Question

The mark of Kiran is greater than or equal to the marks of Hina. Hina and Tina got equal marks. The mark of Tina is greater than Urvi, but Urvi's marks are less than or equal to the marks of Ira. Based on the above information, which of the following statements is/are definitely true?
I. Urvi got less marks than that of Kiran.
II. Ira's marks are less than or equal to the marks of Tina.

• A. Only statement II
• B. Only statement I
• C. Both statements I and II
• D. Neither statement I nor II

Hint:

In logical deduction problems involving inequalities, always try to form a single chain of relationships. If a variable cannot be placed in the chain, its relationship with other variables in the chain may be uncertain.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given a set of comparisons between the marks of five individuals: Kiran, Hina, Tina, Urvi, and Ira. We need to combine these comparisons to determine which of the two given statements must be true. 
Step 2: Key Formula or Approach: 
We will represent the given information using mathematical inequality symbols (>, <, \(\geq\), \(\leq\), =). Then, we will combine these inequalities to establish a clear relationship between the individuals' marks. 
Let K, H, T, U, and I be the marks of Kiran, Hina, Tina, Urvi, and Ira, respectively. 
Step 3: Detailed Explanation: 
From the problem statement, we can deduce the following relationships: 
1. The mark of Kiran is greater than or equal to the marks of Hina: \(K \geq H\) 
2. Hina and Tina got equal marks: \(H = T\) 
3. The mark of Tina is greater than Urvi: \(T>U\) 
4. Urvi's marks are less than or equal to the marks of Ira: \(U \leq I\) 
Now, let's combine these relationships: 
From (1) and (2), we get \(K \geq H = T\), which simplifies to \(K \geq T\). 
Combining this with (3), we get the chain of inequalities: \(K \geq T>U\). 
From \(K \geq T\) and \(T>U\), it is definitively true that \(K>U\). 
Now let's evaluate the given statements: 
Statement I: Urvi got less marks than that of Kiran. 
This statement translates to \(U<K\). Our combined inequality \(K>U\) proves this statement is definitely true. 
Statement II: Ira's marks are less than or equal to the marks of Tina. 
This statement translates to \(I \leq T\). We know \(T>U\) and \(U \leq I\). There is no direct relationship that can be established between T and I from this information. For example, if T=10 and U=8, I could be 9 (making \(I<T\)) or I could be 12 (making \(I>T\)). Since we cannot be certain about the relationship between I and T, this statement is not definitely true. 
Step 4: Final Answer: 
Only statement I is definitely true.