Hi All,
When dealing with questions that talk about groups of unknown numbers, it often helps to come up with some examples that fit the limited information that you have. In that way, you can TEST VALUES by considering what the group of numbers COULD contain.
Here, we're told that the group of numbers consists of MORE than 2 numbers (so 3 or more numbers). We're asked if EACH of the numbers is 0. This is a YES/NO question.
Fact 1: The product of any two numbers in the list is equal to zero
Since the product of ANY number and 0 is 0, this means that the list COULD contain a non-0 number....In the second option, choosing any 2 numbers WILL result in a product that = 0.
IF the group of numbers is....
{0, 0, 0} then the answer to the question is YES
{0, 0, 1] then the answer to the question is NO
Fact 1 is INSUFFICIENT
Fact 2: The sum of any two numbers in the list equal to 0.
Since we're dealing with MORE than 2 numbers, this Fact provides a specific 'restriction' - we CAN'T have ANY non-0 numbers because then would could end up with a sum that is NOT 0.
IF...
{0, 0, 0} then the answer to the question is YES
IF....
{-1, 1, 1} then we could end up with (1) + (1) = 2, which does NOT fit the given Fact. Thus, this example is NOT possible and neither is any other example that could lead to a Non-0 sum. By extension, that means that EVERY number in the group MUST be 0.
Fact 2 is SUFFICIENT
Final Answer:
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Rich
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