GMATGuruNY wrote:

lheiannie07 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.

Statement 1:
Case 1: All 20 numbers are 5 --> {5, 5, 5...5, 5, 5}
Here, no matter which 2 numbers we choose, the sum will be an integer.
In this case, all of the numbers are equal, so the answer to the question stem is YES.

Case 2: The first 19 numbers are 5, the last number is 1 --> {5, 5, 5...5, 5, 1}
Here, no matter which 2 numbers we choose, the sum will be an integer.
In this case, all of the numbers are NOT equal, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2:
Case 1: All 20 numbers are 5 --> {5, 5, 5...5, 5, 5}
Here, no matter which 2 numbers we choose, the sum will be 5+5 = 10.
In this case, all of the numbers are equal, so the answer to the question stem is YES.

Now let's test whether it is possible to change any of the numbers in Case 1.

Case 2: The first 19 numbers are 5, the last number is 1 --> {5, 5, 5...5, 5, 1}
Here, 5+1 = 6 , violating the constraint that the sum of any two numbers is 10.
Thus, Case 2 is not viable.

Do you see the situation?
If we change any of the numbers in Case 1, we can't satisfy statement 2.
Implication:
Statement 2 will be satisfied only if every number is 5, with the result that all of the numbers are equal.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.

Brent@GMATPrepNow wrote:Here's a similar question to practice with: https://www.beatthegmat.com/are-all-numb ... 74636.html

Cheers,
Brent