j_shreyans wrote:What is the product of three consecutive integers?

(1) At least one of the integers is positive.
(2) The sum of the integers is less than 6.

Target question: What is the product of three consecutive integers?

Statement 1: At least one of the integers is positive.
There are several sets of consecutive integers that satisfy this condition. Here are two:
Case a: the numbers are 1, 2 and 3, in which case their product is 6
Case b: the numbers are 2, 3 and 4, in which case their product is 24
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The sum of the integers is less than 6.
There are several sets of consecutive integers that satisfy this condition. Here are two:
Case a: the numbers are -3, -2 and -1, in which case their product is -6
Case b: the numbers are 0, 1 and 2, in which case their product is 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that the sum of the integers is less than 6
Notice that the three consecutive integers 1, 2 and 3 have a sum of 6.
This tells us that the greatest of the three integers is LESS than 3

Statement 1 tells us that at least one of the integers is positive.

There are only 2 possible cases that satisfy both statements. They are:
Case a: the numbers are 0, 1 and 2 in which case their product is 0
Case b: the numbers are -1, 0 and 1, in which case their product is 0

IMPORTANT: Although we can't be certain whether the three numbers are {0,1,2} or {-1,0,1}, the answer to the target question is THE SAME for both cases.
In other words, we can be CERTAIN that the product of the three integers is 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent