Q. Four students – Ankita, Bhavna, Chitra, and Deepa – scored different marks. Who scored the highest marks?
(I) Bhavna scored more than Ankita but less than Chitra.
(II) Deepa scored more than Bhavna but less than Chitra.
Data Sufficiency: Highest Score Analysis
The problem requires determining who scored the highest marks among four students: Ankita, Bhavna, Chitra, and Deepa, using two given statements.
Statement (I) Analysis
Statement (I) provides the following information:
- Bhavna scored more than Ankita: \( \text{Bhavna} > \text{Ankita} \)
- Bhavna scored less than Chitra: \( \text{Bhavna} < \text{Chitra} \)
Combining these, we get the order: \( \text{Chitra} > \text{Bhavna} > \text{Ankita} \). This statement alone tells us Chitra scored more than Bhavna and Ankita, but Deepa's position is unknown. Thus, Statement (I) alone is insufficient.
Statement (II) Analysis
Statement (II) provides the following information:
- Deepa scored more than Bhavna: \( \text{Deepa} > \text{Bhavna} \)
- Deepa scored less than Chitra: \( \text{Deepa} < \text{Chitra} \)
Combining these, we get the order: \( \text{Chitra} > \text{Deepa} > \text{Bhavna} \). This statement alone tells us Chitra scored more than Deepa and Bhavna, but Ankita's position is unknown. Thus, Statement (II) alone is insufficient.
Combined Analysis
Combining the information from both statements:
- From Statement (I): \( \text{Chitra} > \text{Bhavna} > \text{Ankita} \)
- From Statement (II): \( \text{Chitra} > \text{Deepa} > \text{Bhavna} \)
By combining these, we can establish the following:
- \( \text{Chitra} \) scored more than \( \text{Bhavna} \).
- \( \text{Chitra} \) scored more than \( \text{Ankita} \) (from I).
- \( \text{Chitra} \) scored more than \( \text{Deepa} \) (from II).
This implies that Chitra scored the highest marks among all four students. Therefore, the data in both statements together are sufficient to answer the question.
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Important Questions from Data Sufficiency
Consider two Statements and a Question:
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Statement 2: Ena is 2 ranks above Seema and is 37" from the bottom.
Question: What is Seema’s rank from the top in the class of 40 students ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question:
Statement 1: Each of A and D is heavier than each of B, E and F, but none of them is the-heaviest.
Statement 2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A,B,C, D and E?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question :
Statement-1 : The last day of the month is a Wednesday.
Statement-2 : The third Saturday of the month was the seventeenth day.
Question : What day is the fourteenth of the given month ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider the Question and two Statements given below :
Question : Is xan integer?
Statement-1 : x / 3 is not an integer.
Statement-2 : 3 xis an integer.
Which one of the following is correct in respect of the Question and the Statements?
Consider the Question and two Statements given below:
Question : What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother.
Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3 : 5.
Which one of the following is correct in respect of the Question and the Statements?
