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Statement (1):
sum of numbers from one to x = x(x+1)/2
average = (x(x+1)/2)/x = 11
(x+1)/2 = 11
x+1 = 22; therefore x = 21
now that we know x the median is easy to find
median = 11

Statement (2):
Range = x - 1 = 20; therefore x = 21

The Q stem does not say consecutive ....".....set of integers ......" so I guess the ans should be E

What does this mean "the set of integers from 1 to x inclusive?"?
doesn't it mean all the integers between 1 and X? If the set of numbers is not given in consecutive order they still have to be ordered to get the median.

Last edited by trublu on 13 Feb 2006, 19:22, edited 1 time in total.

explain it to me then. You said the question was about the median not about x. However, you need x to get the median so I don't understand your reasoning.

@jacksparrow I dont think order matters. for example, the sums for the following sets is equal {1,2,3} or {3,1,2}

explain it to me then. You said the question was about the median not about x. However, you need x to get the median so I don't understand your reasoning.

@jacksparrow I dont think order matters. for example, the sums for the following sets is equal {1,2,3} or {3,1,2}

the question is not that much difficult one and doesnot need this much discussion. it is pretty much clear and easy. anyway, let me try:

from i, avg = 11. but we donot know how many integers are there in between 1 to x.

suppose the no. of integers is = 3 and the integers are 1, 11 and 21. the median is 11.
suppose the integers are 1, 10, 22. the median is 10.

we can vary the number of integers such as 2,4,5,6,7,8........infinite.
so there is not one median. i is insufficient.

from ii, the first and last integers are 1 and 21. but we donot know how many integers are there in between 1 and 21. we can insert infinite number of integers in between 1 and 21. so this is also not suff.

even combining statements i and ii, we cannot make sure the value of median. so the answer is E.

hope this helps. if not, you need to contact honghu.

I see what you mean but I thought "the set of integers from 1 to x inclusive" meant ALL the numbers between 1 and x with both included. So if x = 8 the set is {1,2,3,4,5,6,7,8}.

x is an integer greater than 7. What is the median of the set of integers from 1 to x inclusive?

(1) The average of the set of integers from 1 to x inclusive is 11.

(2) The range of the set of integers from 1 to x inclusive is 20.

The question is unclear, in my opinion, which you should not expect from the official GMAT. If the stem says "the set of consecutive integers" then D would be the answer. However here we do not know how many integers are in the set, although the use of "the" instead of "a" made it sounds like there could only be one set of integers from 1 to x.

I would personally choose E as well. Even if we know x we don't know the median of the set if we don't know how the set looks like. For example, a set can be {1,21} with a median 11. But another set could be {1,8,12,13,21} where the median is 12.
_________________

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x is an integer greater than 7. What is the median of the set of integers from 1 to x inclusive?

(1) The average of the set of integers from 1 to x inclusive is 11.

(2) The range of the set of integers from 1 to x inclusive is 20.

The question is unclear, in my opinion, which you should not expect from the official GMAT. If the stem says "the set of consecutive integers" then D would be the answer. However here we do not know how many integers are in the set, although the use of "the" instead of "a" made it sounds like there could only be one set of integers from 1 to x.

I would personally choose E as well. Even if we know x we don't know the median of the set if we don't know how the set looks like. For example, a set can be {1,21} with a median 11. But another set could be {1,8,12,13,21} where the median is 12.

you are right HongHu the question is not clear and yes it's not from offical GMAT its MGMAT question ..