Data Sufficiency

BTGmoderatorLU wrote:Source: GMAT Prep

At a business school conference with 100 attendees, are there any students of the same age (rounded to the nearest year) who attend the same school?

(1) The range of ages of the participants is 22 to 30, inclusive
(2) Participants represent 10 business schools.

The OA is C.

1) The range of ages of the participants is 22 to 30, inclusive.

There are nine age groups: 22, 23, 24, 25, 26, 27, 28, and 29. We have no information about the number of schools. If all the 100 students are from the same school, there must be some students of the same age who attend the same school.

However, if the 100 students are from 100 schools, the answer is No. No unique answer. Insufficient.

(2) Participants represent 10 business schools.

No idea about the ages. Insufficient.

(1) and (2) together

With 9 age-groups and 10 business schools, there would be 9*10 = 90 groups.

If out of 100 students, only one student belongs to one of the 90 groups, there would still be 100 - 90 = 10 students left. These 10 students must belong to any of the 90 groups, making us conclude that there are at least 10 students of the same age who attend the same school. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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