Are all the numbers in a certain list of 20 numbers equal?

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Dec 19, 2017 7:14 am

Are all the numbers in a certain list of 20 numbers equal?

(1) The sum of any 2 numbers in the list is an integer.
(2) The sum of any 2 numbers in the list is 10.

The OA is option B.

How can I use statement (2) to get an answer here? Experts, I would like your explanation here. Please.

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Source: Beat The GMAT — Problem Solving | Tue Dec 19, 2017 7:14 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue Dec 19, 2017 11:09 am

Vincen wrote:Are all the numbers in a certain list of 20 numbers equal?

(1) The sum of any 2 numbers in the list is an integer.
(2) The sum of any 2 numbers in the list is 10.

The OA is option B.

How can I use statement (2) to get an answer here? Experts, I would like your explanation here. Please.

Well, there are an infinite number of ways to pick two numbers to add to 10. So, assume you have one of those two number pairs among the 20 numbers.

But since there are 18 other numbers to chose from, you can't guarantee that any pair selected will add to 10.

Unless you make all the numbers the same, in this case, 5

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