Decide whether the data provided in the statements numbered I and II is sufficient to answer the given question. What is the ratio of boys to girls in a class? Statements: I. There are 20 boys in the class.
Question:
Statement II alone is sufficient while I alone is not sufficient.
Understanding the Data Sufficiency Question on Class Ratios
The question asks us to determine if the information given in statements I and II is enough to find the ratio of boys to girls in a class. We need to evaluate each statement independently and then potentially together, although in data sufficiency, if one statement alone is sufficient, combining is not necessary to determine sufficiency.
Analyzing Statement I: Number of Boys
Statement I tells us:
- There are 20 boys in the class.
Knowing only the number of boys does not give us any information about the number of girls or the total number of students. Without knowing the number of girls, we cannot determine the ratio of boys to girls.
Therefore, statement I alone is not sufficient to answer the question about the ratio of boys to girls in the class.
Analyzing Statement II: Ratio of Girls to Total Students
Statement II tells us:
- The ratio of girls to the number of students in the whole class is 3 : 7.
Let's represent the number of girls and the total number of students using a common variable based on this ratio. If the ratio of girls to the total is 3:7, we can assume:
- Number of girls \(= 3x\)
- Total number of students \(= 7x\)
Here, \(x\) is a positive integer multiplier.
The total number of students in the class is the sum of the number of boys and the number of girls.
\(\text{Total Students} = \text{Number of Boys} + \text{Number of Girls}\)
We can express the number of boys using this equation:
\(\text{Number of Boys} = \text{Total Students} - \text{Number of Girls}\)
Substituting the expressions using \(x\):
\(\text{Number of Boys} = 7x - 3x = 4x\)
Now we have expressions for the number of boys and the number of girls in terms of \(x\):
- Number of boys \(= 4x\)
- Number of girls \(= 3x\)
The question asks for the ratio of boys to girls. We can find this ratio:
\(\text{Ratio of Boys to Girls} = \frac{\text{Number of Boys}}{\text{Number of Girls}} = \frac{4x}{3x}\)
Since \(x\) is a common multiplier (and \(x \neq 0\)), it cancels out:
\(\text{Ratio of Boys to Girls} = \frac{4}{3}\)
So, the ratio of boys to girls is 4:3. Statement II alone provides enough information to determine this ratio.
Therefore, statement II alone is sufficient to answer the question about the ratio of boys to girls in the class.
Conclusion on Data Sufficiency
Based on our analysis:
- Statement I alone is not sufficient.
- Statement II alone is sufficient.
Thus, only statement II is needed to answer the question.
| Statement | Information Provided | Sufficient to find Boy:Girl Ratio? | Reason |
|---|---|---|---|
| I | Number of boys = 20 | No | Number of girls is unknown. |
| II | Ratio of girls to total students = 3:7 | Yes | Allows calculation of the ratio of boys to girls (4:3). |
Revision Table: Key Concepts for Data Sufficiency Ratios
| Concept | Description | Application in this Problem |
|---|---|---|
| Data Sufficiency | Determining if given information is enough to answer a question. | Evaluating Statements I & II for sufficiency. |
| Ratio | A comparison of two quantities (e.g., a:b). | Finding the ratio of boys to girls. |
| Ratio Parts | Representing quantities as parts of a ratio (e.g., 3x, 7x). | Using 3x for girls and 7x for total students. |
| Total = Parts Sum | Total number of items is the sum of its constituent parts (e.g., Total = Boys + Girls). | Calculating number of boys as Total - Girls (7x - 3x). |
Additional Information: Working with Ratios and Data Sufficiency
Data sufficiency questions test your ability to identify necessary and sufficient information, not just your ability to calculate the final answer. When dealing with ratios in these problems, remember the following points:
- A ratio represents a proportion, not absolute numbers, unless a total or one part's absolute number is given.
- If a ratio of part to whole is given (like girls to total class is 3:7), you can easily deduce the ratio of the other part to the whole (boys to total class is 4:7) and the ratio of the two parts to each other (boys to girls is 4:3). This is because if the total is 7 parts, and girls are 3 parts, the remaining part (boys) must be \(7 - 3 = 4\) parts.
- Knowing the number of one part (like 20 boys) combined with a ratio relating parts or part-to-whole *is* sufficient to find the absolute numbers of all parts and the total. For example, if Statement I (20 boys) and Statement II (boys:girls = 4:3, derived from the given ratio) were combined, you could say \(4x = 20\), so \(x=5\). Then girls would be \(3x = 15\), total students \(7x = 35\). The ratio of boys to girls is 20:15, which simplifies to 4:3. However, we found Statement II alone was sufficient, so the combination wasn't needed for sufficiency.
- Always clearly identify what the question is asking for (in this case, a ratio). Sometimes, you can find the ratio even if you cannot find the exact number of students.
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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?
