Question

What is Priya's rank from the top in a class of seventy students?
I. There are six students between Priya and Charan.
II. Charan is eight from the top.

• A. If the statement I alone is sufficient to answer the question.
• B. If the statement II alone is sufficient to answer the question.
• C. If the statements I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. If the statements I and II together are not sufficient to answer the question and additional data is required.

Hint:

In ranking problems, carefully analyze the conditions about the positions of the individuals to calculate their exact ranks using simple algebraic expressions.

Answer 1

The Correct Option is D

Let us assume Priya's rank from the top is \( P \) and Charan's rank from the top is \( C \). We are given that there are six students between Priya and Charan, which means the difference in their ranks is 7. Hence, we can write: \[ |P - C| = 7 \] From condition II, Charan's rank is 8th from the top: \[ C = 8 \] Now, using the equation \( |P - 8| = 7 \), we can solve for Priya's rank \( P \): \[ P - 8 = 7 \quad \text{or} \quad 8 - P = 7 \] Solving the first equation: \[ P = 15 \] Solving the second equation: \[ P = 1 \] So, Priya can either be 1st or 15th. Since there are 70 students in the class, Priya's rank from the top is the 15th position. Thus, Priya's rank is \( \boxed{15} \).