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
Which of the following statement is correct?
I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.
II. The value of
\(\left(k^2+ \frac{1}{k^2} \right) \left(k- \frac{1}{k} \right) \left(k^4+ \frac{1}{k^4} \right) \) \(\left(k+ \frac{1}{k} \right)\left(k^4- \frac{1}{k^4} \right)\) is \(k^{16}- \frac{1}{k^{16}}\).
Given below is a question followed by two statements I and II. Read both statements carefully to decide which one of them is sufficient to answer the question.
Six people - A, B, C, D, E and F are sitting in a straight line facing north. Who sits to the immediate left of D?
(I) A sits second from one of the extreme ends of the line. Only two people sit between A and B. E sits to the immediate right of C.
(II) C sits third from the left end of the line. Only one person sits between C and F. E sits third to the right of F.
Please read the below equation and select an appropriate option from the following.
x + y = 10 ; y = x - 2
Quantity A is x.
Quantity B is y.
A lady wants to buy the following items in the given price range-
1. Tomato between Rs. 40 and Rs. 45 per kg.
2. Grapes in the price range of Rs. 80 and Rs. 90 per kg.
3. Milk packets at Rs. 23 per liter.
In which shop from the following will she definitely get all her items/
A. Shop S sells tomato at Rs. 22.5 per half kg, Grapes at Rs. 82 per kg and milk at Rs. 24 per liter.
B. Shop H sells grapes at Rs. 21 per quarter kg, milk at 12.5 per half litre and tomato at Rs. 22 per half kg.
C. Shop O sells milk at Rs. 11.5 per half litre, tomato at 21 per half kg and grapes at Rs. 43 per half kg.
D. Shop P sells tomato at Rs. 23.5 per half kg, grapes at Rs. 85 per kg and milk at Rs. 23 per litre.You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
When is Yuvi's wedding anniversary?
Statements:
1: On the 7 th day of a month.
2. The month has 29 days only in a leap year.
