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# If there are more than two numbers in a certain list

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If there are more than two numbers in a certain list , is each of the number in the list equal to 0?
1. The product of any two numbers in the list is equal to 0.
2. The sum of any two numbers in the list is equal to 0.

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(1) The product of any two numbers in the list is equal to 0 --> it certainly possible all numbers to equal to 0 but it's also possible one number to be different from 0 and all other numbers to equal to 0 (in this case the product of ANY two numbers in the list will also be equal to 0). Not sufficient.
(2) The sum of any two numbers in the list is equal to 0 --> as there are more than 2 numbers in the list then all numbers must equal to 0 (if we were not told that there are more than 2 numbers in the list then it would be possible to have a list like {-1, 1} but as there are more than 2 numbers then in order the sum of ANY two numbers in the list to be equal to 0 all numbers must equal to zero). Sufficient.
answered Apr 5, 2016 by Guru (5,628 points)
selected May 7, 2016 by
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Jyotsna Mehta