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A certain list consists of 400 different numbers. Is the average......

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A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 22 May 2016, 22:36
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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.
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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 23 May 2016, 05:04
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nalinnair wrote:
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.



400 different numbers... Median = average of 200th and 201st....

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

here 280 are less, so ofcourse 200th and 201st will also be less than average...
ans YES
Suff

(2) Of the numbers in the list, 30 percent are greater than or equal to the average
30% of 400 = 120 so ONLY 120 are greater than average, same as above
Suff

D
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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 23 May 2016, 19:23
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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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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 11 Apr 2017, 04:35
Hi, why do we assume that all the numbers are arranged in order even though it is not mentioned?

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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 11 Apr 2017, 19:33
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hannahkagalwala wrote:
Hi, why do we assume that all the numbers are arranged in order even though it is not mentioned?

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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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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 18 Jul 2017, 07:03
MathRevolution wrote:
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.


did you mean to say 'there is a high chance that D is the correct answer' , not E?

please elaborate and clarify why there's a 95% chance D is the answer with these situations
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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 30 Jul 2017, 16:24
nalinnair wrote:
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.


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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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 29 Jan 2018, 09:28
Can we rephrase the question as whether the list contains numbers that are in A.P or are equally spaced? Since in A.P. mean = median. So is the rephrasing correct?
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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 31 Jan 2018, 09:46
MathRevolution wrote:
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 medianPlease remember that if 1)=2), then D is the correct answer with 95% of chance.


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

Thanks
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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 30 Jun 2018, 05:48
Why do we assume that for Statement B, 30% of the numbers ARE GREATER than the average? Aren't they also saying OR EQUAL? In which case we would not be able to come up with an answer? Thx
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A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 01 Jul 2018, 09:08
chetan2u wrote:
nalinnair wrote:
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.



400 different numbers... Median = average of 200th and 201st....

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

here 280 are less, so ofcourse 200th and 201st will also be less than average...
ans YES
Suff

(2) Of the numbers in the list, 30 percent are greater than or equal to the average
30% of 400 = 120 so ONLY 120 are greater than average, same as above
Suff

D



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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Re: A certain list consists of 400 different numbers. Is the average......  [#permalink]

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New post 02 Jul 2018, 01:20
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dave13 wrote:
chetan2u wrote:
nalinnair wrote:
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.



400 different numbers... Median = average of 200th and 201st....

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

here 280 are less, so ofcourse 200th and 201st will also be less than average...
ans YES
Suff

(2) Of the numbers in the list, 30 percent are greater than or equal to the average
30% of 400 = 120 so ONLY 120 are greater than average, same as above
Suff

D



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 :-)


Hi dave13

Unfortunately, there is no correlation between median and mean

Consider a set A = {1,1,1,1,1} which has a median and mean of 1
Another set B = {1,2,3,6,8} has median of 3, but mean of 4

So as you see, for different sets, the mean and median may not correlate

Hope this helps you!
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Re: A certain list consists of 400 different numbers. Is the average...... &nbs [#permalink] 02 Jul 2018, 01:20
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