Brent@GMATPrepNow wrote:

mparakala wrote:Source: Beat the GMAT (this question was not answered by experts and hence, the repost)

If x > 0, then is x^3 - 3(x^2) + 2x divisible by 4?

1. x = 4y + 4, where y is an integer
2. x = 2z + 2, where z is an integer

I think the answer is A. I do no know the correct answer. Can any expert explain in detail?

Thank you!
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Target question: Is x^3- 3x^2 + 2x divisible by 4?

Notice that the expression can be factored as (x-2)(x-1)(x) [aside: I wrote the terms in this order for a reason, as you'll see]

Rephrased Target question: Is (x-2)(x-1)(x) divisible by 4?

IMPORTANT: notice that x-2, x-1 and x are three consecutive integers.

Question: Under what conditions will the product of 3 consecutive integers be divisible by 4?
This will occur if one of the 3 integers is divisible by 4 or if the first and last numbers (x-2 and x) are even.
If the x and x-2 are even (i.e., divisible by 2) then (x-2)(x-1)(x) must be divisible by 4

Onto the statements.

Given: x = 4y + 4, where y is an integer
Factor to get: x = 4(y + 1)
This tells us that x is divisible by 4, which means x is even
If x is even, then (according to my point in green above) (x-2)(x-1)(x) must be divisible by 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 2z + 2, where z is an integer
Factor to get: x = 2(z + 1)
This tells us that x is divisible by 2, which means x is even
If x is even, then (according to my point in green above) (x-2)(x-1)(x) must be divisible by 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent