3. Two people will be selected from a group of n (n ≥ 10) people. If there are at least 2 adults and 2 children, and n is an even number, how many people in the group are adults?
Answer: A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Based on the information provided in statement (1), we can determine the number of adults in the group, while statement (2) lacks sufficient information to reach a conclusion.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
This option is correct because statement (1) provides specific information that allows us to calculate the number of adults in the group based on the conditions provided. It offers enough data to understand the composition of the group fully.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
This option is incorrect because statement (2) does not provide enough information to determine the number of adults in the group. It fails to define any specific parameters that would help identify the count of adults.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
This option is incorrect because if statement (1) alone is sufficient, then it is unnecessary to combine both statements. The sufficiency of statement (1) negates the need for statement (2) to clarify the number of adults.
D) EACH statement ALONE is sufficient.
This option is incorrect because statement (2) alone does not provide enough information, while statement (1) does. Therefore, it cannot be claimed that each statement alone is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.
This option is incorrect as it contradicts the finding that statement (1) alone is sufficient. The combination of both statements is not needed to determine the number of adults, making this option invalid.
Conclusion
The correct option, A, is valid as statement (1) provides sufficient information to ascertain the number of adults in the group, while statement (2) fails to offer any useful data on its own. Thus, option A is the only one that accurately reflects the sufficiency of the statements regarding the group's composition.