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If x, y, z are integers, is xyz a multiple of 3?

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by Max@Math Revolution » Sun May 15, 2016 8:24 pm
If x, y, z are integers, is xyz a multiple of 3?
1) x+y+z is a multiple of 3
2) x, y, z are consecutive

*An answer will be posted in two days.
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by 800_or_bust » Mon May 16, 2016 8:19 am
Max@Math Revolution wrote:If x, y, z are integers, is xyz a multiple of 3?
1) x+y+z is a multiple of 3
2) x, y, z are consecutive

*An answer will be posted in two days.
(1) is INSUFFICIENT. Testing values - if x = y = z = 2, then x+y+z = 6, but the product xyz=8. If x = y = z = 3, then x + y + z = 9 and xyz = 27. So (1) can be true, and xyz could be a multiple of 3, but it doesn't have to be.

(2) is SUFFICIENT. If x, y and z are consecutive integers then at least one of x, y or z must be a multiple of 3. Therefore the product xyz must also be a multiple of 3. Note this is true even if x, y and z are -1, 0 and 1 (0 is a multiple of 3), or if all three are negative (negative integers can be expressed as multiples as well).
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by Max@Math Revolution » Tue May 17, 2016 3:13 pm
If we multiply the consecutive 3 integers, the outcome is always a multiple of 6. The condition 2) gives an answer that is always yes and the condition is sufficient. Hence, the correct answer is B. The condition is not sufficient because it gives 2 answers, 1+2+3 yes and 2+2+2 no.
 
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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