Hi All,
We're told that there are 20 numbers in a list. We're asked if all of the numbers are EQUAL. This is a YES/NO question.
Fact 1: The sum of ANY 2 numbers in the list is an integer.
This Fact tells us that ALL of the numbers are either integers OR ALL of the numbers end in .5
IF.....
The list is twenty 1/2s, then taking the sum of ANY 2 will give you an integer.
The answer to the question is YES.
IF....
The list is the twenty integers from 1 to 20 inclusive, then taking the sum of ANY 2 will give you an integer.
The answer to the question is NO.
Fact 1 is INSUFFICIENT.
Fact 2: The sum of ANY 2 numbers in the list is 10.
You have to think about what this means conceptually....
The 'easy' way to think about this is if ALL twenty numbers are 5s. In this way, taking the sum of ANY 2 of these numbers will give a sum of 10.
The answer to the question is YES.
You might also consider a list that is made up of ten 0s and ten 10s. HOWEVER, taking the sum of 2 numbers from this list does NOT NECESSARILY give us a sum of 10. If you take two 0s, then the sum is 0. If you take two 10s, then the sum is 20. This example PROVES that the list CANNOT have different values in it (and by extension, ALL 20 terms MUST be 5).
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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