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The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

1) Exactly half of the numbers are less than 10. 2) The mode of the set of numbers is 10.

I'm getting C. Knowing both Stat 1 and Stat 2, we can say that the median value will never be 10.

Median = (5th term + 6th term)/2

Stat 1:
set = 5, 5, 5, 5, 5, 15, 15, 15, 15, 15
In this case median = 10.

set = 4, 4, 4, 4, 9, 15, 15, 15, 15, 15
median is not equal to 10.

Insuff

Stat 2:
set = 10 times 10.
Median = 10

set = 3, 4, 4, 5, 9, 10, 10, 10, 20, 25
median is not equal to 10

Insuff.

Stat 1 & 2:

Since exactly half the values are under 10 then the 5th term has to be less than 10. Since the mode is 10, the 6th term has to be 10.
(10+number less than 10)/2 has to be less than 10.

I get the same - C - using the same rationale as GK_GMAT. What's the OA?

I also got (C) using the same logic as GK_GMAT...(i didn't assume the numbers to be whole numbers since it's not mentioned anywhere)...but the OA is (E)

St1:
The set could be {0,0,0,0,1,10,10,10,10,59}. Mean = 10, Median = 5.5
The set could be {0,0,0,0,0,20,20,20,20,20}. Mean = 10, Median = 10.
Insufficient.

St2:
The set could be {10,10,10,10,10,10,10,10,10,10}. Mode = Mean = Median = 10
The set could be {1,2,3,4,5,6,10,10,10,49}. Mode = 10. Mean = 10. Median = 5.5
Insufficient.

St1 and St2:
The set could be {1,2,3,4,5,10,10,10,10,45}. Mode = Mean = 10. Median = 7.5
The set could eb {0,0,0,0,0,10,10,10,10,60}. Mode = Mean = 10. Median = 5.
Insufficient.

St1: The set could be {0,0,0,0,1,10,10,10,10,59}. Mean = 10, Median = 5.5 The set could be {0,0,0,0,0,20,20,20,20,20}. Mean = 10, Median = 10. Insufficient.

St2: The set could be {10,10,10,10,10,10,10,10,10,10}. Mode = Mean = Median = 10 The set could be {1,2,3,4,5,6,10,10,10,49}. Mode = 10. Mean = 10. Median = 5.5 Insufficient.

St1 and St2: The set could be {1,2,3,4,5,10,10,10,10,45}. Mode = Mean = 10. Median = 7.5 m The set could eb {0,0,0,0,0,10,10,10,10,60}. Mode = Mean = 10. Median = 5. Insufficient.

Ans E

how does it make C insufficient?
If we take both sets together 10 can never be median..question solved.

St1: The set could be {0,0,0,0,1,10,10,10,10,59}. Mean = 10, Median = 5.5 The set could be {0,0,0,0,0,20,20,20,20,20}. Mean = 10, Median = 10. Insufficient.

St2: The set could be {10,10,10,10,10,10,10,10,10,10}. Mode = Mean = Median = 10 The set could be {1,2,3,4,5,6,10,10,10,49}. Mode = 10. Mean = 10. Median = 5.5 Insufficient.

St1 and St2: The set could be {1,2,3,4,5,10,10,10,10,45}. Mode = Mean = 10. Median = 7.5 m The set could eb {0,0,0,0,0,10,10,10,10,60}. Mode = Mean = 10. Median = 5. Insufficient.

Ans E

how does it make C insufficient? If we take both sets together 10 can never be median..question solved.

my bad.... it should be C. I thought the question was asking for the value of the median in which case the answer would be E.

Re: DS : Mean/Median/Mode [#permalink]
11 May 2008, 05:43

vshaunak@gmail.com wrote:

Should be 'E'.

S1 + S2 not suff

case1 - set = {7,8,9,10,10,16} mean=median=mode=10 and 3 elements are smaller than 10. case2- set={1,2,3,4,10,10,10,40} mean=10, mode=10, median=7 and 4 elements and smaller than 10.

Re: DS : Mean/Median/Mode [#permalink]
11 May 2008, 05:52

tarkumar wrote:

vshaunak@gmail.com wrote:

Should be 'E'.

S1 + S2 not suff

case1 - set = {7,8,9,10,10,16} mean=median=mode=10 and 3 elements are smaller than 10. case2- set={1,2,3,4,10,10,10,40} mean=10, mode=10, median=7 and 4 elements and smaller than 10.

St1: The set could be {0,0,0,0,1,10,10,10,10,59}. Mean = 10, Median = 5.5 The set could be {0,0,0,0,0,20,20,20,20,20}. Mean = 10, Median = 10. Insufficient.

St2: The set could be {10,10,10,10,10,10,10,10,10,10}. Mode = Mean = Median = 10 The set could be {1,2,3,4,5,6,10,10,10,49}. Mode = 10. Mean = 10. Median = 5.5 Insufficient.

St1 and St2: The set could be {1,2,3,4,5,10,10,10,10,45}. Mode = Mean = 10. Median = 7.5 The set could eb {0,0,0,0,0,10,10,10,10,60}. Mode = Mean = 10. Median = 5. Insufficient.

Ans E

Quick question.

In you example St1 and St2. Wouldn't the mode be 0 as it's used 5 times and 10 is used 4 times.