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# There are 5 integers such that the difference of the biggest number an

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Senior SC Moderator
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There are 5 integers such that the difference of the biggest number an  [#permalink]

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27 Mar 2017, 17:59
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75% (hard)

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48% (02:08) correct 52% (02:57) wrong based on 77 sessions

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There are 5 integers such that the difference of the biggest number and the median is 3. Is the average (arithmetic mean) of the integers smaller than the median?

1) The median of the 5 integers is 16.
2) The difference of the median and the smallest number is 8.

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Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

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27 Mar 2017, 23:02
given that difference of the biggest number and the median is 3. Is the average (arithmetic mean) of the integers smaller than the median?

STE 1 : Median of 5 numbers is equal to 16. Doesn't give any info about the avg : not sufficient
STE 2 : Difference between the median and smallest number is 8. if median is X then the max value of next two terms can be X+3,X+3 ie a +ve deviation of 6 but we have a negative deviation of 8 ,which brings the avg below the median. Sufficient

Ans B
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Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

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27 Mar 2017, 23:08
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Let the median be = x
Biggest number = x + 3

St1: Median = x = 16 --> Biggest number = 19
If the 5 integers are 1, 1, 16, 16, 19, then Average < Median
If the 5 integers are 16, 16, 16, 19, 19 then Average > Median
Not Sufficient

St2: The 5 integers in ascending order are x - 8, ___, x, ___, x + 3
Maximizing the possible values we have, x - 8, x, x, x +3, x + 3 --> Average = (5x - 2)/5 < Median
Sufficient

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Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

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27 Mar 2017, 23:29
2
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ziyuen wrote:
There are 5 integers such that the difference of the biggest number and the median is 3. Is the average (arithmetic mean) of the integers smaller than the median?

1) The median of the 5 integers is 16.
2) The difference of the median and the smallest number is 8.

With 5 integers, median will be the middle number.

5 integers: ______, _______, M, ______, M+3

Question: Is the average smaller than M?
In other words, from M, is the deviation of integers smaller than M more than the deviation of integers greater than M?

Since the greatest integer is M+3, we know that the maximum deviation of numbers greater than M, from M is 3 + 3 = 6 (in case both numbers are M+3).

1) The median of the 5 integers is 16.
Tells us nothing about the deviation of integers.
Not sufficient.

2) The difference of the median and the smallest number is 8.
The smallest number has a deviation of 8 from M. This means that the deviation of numbers smaller than M IS CERTAINLY MORE THAN the deviation of numbers greater than M (which is 6).
Sufficient.

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Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

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11 Apr 2019, 04:10
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Re: There are 5 integers such that the difference of the biggest number an   [#permalink] 11 Apr 2019, 04:10
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