karthikpandian19 wrote:What is the sum of the digits of positive integer q ?

(1) The sum of the digits of q is an element of the set 226,313,447,617

(2) q = (n^3)-n for some positive integer n.

Statement 1: The sum of the digits of q is an element of the set 226,313,447, 617.
Since the sum of the digits could be 226, 313, 447, or 617, INSUFFICIENT.

Statement 2: q = (n^3)-n for some positive integer n.
q = n(n²-1) = n(n+1)(n-1).
Thus, q is the product of 3 consecutive integers: n-1, n and n+1.
Of every 3 consecutive integers, exactly one is a multiple of 3.
Thus, one of the factors of q is a multiple of 3, implying that q itself is a multiple of 3.
The sum of the digits of a multiple of 3 must also be a multiple of 3.
Thus, the sum of the digits of q must be a multiple of 3.
No way to determine the exact sum.
INSUFFICIENT.

Statements 1 and 2:
To satisfy statement 2, the sum of the digits of q must be a multiple of 3.
The sum of the digits of q must also be among the values listed in statement 1.
Of the values listed, only 447 has digits whose sum is a multiple of 3:
4+4+7 = 15.
Thus, the only multiple of 3 listed in statement 1 is 447.
Thus, the sum of the digits of q must be 447.
SUFFICIENT.

The correct answer is C.

karthikpandian19 wrote:What is the sum of the digits of positive integer q ?

(1) The sum of the digits of q is an element of the set 226,313,447,617

(2) q = (n^3)-n for some positive integer n.

is it C?

clearly 1 is not possible
2 doesn't say anything about how to determine sum of digits

but using both...
q=(n-1)*n*(n+1)
=> product of 3 consecutive numbers
=> q should be divisible by 6 for sure. that means it will be divisible by 3
but if sum of digits in a number is divisible by 3 then we can say it is divisible by 3
from (1) it is given that sum of digits of q is the list given
looking at the list of given numbers, we can say 447 clearly satisfies(4+4+7 = 15 which is divisible by 3)
so we can say that sum of digits is 447. hence sufficient.

it took a long time to figure out. I would have kept E and moved on.
anyways good question & good stuff to take away

user123321

OA is C