Question

Directions: Twenty students are standing in a straight line facing north. Rina is standing sixth from the left end. There are only three students between Rina and Shweta. Radha is standing exactly between Shweta and Rina. Tina is standing sixth to the right of Radha. Anita is standing fourth from the right end of the line. There are more than four students between Rina and Tina.

How many people are standing between Anita and Tina?

• A. One
• B. Two
• C. Three
• D. None

Hint:

First fix everyone's position from the left end using the given clues, testing both possibilities for Shweta's position.

Answer 1

The Correct Option is B

Step 1: Note the fixed positions.
There are 20 students in the line, numbered 1 (left end) to 20 (right end). Rina is sixth from the left end, so Rina is at position 6. Anita is fourth from the right end, so Anita is at position \(20 - 4 + 1 = 17\).

Step 2: Place Shweta and Radha, then test both cases.
"Only three students between Rina and Shweta" means their positions differ by 4 (three people in between means a gap of 4). So Shweta is at position \(6 + 4 = 10\) or \(6 - 4 = 2\). Radha stands exactly between Shweta and Rina, so Radha's position is the average of the two.
Case 1: Shweta = 2, then Radha = \((6+2)/2 = 4\), and Tina, being sixth to the right of Radha, is at \(4 + 6 = 10\). The students between Rina (6) and Tina (10) number only 3, which is not "more than four," so this case is rejected.
Case 2: Shweta = 10, then Radha = \((6+10)/2 = 8\), and Tina = \(8 + 6 = 14\). The students between Rina (6) and Tina (14) number 7, which is more than four, so this case fits all the clues.

Step 3: Count students between Anita and Tina.
Anita is at position 17 and Tina is at position 14. The students strictly between them are at positions 15 and 16, so exactly 2 students stand between them.

Final Answer:
Two students stand between Anita and Tina, so option B is correct. \[ \boxed{2} \]