A comparison of marks socred by Gauri , Aaban, Seerat and Alvina in an examination is as follows
I. Gauri has scored 15 marks ess than Aaban.
II. Gauri has scored 20 marks more than Seerat .
III. Alvina has scored 10 marks less than Seerat
To decide who has scored the highest marks, identify the statement from those given in the alternatives in respect of sufficiency of data

Options

A. Data given in I and II are sufficient
B. Data given in I and III are sufficient
C. Data given in II and III are sufficient
D. Data given in I, II and III are sufficient

Answer

To solve the problem, we need to analyze the information given in the statements about the marks scored by Gauri, Aaban, Seerat, and Alvina. Let's break it down step by step.

### Step 1: Define Variables
Let:
- G = Marks scored by Gauri
- A = Marks scored by Aaban
- S = Marks scored by Seerat
- Al = Marks scored by Alvina

### Step 2: Translate Statements into Equations
From the statements, we can create the following equations:

1. **From Statement I:** Gauri has scored 15 marks less than Aaban.
\[ G = A - 15 \]

2. **From Statement II:** Gauri has scored 20 marks more than Seerat.
\[ G = S + 20 \]

3. **From Statement III:** Alvina has scored 10 marks less than Seerat.
\[ Al = S - 10 \]

### Step 3: Substitute to Find Relationships
Now, we can substitute the equations to find relationships among the scores:

- From the first equation, we can express Aaban's marks in terms of Seerat's marks using the second equation:
\[ A = G + 15 = (S + 20) + 15 = S + 35 \]

- Now, we have:
\[ A = S + 35 \]
\[ G = S + 20 \]
\[ Al = S - 10 \]

### Step 4: Compare the Scores
Now we can compare the scores of all four individuals:

1. **Gauri's score:** \( G = S + 20 \)
2. **Aaban's score:** \( A = S + 35 \)
3. **Seerat's score:** \( S = S \)
4. **Alvina's score:** \( Al = S - 10 \)

### Step 5: Determine the Highest and Lowest Scores
From the equations:
- Aaban has the highest score since \( A = S + 35 \) (which is greater than both G and S).
- Alvina has the lowest score since \( Al = S - 10 \) (which is less than S).

### Conclusion
To determine who scored the highest marks, we needed all three statements. Therefore, the data from all three statements is necessary to conclude the relationships among the scores.

### Final Answer
The correct alternative is: **Data from statements 1, 2, and 3 are sufficient.**

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