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# A list contains n distinct integers. Are all n integers cons

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Intern
Joined: 30 Apr 2017
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Re: A list contains n distinct integers. Are all n integers cons  [#permalink]

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23 Jul 2018, 05:50
where does it state that list should be arranged in ascending order? my list could be {1,3,4,6,2,5} and still satisfy statement 1. now that list in not consecutive numbers in that particular order!
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Re: A list contains n distinct integers. Are all n integers cons  [#permalink]

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23 Jul 2018, 20:00
Jasveensingh wrote:
where does it state that list should be arranged in ascending order? my list could be {1,3,4,6,2,5} and still satisfy statement 1. now that list in not consecutive numbers in that particular order!

Hello

Well, in your example, the numbers used are still consecutive isnt it?
You have WRITTEN the six numbers in a non-consecutive order, but dont you think the numbers are still consecutive. 1, 2, 3, 4, 5, 6.
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Re: A list contains n distinct integers. Are all n integers cons  [#permalink]

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15 Dec 2018, 05:26
Solution:
Given: List contains n distinct integers.
To find: Are all n integers consecutive?

Analysis of statement 1: The average (arithmetic mean) of the list with the lowest number removed is 1 more than the average (arithmetic mean) of the list with the highest number removed.

I feel the best way to solve the question is by taking consecutive numbers and checking whether the given statement is true or not!!! If it satisfies the statement then answer will be “n” distinct integers are consecutive in nature else not.

Let’s take set of consecutive integers as {11, 12, 13, 14}
Case 1: When the lowest number is removed: When 11 is removed, the set will be {12, 13,14},
So the average = 13.
Case 2: When the highest number is removed: When 14 is removed; the set will be {11, 12, 13}.
So the average = 12.
So, statement 1 is true for all consecutive distinct integers.
Hence statement 1 is sufficient to answer. We can eliminate options B, C and D.

Analysis of statement 2: The positive difference between any two numbers in the list is always less than n.
Let’s take a set of consecutive integers as {11, 12, 13, 14} here n = 4; even if we are taking the difference between highest integer and lowest integer, i.e.
$$|14-11| = 3$$. So satisfies the statement 2.

If we take this algebraically: Let the set be $${x, x+1, x+2………..x+n-1}.$$
Positive difference of highest integer and lowest integer, we get =$$|x+n-1-x|=n-1.$$
Therefore it is clear that the difference between the two numbers will be always less than n.
So, statement 2 is sufficient. We can eliminate option A.

Therefore the correct answer option is “D”.

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Re: A list contains n distinct integers. Are all n integers cons  [#permalink]

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07 Jan 2019, 05:01
Hello,
I have a question:
For Statement 1:
if we take consecutive even numbers {2,4,6}:
When lowest number is removed, set becomes {4,6} - the average 5
When the highest number is removed, set becomes {2,4} - the average is 3.
Why above presented can not prove statement 1 as insufficient?
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Re: A list contains n distinct integers. Are all n integers cons  [#permalink]

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07 Jan 2019, 12:20
1
futurephilantropist wrote:
Hello,
I have a question:
For Statement 1:
if we take consecutive even numbers {2,4,6}:
When lowest number is removed, set becomes {4,6} - the average 5
When the highest number is removed, set becomes {2,4} - the average is 3.
Why above presented can not prove statement 1 as insufficient?

Hi futurephilantropist,

TESTing VALUES is a great way to approach this question, but you have to choose values that 'fit' the given information. The information in Fact 1 tells us that the difference in the two averages is 1. In your example, the difference is 2 - so your example is not applicable.

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Intern
Joined: 16 Dec 2017
Posts: 7
Re: A list contains n distinct integers. Are all n integers cons  [#permalink]

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07 Jan 2019, 16:17
HI GMAT Assassin/Co-Founder,

Thank you so much for the answer. It does make sense now.
Re: A list contains n distinct integers. Are all n integers cons   [#permalink] 07 Jan 2019, 16:17

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