Question

A, B, C, D, E and F are friends. A is shorter than B but taller than D. C is tallest among them. F is taller than E but shorter than D. If G is to stand in the middle in order of their heights, then he will stand in between :

• A. D and E
• B. A and B
• C. C and F
• D. A and D

Hint:

To avoid confusion, write down inequalities clearly using the "$>$" sign.
Once the full chain is constructed, count the number of variables to make sure no elements were missed.
Finding the median position is then a straightforward task.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This is a logical reasoning problem based on linear ranking and comparison of heights.
We are given relative height relationships among six friends (A, B, C, D, E, F).
We need to establish a complete descending order of their heights, introduce a seventh person G who stands exactly in the middle of this order, and find between whom G will stand.

Step 2: Detailed Explanation:

• Extract Relative Inequalities from the Text:
- "A is shorter than B but taller than D":
\[ B > A > D \]
- "C is tallest among them":
\[ C > \text{all others} \]
- "F is taller than E but shorter than D":
\[ D > F > E \]

• Combine the Inequalities:
By linking the statements together:
\[ B > A > D \quad \text{and} \quad D > F > E \] This gives:
\[ B > A > D > F > E \] Since C is the tallest of all six friends, we place C at the beginning:
\[ C > B > A > D > F > E \]

• Position G in the Middle:
The original group has 6 people. Introducing G makes a total of 7 people.
In an ordered sequence of 7 people, the "middle" position is the 4th position, with exactly 3 people taller and 3 people shorter than them.
Looking at our ordered sequence:
- Taller than middle (3 people): C, B, A
- Shorter than middle (3 people): D, F, E
Therefore, G must be placed at the 4th position, which lies directly between A (3rd position) and D (5th position).

Step 3: Final Answer:
G will stand in between A and D.
Thus, the correct option is (D).