GMATMadeEasy wrote:If X is even, and N = (X)(X+1)(X+2),
is N divisible by 24?

OA is YES

Could someone explain please the solution for it.

I agree X must have a 2, X+2 must have a 2, and a 3 in total because there are three consecutive intergs.
That makes 2*2*3 , divisible by 12 maximum.

Thanks for conceptual explanation please.

GMATMadeEasy wrote:If X is even, and N = (X)(X+1)(X+2),
is N divisible by 24?

OA is YES

Could someone explain please the solution for it.

I agree X must have a 2, X+2 must have a 2, and a 3 in total because there are three consecutive intergs.
That makes 2*2*3 , divisible by 12 maximum.

Thanks for conceptual explanation please.

ankur.agrawal wrote:I have a confusion here:

Sumwhere in the manhattan guides i have read that even Number '0' is considered even. If we apply this, does it makes a difference to this question?

ankur.agrawal wrote:I have a confusion here:

Sumwhere in the manhattan guides i have read that even Number '0' is considered even. If we apply this, does it makes a difference to this question?

GMATGuruNY wrote:

Yes, 0 is even. It is also divisible by -- and thus a multiple of -- every other integer.

goyalsau wrote:

GMATGuruNY wrote:

Yes, 0 is even. It is also divisible by -- and thus a multiple of -- every other integer.

Can you please explain it in detail.
As i understand 0 is even and a multiple of every other integer.

And i read some where is not positive but neither negative.

I am really confused with Zero.

What i understand is that it is a positive , a even integer and a multiple of every integer ( whether it is positive or negative )
In other way 0 is not a negative integer.

Please Guru Correct me if I am wrong in any way, I think this is a very serious concept problem and i as know Gmat love to test it.

I would like to ask one more than is 1 a odd integer.

And this is the link of a question that i got wrong because of this Zero Concept
https://www.beatthegmat.com/sequence-t66944.html#301225

This is where I have the issue .

X is even so we know X has one 2 and we know X+2 has to one 2 or two 2s
X has two 2s as factors (or divisible by 4)

basically, I try to put different approaches , things start to look convoluted.

Do we have authentic way of solving it by figuring out factors (2*2*2*3) in the expression given.

Let's ignore the issue of 0. For those who are curious, 0 is neither positive nor negative but is an even integer. . use this definition and should be on your way. From OG .

Ian Stewart wrote:

GMATGuruNY wrote: 24 = 2*3*4, so to be divisible by 24, N must be divisible by 2, 3 and 4.

If x=2, then N = 2(2+1)(2+2) = 2*3*4.
Since x must be a multiple of 2, N must be a multiple of 2*3*4, which means it must be divisible by 2, 3 and 4.
Thus, N is divisible by 24.

This isn't a legitimate proof. If you were instead asked "If x is divisible by 3, is x(x+1)(x+2) divisible by 60?" you'd certainly get the wrong answer if you simply tested the value x=3 and tried to generalize from there; you'd think the answer was yes, but the answer is 'not necessarily' (if x = 6, for example, x(x+1)(x+2) is not divisible by 5, and thus not divisible by 60).

In the original question above, if x is even, then x and x+2 are consecutive even integers. Every second even integer is a multiple of 4. So if you take any two consecutive even integers, exactly one of them will be divisible by 4. For that reason, in this question, x(x+2) must be a multiple of 2*4 = 8. Further, among any three consecutive integers, you always have exactly one multiple of 3, since multiples of 3 are three apart. So one of x, x+1 or x+2 is divisible by 3, and the product x(x+1)(x+2) is divisible by 3*8 = 24.

Ian Stewart wrote:

GMATGuruNY wrote: 24 = 2*3*4, so to be divisible by 24, N must be divisible by 2, 3 and 4.

If x=2, then N = 2(2+1)(2+2) = 2*3*4.
Since x must be a multiple of 2, N must be a multiple of 2*3*4, which means it must be divisible by 2, 3 and 4.
Thus, N is divisible by 24.

This isn't a legitimate proof. If you were instead asked "If x is divisible by 3, is x(x+1)(x+2) divisible by 60?" you'd certainly get the wrong answer if you simply tested the value x=3 and tried to generalize from there; you'd think the answer was yes, but the answer is 'not necessarily' (if x = 6, for example, x(x+1)(x+2) is not divisible by 5, and thus not divisible by 60).

In the original question above, if x is even, then x and x+2 are consecutive even integers. Every second even integer is a multiple of 4. So if you take any two consecutive even integers, exactly one of them will be divisible by 4. For that reason, in this question, x(x+2) must be a multiple of 2*4 = 8. Further, among any three consecutive integers, you always have exactly one multiple of 3, since multiples of 3 are three apart. So one of x, x+1 or x+2 is divisible by 3, and the product x(x+1)(x+2) is divisible by 3*8 = 24.