Which of the statements is sufficient to answer the question? Question: Find the total number of students in a class if the class has some boys and some girls. Statements: I. The number of boys in a class is 10. II. The number of girls in a class is 2 more than the number of boys.
Both statements I and II are sufficient
Understanding the Data Sufficiency Question
The question asks for the total number of students in a class. We are told the class consists of some boys and some girls. To find the total number of students, we need to know the number of boys and the number of girls. The problem provides two statements, and we need to determine which statement or combination of statements is sufficient to find this total number.
Analyzing Statement I: Number of Boys
Statement I says: The number of boys in a class is 10.
This statement gives us the specific number of boys. However, it provides no information about the number of girls. Since the total number of students is the sum of boys and girls, knowing only the number of boys is not enough to determine the total number of students in the class.
Therefore, Statement I alone is not sufficient to answer the question about the total number of students.
Analyzing Statement II: Relation of Girls to Boys
Statement II says: The number of girls in a class is 2 more than the number of boys.
This statement gives us a relationship between the number of girls and the number of boys. It tells us that if we knew the number of boys, we could calculate the number of girls (Number of girls = Number of boys + 2). However, Statement II itself does not give us the actual number of boys. Without the actual number of boys (or girls), we cannot find the specific number of girls or the total number of students.
Therefore, Statement II alone is not sufficient to answer the question about the total number of students.
Analyzing Statements I and II Combined: Total Students Calculation
Let's consider both statements together:
- From Statement I: Number of boys = 10
- From Statement II: Number of girls = Number of boys + 2
Using the information from both statements, we can substitute the number of boys from Statement I into the relationship given in Statement II:
Number of girls = 10 + 2 = 12
Now that we know the number of boys (10) and the number of girls (12), we can calculate the total number of students:
Total students = Number of boys + Number of girls
Total students = 10 + 12 = 22
Since combining both statements allows us to find a unique value for the total number of students, both statements together are sufficient to answer the question.
Conclusion on Data Sufficiency
Based on the analysis:
- Statement I alone is not sufficient.
- Statement II alone is not sufficient.
- Statements I and II together are sufficient.
Thus, both statements I and II are required to answer the question about the total number of students in the class.
Revision Table: Statement Sufficiency
| Statements Considered | Sufficient? | Reason |
|---|---|---|
| Only Statement I | No | Gives number of boys but not girls. |
| Only Statement II | No | Gives relation between girls and boys but not specific numbers. |
| Statements I and II Together | Yes | Gives number of boys and relationship to find number of girls, allowing total calculation. |
Additional Information: Data Sufficiency Concepts
Data Sufficiency questions test your ability to determine if the provided information is enough to answer a specific question, rather than requiring you to actually calculate the answer. You evaluate each statement independently first, and then combine them if neither is sufficient alone.
Possible outcomes for a data sufficiency question with two statements (I and II):
- Statement I alone is sufficient, but Statement II alone is not.
- Statement II alone is sufficient, but Statement I alone is not.
- Both statements I and II together are sufficient, but neither statement alone is sufficient. (This is the case in our current problem).
- Each statement alone is sufficient.
- Statements I and II together are not sufficient.
Understanding these different outcomes helps in systematically approaching data sufficiency problems. The key is to avoid making assumptions and only use the information explicitly given in the statements.
Important Questions from Data Sufficiency
Consider two Statements and a Question:
Statement 1: Priya is 4 ranks below Seema and is 31 st from the bottom.
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?
