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# Is x(x+1)(x+2) divisible by 4 (where x is an integer)?

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Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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16 Jul 2010, 12:26
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Is x(x + 1)(x + 2) divisible by 4 (where x is an integer)?

(1) x is even
(2) x is 2
Intern
Joined: 16 Jan 2007
Posts: 17
Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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16 Jul 2010, 12:33
This question is form Manhattan guide. I couldn't understand the reasoning for A is being sufficient.
Manhattan said that if x is even then we have 2, 3, 2+2 so basically two prime factor with 2 in it and hence divisible by 4.

But how about x=0. zero is also even and in the above case the product is zero. Oh so basically 0 is divisible by 4 and hence having x as even satisfy the condition??? am I getting this correct??

By the way the answer in above should be D.
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Posts: 56257
Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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16 Jul 2010, 12:45
1
paam0101 wrote:
This question is form Manhattan guide. I couldn't understand the reasoning for A is being sufficient.
Manhattan said that if x is even then we have 2, 3, 2+2 so basically two prime factor with 2 in it and hence divisible by 4.

But how about x=0. zero is also even and in the above case the product is zero. Oh so basically 0 is divisible by 4 and hence having x as even satisfy the condition??? am I getting this correct??

By the way the answer in above should be D.

Zero is even and divisible by every integer (except zero itself, as division by zero is undefined).

Integer $$a$$ is divisible by integer $$b$$ means that $$\frac{a}{b}=integer$$ (so remainder is zero).

Now, if $$a=0$$ --> $$\frac{a}{b}=\frac{0}{b}=0=integer$$, that's why zero divisible by every integer (except zero itself, as division by zero is undefined).

Hope it helps.
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Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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19 Jul 2010, 09:09
very well explained by "Bunuel"

is OA D ?
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Joined: 07 Jul 2010
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Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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20 Jul 2010, 02:08
i had taken X=-2 as well just to be doubly sure because negatives can be even as well ,its also even so x+1=-1,and x+2=0 (so -2 x-1 x0=0)which is also divisivble by 4 .....thanks !!!!!!!
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Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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21 Jul 2010, 04:02
Hi Guys,

As Bunuel said " Zero is even and divisible by every integer (except zero itself, as division by zero is undefined). "

Can we say that Zero is even and divisible by every number of number line( exp zero)"

because 0/2.5 is also equal to zero !

Plz help.

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Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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21 Jul 2010, 08:20
Both are sufficient. Hence D.
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Posts: 56257
Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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21 Jul 2010, 10:38
KissGMAT wrote:
Hi Guys,

As Bunuel said " Zero is even and divisible by every integer (except zero itself, as division by zero is undefined). "

Can we say that Zero is even and divisible by every number of number line( exp zero)"

because 0/2.5 is also equal to zero !

Plz help.

Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

On GMAT when we are told that $$a$$ is divisible by $$b$$, we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

So the term "divisible" (at least on GMAT) is used only about integers.

Hope it helps.
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Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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22 Jul 2010, 05:22
Bunuel wrote:
KissGMAT wrote:
Hi Guys,

As Bunuel said " Zero is even and divisible by every integer (except zero itself, as division by zero is undefined). "

Can we say that Zero is even and divisible by every number of number line( exp zero)"

because 0/2.5 is also equal to zero !

Plz help.

Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

On GMAT when we are told that $$a$$ is divisible by $$b$$, we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

So the term "divisible" (at least on GMAT) is used only about integers.

Hope it helps.

10 Q
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Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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22 Jul 2010, 08:23
Is x(x+1)(x+2) divisible by 4 (where x is an integer)?
1) x is even
If X=2 (or 4, 6, etc.), then the answer to question is yes.

If X=0 (as Bunnuel reminded, zero is even) the answer is also yes.

So Suff.

2) x is 2

2*3*4 => Suff

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Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?  [#permalink]

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20 Jun 2019, 12:09
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Re: Is x(x+1)(x+2) divisible by 4 (where x is an integer)?   [#permalink] 20 Jun 2019, 12:09
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