Official Guide Explanation:
Data Sufficiency #D45

Background

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Solution and Metadata

Question: D45
Page: 25
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Other >

Explanation: If there are 66 people in the auditorium and no more than 6 of them have their birthdays in any given month, there must be birthdays in at least 11 of the 12 months. There will be birthdays in exactly 11 months if there are exactly 6 people with birthdays in each of those months. (6 * 11 = 66). If there are any months where there are fewer than 6 birthdays, there must be birthdays in all 12 months.

Statement (1) is sufficient. If there are more birthdays in February than in March, there can be no more than 5 birthdays in March. Thus, there must be birthdays in all 12 months (necessarily including January).

Statement (2) is also sufficient. Again, we learn that there are no more than 5 birthdays in one of the months, meaning that there must be birthdays in all 12 months. Choice (D) is correct.

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