark (?)

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Verified Answer
A. 21
B. 27
C. 25
D. 23

Explanation:

The question presents three circles with numbers arranged in a specific pattern. We need to find the missing number in the third circle. Let's analyze the pattern in the first two circles. Each circle has a top number, a bottom number, and a middle number. For Circle 1: Top number $= 484$, Bottom number $= 14$, Middle number $= 8$. We find the square root of the top number: $\sqrt{484} = 22$. Then, $22 - 14 = 8$. This matches the middle number. For Circle 2: Top number $= 576$, Bottom number $= 19$, Middle number $= 5$. We find the square root of the top number: $\sqrt{576} = 24$. Then, $24 - 19 = 5$. This matches the middle number. The pattern is: (Square root of the top number) - (Bottom number) = (Middle number). Now, apply this pattern to Circle 3: Top number $= 729$, Middle number $= 4$, Bottom number $= ?$ (Let this be $X$). First, find the square root of the top number: $\sqrt{729} = 27$. Using the pattern, we have: $27 - X = 4$. Solving for $X$: $X = 27 - 4 = 23$. Therefore, the missing number is $23$. Let's analyze the options: A) $21$: If $X=21$, $27-21=6 \neq 4$. B) $27$: If $X=27$, $27-27=0 \neq 4$. C) $25$: If $X=25$, $27-25=2 \neq 4$. D) $23$: This option perfectly matches the derived pattern.