VJesus12 wrote:Are i, j, k consecutive integers?
(1) The remainder when i + j + k is divided by 3 is 2
(2) The remainder when i*j*k is divided by 3 is 1
Statement 1:
Three consecutive integers can be represented as follows:
x, x+1, x+2.
Thus, the sum of three consecutive integers = x + (x+1) + (x+2) = 3x + 6 =
3(x+2).
The value in blue indicates that the sum of three consecutive integers must be a MULTIPLE OF 3.
When a multiple of 3 is divided by 3, the remainder is 0.
Since i+j+k yields a remainder of 2 when divided by 3, i+j+k is NOT a multiple of 3 and thus CANNOT be the sum of 3 consecutive integers.
Thus, the answer to the question stem is NO.
SUFFICIENT.
Statement 2:
Of every 3 consecutive integers, exactly 1 will be a multiple of 3.
For this reason, the product of any 3 consecutive integers must also be multiple of 3, since this product will include a multiple of 3 among its three factors.
When a multiple of 3 is divided by 3, the remainder is 0.
Since ijk yields a remainder of 1 when divided by 3, ijk is NOT a multiple of 3 and thus CANNOT be the product of 3 consecutive integers.
Thus, the answer to the question stem is NO.
SUFFICIENT.
The correct answer is
D.
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