UP High Court RO / ARO 06 Jan 2022 Shift 1

Which letter/number is exactly in the middle between the $9^{\text{th}}$ letter/number from the right end and the $17^{\text{th}}$ letter/number from the left end of the sequence given below?\nSequence: RE5DAP3TIQ79B2KU1MW

Verified Answer
A. 2
B. P
C. 3
D. T

Explanation:

First, let's write down the sequence and determine the total number of elements.\nSequence: `R E 5 D A P 3 T I Q 7 9 B 2 K U 1 M W`\nTotal number of elements = 20. \nNext, let's find the position of the specified elements: 1. **$9^{\text{th}}$ letter/number from the right end:** Counting from the right: W (1st), M (2nd), 1 (3rd), U (4th), K (5th), 2 (6th), B (7th), 9 (8th), **7 (9th)**. So, the $9^{\text{th}}$ element from the right is `7`. To find its position from the left: Total elements - (Position from right) + 1 = $20 - 9 + 1 = 12$. So, `7` is the $12^{\text{th}}$ element from the left. 2. **$17^{\text{th}}$ letter/number from the left end:** Counting from the left: R (1st), E (2nd), 5 (3rd), D (4th), A (5th), P (6th), 3 (7th), T (8th), I (9th), Q (10th), 7 (11th), 9 (12th), B (13th), 2 (14th), K (15th), U (16th), **1 (17th)**. So, the $17^{\text{th}}$ element from the left is `1`. \nNow we need to find the element exactly in the middle between the $12^{\text{th}}$ element (`7`) and the $17^{\text{th}}$ element (`1`) from the left. \nThe elements from the $12^{\text{th}}$ to the $17^{\text{th}}$ position are: $E_{12}$ (`7`), $E_{13}$ (`9`), $E_{14}$ (`B`), $E_{15}$ (`2`), $E_{16}$ (`K`), $E_{17}$ (`1`).\nThere are 6 elements in this range. When there's an even number of elements, there isn't a single 'exact' middle element; there are two middle elements. In this case, the middle elements are $E_{14}$ (`B`) and $E_{15}$ (`2`). \nHowever, if the question implies a single middle element, it often refers to the element at the average of the indices, possibly rounded up or down. The average index is $\frac{12 + 17}{2} = \frac{29}{2} = 14.5$.\nIf we round up to $15$, the $15^{\text{th}}$ element from the left is `2`. \nLet's check the options:\nOption (A) $2$: This is the $15^{\text{th}}$ element from the left. This is a plausible interpretation for 'exactly in the middle' when the average index is 14.5.\nOption (B) $P$: This is the $6^{\text{th}}$ element from the left, which is incorrect.\nOption (C) $3$: This is the $7^{\text{th}}$ element from the left, which is incorrect.\nOption (D) $T$: This is the $8^{\text{th}}$ element from the left, which is incorrect. \nGiven that '2' is an option and corresponds to the $15^{\text{th}}$ element (rounding up the average position), it is the most likely intended answer. \nTherefore, the correct option is (A).