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.
For me its clearcut A. Can someone please let me know if you think it not correct? OA is not provided unfortunately.
It's not A, because you don't know how many schools are represented. It might be that each of the 100 students if from a different school, in which case the answer is 'no', or they may all be from the same school, in which case the answer is 'yes'. Similarly Statement 2 is not sufficient, because we don't know how many ages are represented.
Using both Statements, we know that there are only 10 schools at the conference, and only 9 different ages (from 22 to 30 inclusive). Certainly it's possible that there are two, say, 28 year-olds from the same school, so the answer can be 'yes'. Can the answer be 'no'? Then we'd need every person of the same age to attend a different school. That means we could have at most ten 22 year olds, at most ten 23 year olds, and so on, and so at most 9*10 = 90 people. But we have 100 people, so it's impossible that the answer is 'no', and there must be at least two people of the same age at the same school, and the answer is C.
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