18. Are all of the numbers in a certain list of 15 numbers equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.

I am thinking the answer is (B)

since the only way any 3 numbers total 12 is if they
are all equal to 4 (12/3). SUFFICIENT.

Is that the official answer?
-Raj.

yup. B is the correct answer.
Thanks

I was looking over this problem, and was wondering about one thing.
Couldn't the sum of any 3 numbers equal to 12 include the number 1, 9, and 2 which all add up to 12?
But then the numbers could also all be 4....then wouldn't b be insufficient???

If you had (1, 9, 2) in the list of 15 integers, you could have

(1, 9, 2, 4,4,4,4,4,4,4,4,4,4,4,4)

and if you chose 3 numbers randomly from this list, let's say, (9, 2, 4), then the sum of those three will be 15, and not 12 as Statement 2 says.

All of the 15 numbers in the list would have to be equal for the sum of any 3 numbers to be 12.

Therefore B is correct.

here's a logically sound way to prove that statement 2 is sufficient, if that's your style:

when the problem says that the sum of ANY 3 numbers in the list is 12, it's not kidding. this means that if you select literally any possible group of three numbers out of the fifteen, then they must add up to 12.

let three of the numbers be called x, y, and z. then these add up to 12.
now every single one of the remaining twelve numbers must be equal to z (because you must be able to add each of them to x and y to get 12 -- remember, any combination of three numbers means, well, any combination of three numbers).
but for the same reason, every single one of the remaining numbers must also be equal to y, because you can add any of them to x and z to get 12.
and finally, every single one of the remaining numbers must also be equal to x, because you can add any of them to y and z to get 12.
therefore, x, y, and z are all the same number.
so they're all 4's.
...and so is everything else.

chill!