In a shop ,there were 4 dolls of different heights A,B,C and D.D is neither as tall as A nor as short as C.B is shorter than D but taller than C.If Mani wants to purchase the tallest doll ,which one should she purchase?

Options

A. Only A
B. Only B
C. Either A or D
D. Either B or D

Explanation

To solve the problem step by step, we need to analyze the information given about the heights of the dolls A, B, C, and D.

### Step 1: Analyze the information given
1. **D is neither as tall as A nor as short as C.**
- This means:
- \( D < A \) (D is shorter than A)
- \( D > C \) (D is taller than C)

2. **B is shorter than D but taller than C.**
- This means:
- \( B < D \) (B is shorter than D)
- \( B > C \) (B is taller than C)

### Step 2: Establish the relationships
From the above information, we can summarize the relationships as follows:
- From the first statement:
- \( A > D > C \)
- From the second statement:
- \( C < B < D \)

### Step 3: Combine the inequalities
Now we can combine the inequalities:
- From \( A > D > C \) and \( C < B < D \), we can deduce:
- \( A > D > B > C \)

### Step 4: Determine the tallest doll
From the relationships we have established:
- The tallest doll is A, since \( A > D \), \( A > B \), and \( A > C \).

### Conclusion
Therefore, if Mani wants to purchase the tallest doll, she should purchase **Doll A**.

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