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Consecutive Integers Question

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by Rohit21 » Tue Oct 18, 2011 11:20 am
Hi all,
I'm confused on this one problem from Manhattan GMAT.

If x,y and z are consecutive integers, is x+y+z divisible by 3?

The answer is Yes.

But take -1,0,1 then clearly the sum 0 is not divisible by 3. So is the answer in Manhattan GMAT wrong?
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by shankar.ashwin » Tue Oct 18, 2011 11:28 am
0 is considered divisible by any number except 0 itself.

0/Any NUmber = 0
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by neelgandham » Tue Oct 18, 2011 12:54 pm
Always keep in mind that framing an algebraic equation always helps you in decision making( when confused!)

From the question:

The three consecutive numbers are x,y,z, i.e y=x+1, z=y+1 => x,y,z = x,x+1,x+2 .
When you add them you get 3x+3, which equals 3(x+1).

The above shows that the sum of any three consecutive numbers is always divisible by 3 !
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by Rohit21 » Tue Oct 18, 2011 2:10 pm
Thank you both!
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by Rohit21 » Tue Oct 18, 2011 2:17 pm
shankar.ashwin wrote:0 is considered divisible by any number except 0 itself.

0/Any NUmber = 0
If 0/Any number = 0 then why do we say its 'divisible by any number' in the first place?
Is it not logical to say its not divisible by any number?

I guess i completely forgot my math. :(
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by neelgandham » Tue Oct 18, 2011 2:34 pm
Rohit21 wrote:
shankar.ashwin wrote:0 is considered divisible by any number except 0 itself.

0/Any NUmber = 0
If 0/Any number = 0 then why do we say its 'divisible by any number' in the first place?
Is it not logical to say its not divisible by any number?

I guess i completely forgot my math. :(
I am not sure of the divisibility rule, but am sure of the multiplication rule. 0*a = a*0 = 0 (0 times of anything = 0)

So, 0/any number = 0*(1/any number) = 0 ! where 'any number' !=0 Makes sense?
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by Rohit21 » Tue Oct 18, 2011 3:06 pm
neelgandham wrote:
Rohit21 wrote:
shankar.ashwin wrote:0 is considered divisible by any number except 0 itself.

0/Any NUmber = 0
If 0/Any number = 0 then why do we say its 'divisible by any number' in the first place?
Is it not logical to say its not divisible by any number?

I guess i completely forgot my math. :(
I am not sure of the divisibility rule, but am sure of the multiplication rule. 0*a = a*0 = 0 (0 times of anything = 0)

So, 0/any number = 0*(1/any number) = 0 ! where 'any number' !=0 Makes sense?

This makes sense (from the beginning), but its just the wording.
Whatever, I'll just take this rule granted from now. "O is divisible by any number other than 0".
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by shankar.ashwin » Tue Oct 18, 2011 8:37 pm
Not a big fan of math rules as such, but you could think of it in a very practical sense and guess it would be easy to remember.

Say you have 1 pizza and 4 people to share; you get 1/4th each.
Now you have 0 pizza's, and 'n' number of people, here irrespective of how many people are there, no one gets anything. Hence 0/n=0.
If we have 0 pizzas and 0 people to share it with, seems like a hypothetical situation. (Hence ∞)

Now if we have 1 pizza and infinite people to share it with (1/∞) each one would literally get nothing. Hence 0.

I think its an absurd way to explain divisibility, but hope it makes sense :)
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