A certain list consists of 400 different numbers. Is the average (arithmetic mean) of the numbers in the list greater than the median of the numbers in the list?

(1) Of the numbers in the list, 280 are less than the average.
(2) Of the numbers in the list, 30 percent are greater than or equal to the average.

If the original condition generally includes “rElation” of median, mean, standard deviation, etc, there is high chance that E is the correct answer.
Using both the condition 1) and the condition 2), we know 1)=2). Hence, the correct answer is D.
So, there always is a median in 280 numbers, and median<mean. The answer is yes and the condition is sufficient.
Please remember that if 1)=2), then D is the correct answer with 95% of chance.
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Hi,
We just know that numbers are different..
When we talk of median, we have to arrange these numbers in ascending or descending order..

Here too it may not be given but we have to arrange these in ascending or descending order before moving ahead.
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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We need to determine whether the average (A) of the 400 numbers in the list is greater than the median (M). Note that since there are 400 numbers in the list, the median is the average of the numbers in the 200th and 201st spots when the numbers are listed in increasing order.

Statement One Alone:

Of the numbers in the list, 280 are less than the average.

Since 280 of the 400 numbers are less than the average, the numbers in the 200th and 201st spots are both less than A. Therefore, the median M is less than the average A. Statement one alone is sufficient to answer the question.

Statement Two Alone:

Of the numbers in the list, 30 percent are greater than or equal to the average.

Since there are 400 numbers in the list, this statement is actually saying (0.3)400 = 120 numbers are greater than or equal to the average, which is equivalent to saying 400 - 120 = 280 numbers are less than the average. By our analysis of statement one, we already know that this information is enough to answer the question. Statement two alone is sufficient to answer the question.

Answer: D
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Thanks for this strategy MathRevolution !
Does it apply to other types of DS questions or only to statistics problems?

Thanks

hello chetan2u nice explanation. i wonder if there is any rule that is relevant to the relation between median and arithmetic mean ? i mean the correlation ...

for instance you say only 120 are greater than average ... what if it were 50 / 50 ?

another question 120 numbers could be large numbers for example 280 numbers could be 1, 2, 3 9, 7, etc and 120 number could be starting from number 900 and higher....

thanks and have a great weekend

pushpitkc hi there any idea on the above solution ? thanks
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