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

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.

Note that the problem never mentioned that each school sent at least one student.
So, some of the numbers may be equal to zero.

Consider the following two sets of integers that represent the number of students sent by the 8 schools in decreasing order,

• {34, 33, 19, 4, 3, 2, 1, 0} ---> Third most number = 19 > 15 ---> YES
  {34, 33, 14, 8, 3, 2, 1, 0} ---> Third most number = 14 < 15 ---> NO

Both of the above cases satisfy both the statements but the answer is YES in the 1st case and NO in the 2nd case. So, both statements taken together is also not sufficient.

The correct answer is E.

Note : If we are to assume that each school sent at least one student (if it was a proper GMAT problem, it'd have been explicitly mentioned so), then follow the post made by Brent.

Anju@Gurome wrote:

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.

Note that the problem never mentioned that each school sent at least one student.
So, some of the numbers may be equal to zero.

Consider the following two sets of integers that represent the number of students sent by the 8 schools in decreasing order,

• {34, 33, 19, 4, 3, 2, 1, 0} ---> Third most number = 19 > 15 ---> YES
  {34, 33, 14, 8, 3, 2, 1, 0} ---> Third most number = 14 < 15 ---> NO

Both of the above cases satisfy both the statements but the answer is YES in the 1st case and NO in the 2nd case. So, both statements taken together is also not sufficient.

The correct answer is E.

Yeah, I considered the possibility of one school sending zero students, but if one school sent zero students, can we really say that "8 schools sent a total of 96 students to a math club competition"?

For example, about 2600 athletes from 92 countries participated in the 2010 Winter Olympics. Since there are 196 countries in the world, would it be correct to say that "196 countries sent a total of 2600 athletes to the 2010 Winter Olympics"?

I don't know if there's a definitive answer to this question, so let's say there are two correct answers E and B.

This question will undoubtedly raise a lot of questions among test-takers. At best, the question is ambiguous (definitely not up to the test-maker's high standards). An official GMAT question would include wording to remove this kind of ambiguity.

Cheers,
Brent

Brent@GMATPrepNow wrote:For example, about 2600 athletes from 92 countries participated in the 2010 Winter Olympics. Since there are 196 countries in the world, would it be correct to say that "196 countries sent a total of 2600 athletes to the 2010 Winter Olympics"?

I agree that it won't be correct to say so.
But then again it is a quant problem and we should not make any assumption. A proper GMAT problem won't leave any scope of having this discussion.