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

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Source: — Data Sufficiency |
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Re: If there are more than two numbers in a certain list...

by deloitte247 » Sat Jan 18, 2020 7:45 pm
Let list = L
L contains more than 2 numbers/elements
Question: Is each of the numbers/elements in the list L equal to 0?
Statement 1: The product of any two numbers in the list is equal to 0.
If the list L = {0, 0, 0}, all elements are equal to 0, and the product of any 2 elements equal to 0.
If the list L = {0, 0, 1}, all elements are not equal to 0, and the product of any 2 elements equal to 0
The information provided in this statement gives room for at least one element in list L not to be equal to 0, and if it also possible for all elements to be equal to 0.
Hence, statement 1 is NOT SUFFICIENT.

Statement 2: The sum of any two numbers/elements in the list L is equal to 0.
If the elements in list L are just 2 elements, then for their sum to be equal to 3, it is possible that the 2 elements will not be 0. E.g. -3 and +3.
Since there are more than 2 elements/numbers in the list L, then only for the sum of any two numbers/elements to be equal to 0 is if all elements in the list L are equal to 0. With the information provided here, each of the numbers in the list is equal to 0. Therefore, statement 2 is SUFFICIENT.

Since statement 2 alone is SUFFICIENT, then, the correct answer choice is option B.
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