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DS - Number properties/Find the median

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by krithika1993 » Fri Nov 04, 2016 5:06 am
Hello everybody,

I completed an MGMAT exam yesterday and got the following question wrong:

If x is a positive integer, what is the median of the set of consecutive 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.

Correct answer: D


**************************************************************************************************************************
My reasoning:
I'm understanding the reasoning behind statement 1, but I'm not seeing the logic behind Statement 2. In my opinion, the range, since it only states the difference between the last term and the first term in the set, it does not tell us anything about the actual values themselves. For example, if the range of a set of consecutive integers is 20, the first and last terms could be 10 and 30 respectively, or they could be 1 and 21 respectively. Both such sets satisfy this range requirement but both sets do not have the same median. For this reason, I did not accept this statement to be conclusive.

Please let me know what you think.

Thank you!
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Source: — Data Sufficiency |

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by [email protected] » Fri Nov 04, 2016 9:58 am
Hi krithika1993,

With this prompt, you have to pay careful attention to ALL of the information that you're given.

The prompt tells us that we're dealing with a set of CONSECUTIVE INTEGERS from 1 to X (and X is a positive integer). Fact 2 tells us the RANGE of THAT set of consecutive integers is 20. Thus, the first term in the sequence is 1 and the last term is "20 away" from 1 - thus, it must be 21. We now have the exact set of consecutive integers (1 thru 21, inclusive), so we can figure out the median. Fact 2 is SUFFICIENT.

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by melguy » Sat Nov 05, 2016 8:56 pm
krithika1993 wrote: In my opinion, the range, since it only states the difference between the last term and the first term in the set, it does not tell us anything about the actual values themselves. For example, if the range of a set of consecutive integers is 20, the first and last terms could be 10 and 30 respectively, or they could be 1 and 21 respectively.
Please pay close attention to the language of the question : from 1 to x inclusive. So the first term must be 1.
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by Scott@TargetTestPrep » Fri Nov 11, 2016 7:24 am
krithika1993 wrote:
If x is a positive integer, what is the median of the set of consecutive 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.

Correct answer: D
We are given that x is a positive integer, and we need to determine the median of the set of consecutive integers from 1 to x inclusive. We may recall that when we have an evenly spaced set (or in this case a set of consecutive integers), the average will always be equal to the median.

Statement One Alone:

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

Since we know that the average is equal to 11, the median must also be equal to 11. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

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

Since we have a set of consecutive integers, and we know that the smallest number is 1 and the largest is 1 + 20 = 21, we can determine that the median is:

(21 + 1)/2 = 22/2 = 11

Statement two alone is also sufficient to answer the question.

Answer: D

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