BTGmoderatorDC wrote:Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January?

(1) More of the people in the auditorium have their birthday in February than in March.
(2) Five of the people in the auditorium have their birthday in March.

OA D

Source: Official Guide

If we consider that in each of the 11 months, there are 6 people whose b'day fall in those months, we have 6*11 = 66 people. Since one month may be left, if it is January, the answer is No; however, if it is not, the answer is Yes.

Let's take each statement one by one.

(1) More of the people in the auditorium have their birthday in February than in March.

If we consider that no one's bday falls in January month, then Feb, as well as March, must have 6 people whose bday fall in these two months. However, the statement states that more of the people in the auditorium have their birthday in February than in March, thus, at least one person's bday must be in January. Sufficient.

(2) Five of the people in the auditorium have their birthday in March.

Again since to make no one has b'day in January, March month must have 6 people whose B'day is in March. Since it is not so, at least one person's bday must be in January. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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