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?
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) provides a specific probability for selecting 2 adults, which allows for the calculation of the number of adults in relation to the total group size. However, statement (2) does not provide a precise number of adults, only indicating that they constitute more than 50% of the group, which is insufficient for a definitive calculation.
This statement correctly identifies the sufficiency of statement (1). Given the probability of selecting 2 adults as 1/3, we can derive that if there are at least 2 adults and 2 children, the total number of adults can be determined mathematically, fulfilling the requirement to answer the question.
This statement is incorrect because while statement (2) indicates that adults make up more than 50% of the group, it does not provide enough specific information to determine the exact number of adults. Therefore, this statement alone cannot suffice to answer the question.
This option is also incorrect because statement (1) alone provides enough information to answer the question without needing to combine it with statement (2). Thus, both statements together are not necessary for sufficiency.
This option is false, as statement (2) alone does not provide enough information to determine the number of adults. Only statement (1) is sufficient on its own.
This choice is incorrect since statement (1) alone is indeed sufficient. The combination of both statements is unnecessary.
In this analysis, we find that statement (1) sufficiently provides the necessary probability to derive the number of adults in the group, whereas statement (2) lacks specificity for a conclusive answer. Thus, only statement (1) can stand alone as sufficient, making option A the correct choice.
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