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

Question

Hey fellow clubbers,

this question is from the MGMAT quant "Word Problems Guide" 6th Edition.

For me, the answer to this question is no, because it does not provide any contrainsts like >0 or <0.

Example: x = -1 ; y= 0; z=1 -> -1+0+1=0 not divisble by 3.

Show SpoilerOA

Yes! For any odd number of consecutive integers, the sum of those integers is divisible by the number of integers. There are three consecutive integers (x,y and z), so the rule applies in this case.

Am I missing something or is it a mistake in the guide? Could not find a report officioal errata page of MGMAT though.

I just want to be sure, that I understand it correctly

Cheers,

Marius

Cheers, Marius

BrushMyQuant · Answer

Hi Marius,

First of all, 0 is divisible by all the non zero numbers so zero is divisible by 3

Secondly, take the three consecutive integers as n,n+1,n+2
Their sum = 3n + 3 = 3*(n+1) which is divisible by 3
take any value of n and this relationship will hold good for all the numbers

So, answer will be yes

Hope it helps!

chetan2u · Answer

hi germangoesgmat,

0 is divisible by all numbers.... reason..
when do we call a number divisible by another number.. when the remainder is 0..
when we divide 0 by any number, the remainder is 0..

hope its clear

EMPOWERgmatRichC · Answer

Hi germangoesgmat,

The other explanations in this thread (including the one in the MGMAT Book) confirm the correct answer, so I won't rehash any of that math here. Instead, I want to point out that any math "rule", Number Property pattern, etc. can be proven, so if you're ever in doubt, do a bit of work on the pad and you can confirm a rule...

Here, we're told that X, Y and Z are CONSECUTIVE INTEGERS.

Consider the possibilities:
-4, -3, -2 Sum = -9 = multiple of 3
-3, -2, -1 Sum = -6 = multiple of 3
-2, -1, 0 Sum = -3 = multiple of 3
-1, 0, 1 Sum = 0 = multiple of 3 (as explained, 0 is divisible by everything)
0, 1, 2 Sum = 3 = multiple of 3
1, 2, 3 Sum = 6 = multiple of 3
2, 3, 4 Sum = 9 = multiple of 3
Etc.

The GMAT will test you repeatedly on the 'thoroughness' of your thinking, so be prepared to think about rules that you know, but in ways that you might be used to thinking about.

GMAT assassins aren't born, they're made,
Rich

germangoesgmat · Answer

Thank you all for your kind answers! I should have checked whether 0 is divisible by any number or not. I just thought a found a little reasoning gap and was very happy.

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

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