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x is an integer greater than 7. What is the median of the se

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by varun289 » Wed Mar 13, 2013 9:31 pm
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.






IOM-e,d how
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Source: — Data Sufficiency |

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by Anju@Gurome » Wed Mar 13, 2013 9:56 pm
varun289 wrote: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.
As the set contains all the integers from 1 to x inclusive, the elements of the set are evenly distributed. Hence, the mean and median of the set will be same.

Statement 1: Median = Mean = 11

Sufficient

Statement 2: x - 1 = 20 ---> x = 21
Hence, median = mean = (21 + 1)/2 = 22/2 = 11

Sufficient

The correct answer is D.
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by varun289 » Thu Mar 14, 2013 12:06 am
mam, here main concern is that all integers are not consecutive , it may be 1, 5 9 or 100
so IMO -e
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by Anju@Gurome » Thu Mar 14, 2013 12:17 am
varun289 wrote:mam, here main concern is that all integers are not consecutive , it may be 1, 5 9 or 100
so IMO -e
Yes Varun, you're correct.
I misread the question as its more popular form which says "set of consecutive integers from 1 to x inclusive".

If they are not consecutive integer, the correct answer will be E.

However, I feel the wordings of the question is not proper.
In it's current form it can be interpreted that the integers are consecutive as it is saying "set of integers from 1 to x inclusive". If the question did not mean that then the wordings should have been "set of any integers between 1 to x inclusive". In GMAT you will never see any wordings which are open to multiple interpretations.
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by Anaira Mitch » Mon Dec 12, 2016 4:18 pm
Can any one explain how "E" is the answer as I am getting "D" and below is my logic.

In order to determine the median of a set of integers, we need to find the "middle" value. (1) SUFFICIENT: Statement one tells us that average of the set of integers from 1 to x inclusive is 11. Since this is a set of consecutive integers, the "average" term is always the exact middle of the set. Thus, in order to have an average of 11, the set must be the integers from 1 to 21 inclusive. The middle or median term is also is 11.
(2) SUFFICIENT: Statement two states that the range of the set of integers from 1 to x inclusive is 20. In order for the range of integers to be 20, the set must be the integers from 1 to 21 inclusive. The median term in this set is 11. The correct answer is D.
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by [email protected] » Mon Dec 12, 2016 9:24 pm
Hi Anaira Mitch,

You are correct - the answer is D. The 'debate' in the prior posts is about the 'intent' of the question. When the prompt references the 'set of integers from 1 to X inclusive', we're meant to assume that we're dealing with ALL the integers in that range (even though the prompt doesn't use the word "consecutive" in its description of the range).

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by Jay@ManhattanReview » Fri Feb 10, 2017 10:00 pm
Anaira Mitch wrote:Can any one explain how "E" is the answer as I am getting "D" and below is my logic.

In order to determine the median of a set of integers, we need to find the "middle" value. (1) SUFFICIENT: Statement one tells us that average of the set of integers from 1 to x inclusive is 11. Since this is a set of consecutive integers, the "average" term is always the exact middle of the set. Thus, in order to have an average of 11, the set must be the integers from 1 to 21 inclusive. The middle or median term is also is 11.
(2) SUFFICIENT: Statement two states that the range of the set of integers from 1 to x inclusive is 20. In order for the range of integers to be 20, the set must be the integers from 1 to 21 inclusive. The median term in this set is 11. The correct answer is D.
Agree with Rich. The correct answer is D. With the phrase, 'set of integers from 1 to x inclusive,' it is implied that the integers are consecutive.

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

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by masoom j negi » Fri Dec 21, 2018 9:19 pm
)Statement 1. If a set has equally distant elements i.e. if the set is in A.P., then the mean of the set is also the median of the set.
Here, we are given the mean of the set and we are told that the set is in A.P. So, the median would also be 11. Hence, Sufficient.
Statement 2. Range of a set = (Biggest element - smallest element)
We know that the smallest no is 1 and the range of the set is 20. So, the biggest number should be 21.
Now, We can easily find the median of the set consisting of integers from 1 to 21.
The median is 11. Hence, Sufficient.
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