A chocolate store has n boxes, and each box has a distinct number of c

Question

A chocolate store has n boxes, and each box has a distinct number of chocolates. Is the median number of chocolates per box an integer?
(1) The number of chocolates in each of the n boxes at the store is an odd number.
(2) The number of boxes is odd.

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We have n boxes with each having a distinct number of chocolates 
 We are asked if the median number of chocolates per box is an integer or not 
 It is a YES-NO question

Statement 1:   The number of chocolates in each of the n boxes at the store is an odd number
  If the number of boxes i.e., n is odd, then the median will be the  \frac{n+1}{2} th element which  we know will be integer  
 If the number of boxes i.e., n is even, then the median will be the mean of middle two terms. We know middle two terms are both odd and  mean of two odd numbers is always going to be an integer  
 Thus,  statement 1 alone is sufficient and we can eliminate options B, C and E   
 
  Statement 2:   The number of boxes is odd
  According to this statement, n is odd 
 So, the median will be the  \frac{n+1}{2} th element which  we know will be integer  
 Thus,  statement 2 alone is also sufficient

Hence the right answer is    Option D

EeshitaV · Answer

Do we have to assume #chocolates to be whole numbers? Can't they be integers (like half?)

Bunuel · Answer

Whole numbers  are  integers. I believe you meant to say "proper fraction" instead of "integer" (a proper fraction is a fraction where the numerator is less than the denominator). The answer to your question is no, from the context of the question we can deduce that the number of chocolates per box must be an integer.

P.S. The GMAT does not use the term "whole number" at all; instead, it uses "integer".

iipshitaaaa · Answer

Isn’t the question asking us whether the median number of chocolates per box an integer?

Choice B talks about the number of boxes not the number of chocolates inside those boxes. So the number could be odd or even. 
Can someone please clarify.

Posted from my mobile device

Shane04 · Answer

Can someone explain why the OA is not A?
Questions asks if" the median number of chocolates per box " an integer

Statement 1 clearly tells us about the total number being odd or even so we know the median is an integer

Statement 2 does not provide any info about the number of chocolates in the box.

Bunuel

Bunuel · Answer

The question asks whether the median number of chocolates per box an integer.

For an odd number of items (arranged in ascending or descending order), the median is the middle number. 
  For an even number of items (arranged in ascending or descending order), the median is the average of the two middle numbers.

Statement (2) highlights that the count of boxes is odd. And, since every box has an integer number of chocolates, we can conclude that the median will indeed be an integer.

pappal · Answer

well I Interpreted  median no of chocolates per box  
as, median of chocolates in given boxes / no of boxes ?? and ended up with E choice.
wouldn't it be better to write median no. of chocolates in the boxes??
help!!

A chocolate store has n boxes, and each box has a distinct number of c

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A chocolate store has n boxes, and each box has a distinct number of c

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