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Is the mean of a non-empty set S bigger than its median? 1. All members of S are consecutive multiples of 3 2. The sum of all members of S equals 75 Source: GMAT Club Tests - hardest GMAT questions however i think it should be E.. how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc?
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fresinha12 wrote: Is the mean of a non-empty set S bigger than its median?
1. All members of S are consecutive multiples of 3
2. The sum of all members of S equals 75
OA is A..
however i think it should be E..
how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc? I think OA is ok. -9, -6, -3, 0, 3, sum = -15 mean = -15/5 = -3 median = -3
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fresinha12 wrote: Is the mean of a non-empty set S bigger than its median?
1. All members of S are consecutive multiples of 3
2. The sum of all members of S equals 75
OA is A..
however i think it should be E..
how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc? Stmt1 simply says that the members of S are in arithmatic series and hence mean and median will be the same.
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Statement 1 : Evenly spaced sets means MEDIAN = MEAN, so ---> sufficient
Statement 2: You are only given the sum of numbers in set, they could be (1, 75) or (1, 5, 70) so, ---> not sufficient.
Answer is A.
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Verbal GMAT Forum Moderator
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what if there is an even number of elements in the Set S,For example 27,30,33,36 Mean=31.5 Median=30 or 33 then?
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The median will equal the mean then. Here's a quote from Wikipedia  Quote: If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values mundasingh123 wrote: what if there is an even number of elements in the Set S,For example 27,30,33,36
Mean=31.5
Median=30 or 33
then?
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Answer: A
Median will equal mean in consecutive integers
Not B because it does give any information about the numbers in question.
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A looks good....bu can any one give example of B where Mean is bigger than Median....
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gsd85 wrote: A looks good....bu can any one give example of B where Mean is bigger than Median.... 15+2+1/3 = 18/3 = 6 Mean of 6 > Median of 2
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for consecutive integers: mean = median Also, equals (max + min)/2 example: 7, 8, 9, 10, and 11 mean = (7+11)/2 = 9 median = 9 By the same token, for 12, 14, 16, and 18 mean = (12 + 18)/2 = 15 median also = average of 14 and 16 = 15 Hope this helps.
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I want to know for no's whose sum =75 is there any combination where mean > median........ for e.g 25+25+25 ..........mean= median for 25 +25+16+9 ............mean < median... so i want to know a combination where mean > median........i could not figure out ....so just need help 
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Lets take some examples 1. Let set is two number (3,6) mean=4.5, median=4.5 now let take 3 nos. (15, 18, 21) mean=18, Median=18 now lets take a bigger set (-12, -9,-6,-3,0,3,6,9) Median = -1.5, Mean = -12/8= -3/2 = -1.5 A is answer Golden rule for Consecutive integers is already explained just a addition Regards Jagdeep
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simple one..A is the answer
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celluloidandroid wrote: Answer: A
Median will equal mean in consecutive integers
Not B because it does give any information about the numbers in question. Good information. Thank you.
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Remember that evenly spaced sets, the mean = median. Regardless of # of items.
A) Sufficient
b) Insufficient
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FN wrote: Is the mean of a non-empty set S bigger than its median? 1. All members of S are consecutive multiples of 3 2. The sum of all members of S equals 75 Source: GMAT Club Tests - hardest GMAT questions however i think it should be E.. how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc? REVISED VERSION OF THIS QUESTION IS BELOW: Is the mean of set S greater than its median?(1) Set S consist of consecutive multiples of 3 --> set S is evenly spaced. One of the most important properties of evenly spaced set (aka arithmetic progression) is: in any evenly spaced set the arithmetic mean (average) is equal to the median. So, the mean of S = the median of S. Sufficient. (2) The sum of all terms of set S is 75 --> if S={75} then mean=median but if S={0, 0, 75} then (mean=25)>(0=median). Not sufficient. Answer: A.
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True, as Bunuel said, Mean=Median or evenly spaced sets, so (i) sufficient in (ii) the sets have a sum of 75 ; we can have many combinations to do so (0,0,75),(25,25,25), etc..-insufficient (A)wins
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