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In a certain list of numbers, the greatest number is 100. Is the

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In a certain list of numbers, the greatest number is 100. Is the  [#permalink]

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New post 06 Oct 2015, 10:22
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In a certain list of numbers, the greatest number is 100. Is the average (arithmetic mean) of the list equal to the median of the list?

(1) The average (arithmetic mean) of the list is 100.

(2) The median of the list is 100.

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Re: In a certain list of numbers, the greatest number is 100. Is the  [#permalink]

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New post 06 Oct 2015, 11:49
1
Suppose there are 5 elements in the list
A , B , C, D and E arranged in ascending order .
E=100 , the greatest number

1. Mean =100
Total = 100x5=500
A+B+C+D+E=500
A+B+C+D=400

Since , mean is 100 and none of A ,B ,C or D can be greater than E i.e 100 . Each of them will be 100.
Therefore , Mean is equal to median- C.
Sufficient.

2.Median is 100
C=100
E=100
=> D =100 as the list is sorted in ascending order.

Whether mean is equal to median(100) will depend on values of A and B.

Hence , answer A :)
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Re: In a certain list of numbers, the greatest number is 100. Is the  [#permalink]

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New post 06 Oct 2015, 12:09
draditya wrote:
In a certain list of numbers, the greatest number is 100. Is the average (arithmetic mean) of the list equal to the median of the list?

(1) The average (arithmetic mean) of the list is 100.

(2) The median of the list is 100.



(1) Average=100 and Max Value=100 means all numbers are equal to 100 in this case the average and the median are equal SUFFICIENT
(2) Median=100, let's say we have 3 numbers in a list: 2,100,100 NO, or 100,100,100 YES - NOT SUFFICIENT
Answer (A)
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Re: In a certain list of numbers, the greatest number is 100. Is the  [#permalink]

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New post 06 Oct 2015, 22:47
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Normally, when range=0 and the average (arithmetic mean) equals to the greatest number or the smallest number in the list, all elements in the list have the same value with standard deviation=0/
Looking at condition 1, the arithmetic mean is told to be 100, which is also told to be the greatest number in the list. Hence, the standard deviation=0, and all elements have the same value, and the average (arithmetic mean)= median. The condition is sufficient, and the answer becomes (A).
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Re: In a certain list of numbers, the greatest number is 100. Is the  [#permalink]

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Re: In a certain list of numbers, the greatest number is 100. Is the   [#permalink] 20 Mar 2019, 01:06
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