Difficulty: Medium
Correct Answer: The data in both statements I and II together are sufficient to answer the question.
Explanation:
Introduction / Context:
This data sufficiency question involves a small family and asks how many brothers Tarun has. Two statements give information about the number of children of Tarun's father and the number of sisters Tarun has. The key idea is to check whether this information, individually or together, allows us to determine a unique count of Tarun's brothers.
Given Data / Assumptions:
Concept / Approach:
We must count brothers, which are male siblings of Tarun. If we know the total number of children and how many of them are daughters, we can deduce how many sons there are. Since Tarun is one of the children, we need to be careful to distinguish between Tarun himself and his brothers. The data sufficiency method requires checking each statement alone and then both together to see where we obtain a unique answer.
Step-by-Step Solution:
Step 1: From statement I, the father of Tarun has three children in total. This set includes Tarun and two other children, but their genders are not specified.
Step 2: Statement I alone is not sufficient, because the three children could be any combination of sons and daughters, and we cannot count Tarun's brothers without more information.
Step 3: From statement II, Tarun has two sisters. This means that among the siblings of Tarun, there are exactly two female children. However, statement II alone does not specify the total number of children in the family, so there could also be one or more brothers beyond Tarun himself.
Step 4: Therefore, statement II alone is not sufficient, because it allows for different possibilities regarding the total number of children.
Step 5: Combine the information from both statements. We know from statement I that the father of Tarun has exactly three children. Since Tarun is one of them, there are two other children apart from Tarun.
Step 6: From statement II, we know that Tarun has two sisters. So the other two children must both be sisters of Tarun.
Step 7: Thus, the three children of the father are: Tarun, sister one and sister two.
Step 8: Since the total number of children is three and two of them are sisters, there is no remaining child who could be a brother of Tarun.
Step 9: Therefore, Tarun has zero brothers.
Verification / Alternative check:
We can check internal consistency. If Tarun had at least one brother, then the father would have at least four children: Tarun, at least one brother and two sisters. This would contradict the information that the father has exactly three children.
Thus, the only possibility consistent with both statements is that the siblings of Tarun are exactly two sisters, and no brothers.
Why Other Options Are Wrong:
Option a is wrong because statement I alone does not tell us how many of the three children are daughters or sons.
Option b is wrong because statement II alone tells us about two sisters but does not restrict the total number of children; there could be additional brothers.
Option c is wrong as neither statement alone yields a unique answer.
Option e is wrong because the combined information does fix the number of brothers at zero.
Common Pitfalls:
Some students quickly read that Tarun has two sisters and suppose there may also be a brother, without remembering that the father has only three children in total. Another common error is not to include Tarun among the three children and to imagine three children in addition to Tarun. Careful reading shows that the father has three children in total, including Tarun. The data sufficiency framework emphasises that every word matters, and ignoring even a simple total count can lead to wrong conclusions.
Final Answer:
Tarun has no brothers.
Correct option: The data in both statements I and II together are sufficient to answer the question.
Discussion & Comments