varun289 wrote:8 schools sent a total of 96 students to a math club competition. If one school sent the third most number of students to the competition (and no two schools sent the same number of students), did that school send at least 15 students?
(1) The most number of students that were sent by any one school was 34.
(2) The second most number of students that were sent by any school was 33.
Let's arrange the school delegations in ascending order: A, B, C, D, E,
F, G, H
The target question refers to the school that sent the 3rd greatest number of students (school
F)
Target question:
Did school F send at least 15 students?
Statement 1: The most number of students that were sent by any one school was 34.
In other words, school H sent 34 students.
We get: A, B, C, D, E,
F, G,
34
Does this provide enough information to answer the
target question?
No.
Consider these two conflicting cases:
Case a: the delegations are: 1, 2, 3, 4, 5,
20, 27,
34 in which case
school F sent at least 15 students
Case b: the delegations are: 5, 6, 7, 8, 9
10, 17,
34 in which case
school F did not send at least 15 students
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The second most number of students that were sent by any school was 33.
In other words, school G sent 33 students.
We get: A, B, C, D, E,
F,
33, H
In this scenario, it is
impossible for school F to send 15 students or more.
Here's why...
In order to maximize the number of students school F sends, we must minimize the number of students the other schools send.
So, for example, the fewest students that school A can send is 1.
Since no two schools can send the same number of students, the fewest students that school B can send is 1.
And so on to get: 1, 2, 3, 4, 5,
F,
33, H
Since school H sent the most students, the fewest students that it can send is 34.
So, we get: 1, 2, 3, 4, 5,
F,
33, 34
At this point, we have minimized the number of students sent by the other schools. In the process, we have accounted for 82 students, which means the MOST students that school F can send is 14.
In other words, statement 2 makes it
impossible for school F to send at least 15 students.
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
