Is the Answer [spoiler]{A}[/spoiler]?

Question; (x+3)(x+4)(x+5)/4

Statement 1: (x+2)/8
_ Point of consideration.. if a number is divisible by 8 then it will surely be divisible by 4.
_ in a sequence of any 4 consective number.. one number will be divisible by 4.

Applying these.. (x+2) is divisible.. so x+3, x+4, x+5 cannot be
SUFFICIENT

Statement 2: (x+3)/3 --> odd => x/3 is even
Try 6 --> doesn't satisfy
Try 12 --> Satisfies..
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]

Is it A?

Statement 1
X+2 has to be divisible by 8. So, it can be 8,16,24,32 and so on.So x can be 6, 14,22

Then substitute the values of x thus obtained in the original equation

We get the main equation as not divisible by 4 Sufficient

Statement 2
(x+3)/3 is an odd integer, then x+3 can be 9,15,21,27 and so on, Thus x can be 6,12,18,24

Here when x= 6 or 12 the main equation is not divisible by 4

But when x=18, the equation is divisible by 4 Insufficient


I hope I have done it correctly. But this method took me 4 min

please explain to me the math steps , how you got the correct solution ?

(x + 4) * (x² + 8x + 15) =>

(x + 4) * (x + 3) * (x + 5)

This means we're multiplying three consecutive numbers together: x + 3, x + 4, and x + 5.

If (x + 3) is even, then (x + 5) is also even, and we're multiplying two consecutive evens together, e.g. 2 * 4, 4 * 6, 6 * 8, etc. That will ALWAYS be divisible by 8.

If (x + 3) is odd, then our only even number is (x + 4). In that case, we need (x + 4) to be divisible by 4.

S1 tells us that (x + 2) is divisible by 8. Since (x + 4) = (x + 2) + 2, we know that x + 4 = (some multiple of 8) + 2.

Now take a look at the multiples of 8, + 2:

2, 10, 18, 26, 34, ...

None of them divide by 4! This is because we can't have two consecutive evens BOTH be divisible by 4: the multiples of 4 come every OTHER even, or every fourth place on the number line.

From this, we know that (x + 4) CAN'T be divisible by 4, and thus (x + 3) * (x + 4) * (x + 5) also CAN'T be divisible by 4, making S1 sufficient.

Whoops, forgot S2!

(x + 3)/3 = odd

(x + 3) = 3 * odd

(x + 3) = odd

But this doesn't help us: as seen above, we still need to know whether (x + 4) is divisible by 4 or not.