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In a set of 24 positive integers, 12 of the integers are les

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In a set of 24 positive integers, 12 of the integers are les [#permalink] New post 18 Jan 2016, 08:59
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Question Stats:

92% (00:33) correct 7% (01:27) wrong based on 39 sessions
In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.

Quantity A
Quantity B
The median of the 24
integers
50


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




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Question: 9
Page: 339
Difficulty: medium
[Reveal] Spoiler: OA

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Re: In a set of 24 positive integers, 12 of the integers are les [#permalink] New post 18 Jan 2016, 09:01
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Solution

The median of a set of n positive integers, where n is even, is obtained by ordering the integers from least to greatest and then calculating the average (arithmetic mean) of the two middle integers. For this set of 24 integers, you do not know the values of the two middle integers; you know only that half of the integers are less than 50 and the other half are greater than 50.

If the two middle integers in the list are 49 and 51, the median is 50; and if the two middle integers are 49 and 53, the median is 51. Thus the relationship cannot be determined from the information given.

The correct answer is \(D\).
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Re: In a set of 24 positive integers, 12 of the integers are les [#permalink] New post 09 Jun 2016, 09:40
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Carcass Array[WROTE]:
In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.

Quantity A
Quantity B
The median of the 24
integers
50


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Consider these two possible cases:
Case 1: {1,1,1,1,1,1,1,1,1,1,1,1,51,51,51,51,51,51,51,51,51,51,51,51}
In this case the median of the 24 integers is 26, which means Quantity B is greater.

Case 2: {1,1,1,1,1,1,1,1,1,1,1,1,199,199,199,199,199,199,199,199,199,199,199,199}
In this case the median of the 24 integers is 100, which means Quantity A is greater.

[Reveal] Spoiler:
D


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Re: In a set of 24 positive integers, 12 of the integers are les   [#permalink] 09 Jun 2016, 09:40
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