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

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RenB
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A chocolate store has n boxes, and each box has a distinct number of c [#permalink] New post   08 Aug 2023, 18:04
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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.
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Re: A chocolate store has n boxes, and each box has a distinct number of c [#permalink] New post   11 Aug 2023, 00:21
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RenB wrote:
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.


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
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Re: A chocolate store has n boxes, and each box has a distinct number of c [#permalink] New post   20 Aug 2023, 21:46
Do we have to assume #chocolates to be whole numbers? Can't they be integers (like half?)
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Re: A chocolate store has n boxes, and each box has a distinct number of c [#permalink] New post   21 Aug 2023, 00:03
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EeshitaV wrote:
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.

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


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".
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Re: A chocolate store has n boxes, and each box has a distinct number of c [#permalink] New post   21 Aug 2023, 08:45
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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.

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A chocolate store has n boxes, and each box has a distinct number of c [#permalink] New post   25 Aug 2023, 18:44
RenB wrote:
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.



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.

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Re: A chocolate store has n boxes, and each box has a distinct number of c [#permalink] New post   26 Aug 2023, 02:03
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Shane04 wrote:
RenB wrote:
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.



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


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.
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Re: A chocolate store has n boxes, and each box has a distinct number of c [#permalink]
26 Aug 2023, 02:03
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