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# A list contains 5 positive integers. Are all the integers in this list

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DS Forum Moderator
Joined: 21 Aug 2013
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A list contains 5 positive integers. Are all the integers in this list  [#permalink]

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31 May 2018, 01:34
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60% (01:35) correct 40% (02:00) wrong based on 86 sessions

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A list contains 5 positive integers. Are all the integers in this list distinct?

(1) If all possible pairs of integers in this list are added up exactly once, then all the resultant sums of pairs are distinct from each other.

(2) Positive Difference between any two integers in this list is greater than 1.
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Re: A list contains 5 positive integers. Are all the integers in this list  [#permalink]

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31 May 2018, 02:16
amanvermagmat wrote:
A list contains 5 positive integers. Are all the integers in this list distinct?

(1) If all possible pairs of integers in this list are added up exactly once, then all the resultant sums of pairs are distinct from each other.

(2) Positive Difference between any two integers in this list is greater than 1.

(1) If there were at least two same integers on the list, then sums of pairs would not be distinct from each other. Let's take $$(1,1,2,3,4)$$. Here two not distinct sums of pairs can be $$1+2=3$$ and $$1+2=3$$. Sufficient.

(2) If there were at least two same integers on the list, then difference would be $$0$$. Sufficient.

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Re: A list contains 5 positive integers. Are all the integers in this list  [#permalink]

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27 Jun 2018, 06:53
I don't understand Tulkin987 's explaination. Can someone help me to understand this?
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Re: A list contains 5 positive integers. Are all the integers in this list  [#permalink]

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27 Jun 2018, 09:56
prags1989 wrote:
I don't understand Tulkin987 's explaination. Can someone help me to understand this?

Hello

Let the integers be a, b, c, d, e.

(1) Lets add all possible pairs once. So we have a+b, a+c, a+d, a+e, b+c, b+d, b+e, c+d, c+e, d+e. And we are given that these 10 resultant numbers are all distinct from each other.
So if say a+b =/= a+c, then cancel a from both sides to get b =/= c.
Similarly a+b =/= a+d, then cancel a again from both sides to get b =/= d. And so on, we can thus conclude that none of the five integers are same.

(2) If you subtract any two integers from this list, positive difference is greater than 1. So obviously NONE of the differences is 0. If difference between none of the two integers is 0, then none of the two integers are equal to each other in this list.

Re: A list contains 5 positive integers. Are all the integers in this list &nbs [#permalink] 27 Jun 2018, 09:56
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# A list contains 5 positive integers. Are all the integers in this list

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