venkb wrote:If x > 0 and y and z are integers, is x³ - 3x² + 2x divisible by 4?

1:: x = 4y + 4
2:: x = 2z + 2

S1 tells us that x is a multiple of 4. Thus x³ - 3x² + 2x = (multiple of 4)³ - 3*(multiple of 4)² + 2*(multiple of 4). This is just the sum of many multiples of 4, so it itself must be a multiple of 4. SUFFICIENT.

S2 tells us that x is EVEN. Any even integer can be expressed as 2k, where k is some integer, so let's plug x = 2k into our equation, making it (2k)³ - 3((2k)²) + 2(2k), or 8k³ - 12k² + 4k. This is also equal to a sum of three multiples of 4, so it is itself a multiple of 4. SUFFICIENT.

If x > 0 and y and z are integers, is x³ - 3x² + 2x divisible by 4?

1:: x = 4y + 4
2:: x = 2z + 2

x³ - 3x² + 2x = x(x-1)(x-2)
SO x must be multiple of 4 i.e. 4, 8, 12, 16,......
1)x = 4y + 4
x = 4, 8, 12,16
So, Sufficient
2)x = 2z + 2
Assume z =1,2,3,4....
then x = 4, 6, 8, 10....
6 and 10 are not divisible by 4
so, not sufficient.

Why is the answer D for this question?

venkb wrote:1. x=4y+4, where is an integer. Now put -1 for y. then x becomes 0. so is 0 divisible by 4. I think it is no. So u cant answer with 1.

Similar reasoning occurs for 2.

So i felt the answer to be E.

But Manhattan guide says the answer to be D.

0 is divisble by 4. infact 0 is divisible by any no. since it leave a zero remainder.
so the answer here must be D.
factorize the main equation. you will get 4*(some equation). as 4 is present in both the cases, both of them individually are sufficient to answer.

Hey,

I don't understand how statement 2 is sufficient. Could someone pls explain this to me.

THANKS.