A school used several buses for a field trip. If each bus carried

Question

A school used several buses for a field trip. If each bus carried a different number of students, was the median number of students per bus an integer?

(1) Each bus carried an odd number of students.
(2) The number of buses used for the field trip was odd.

BongBideshini · Answer

Statement (1)

Example:
3 buses:
1, 3, 5
Median = 3 (integer)

4 buses:
1, 3, 5, 7
Median = (3 + 5)/2 = 8 (integer)

Statement (1) alone is sufficient.

Statement (2)

With an odd number of observations, the median is always the middle value. Because the number of students in a bus will always be an integer, the middle value will always be an integer.

Statement (2) alone is sufficient.

Answer: D.

prepapr · Answer

We need to determine whether the median number of students per bus is an integer.
Analyzing Statement (1)
Each bus carried an odd number of students.
 
 If there are an odd number of buses, the median is the middle value, which will be an odd integer.  
 If there are an even number of buses, the median is the average of the two middle values. Since the average of two odd numbers is always an integer, the median will still be an integer.   
Therefore, statement (1) alone is sufficient.

Analyzing Statement (2)
The number of buses used was odd.
An odd number of observations means the median is the middle value in the ordered list. Since the number of students on each bus must be an integer, the middle value will also be an integer.
Therefore, statement (2) alone is sufficient.

Since both statements alone are sufficient:
Correct Answer: D

Idonije · Answer

I agree that statement 1 is sufficient but statement 2 isn't because it only speaks to the number of buses being odd. what if the buses in statement 2 had even number of students inside them. The question asks for if the median number of students per bus is an integer, it doesn't ask us about the bus itself.

SS990 · Answer

Adit_ · Answer

Take an example:

Each bus lets say has 6,8,10 students in bus 1,2,3 respectively.

What is the median number of students per bus?
8 right?
It is an integer.

Number of students is always an integer and that is all the matters here.
Because median of odd number of items if always the central value. Central value here is always an integer, thus the answer is YES definitively.

Hence Sufficient.

Aman2487 · Answer

It is d

A school used several buses for a field trip. If each bus carried

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GMAT Data Sufficiency (DS) Questions

A school used several buses for a field trip. If each bus carried

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