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## Comment on

Are w, x and y Consecutive?## hi brent,

those remainders are not necessary for the statements? i dont understand what you explained finally..

## Sorry, I'm not sure what you

Sorry, I'm not sure what you're asking. Can you rephrase your question?

## Same question as the one

## First of all, the part

First of all, the part beginning at 0:20 is meant to PROVE the rule that says: The sum of any 3 consecutive integers is divisible by 3."

To prove the rule, I use n, n+1 and n+2 to represent three integers that ARE consecutive.

Once I prove the rule, then I use it to help analyze statement 1, which tells us that the sum of x, y and z is NOT divisible by 3.

ASIDE: I believe you might be confusing the answer to the target question with the answer to whether or not the statement is sufficient.

The target question is "Are x, y, z consecutive?"

This is a YES/NO question. If we are able to answer this question with absolute certainty (either yes or no), then the statement is sufficient.

From statement 1, we can conclude that x, y and z are definitely NOT consecutive integers.

So, if someone asks "Hey, are x, y and z consecutive integers?", I can respond with 100% certainty "NO, those integers are definitely NOT consecutive."

Since I can use the information in statement 1 to answer the target question with CERTAINTY, I can conclude that statement 1 is SUFFICIENT.

Here's a video about confusing the target question with the sufficiency question: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1097 (start at 3:17 in the video)

## what if in A, the numbers are

## Target question: Are the

Target question: Are the integers x, y and z consecutive?

In the video, we state that the sum of 3 consecutive integers MUST be divisible by 3.

So, if the sum of 3 integers is NOT divisible by 3, then we can be certain that the 3 integers are NOT consecutive.

Statement 1 basically says that the sum x+y+z is NOT divisible by 3.

So, we can conclude (with certainty) that the 3 integers are NOT consecutive.

So, our answer to the target question is "NO, the 3 integers are NOT consecutive"

Since we can answer the target question with certainty, statement 1 is sufficient.

Your suggested integers illustrates this position.

5 + 0 + 0 = 5, and 5 is not divisible by 3.

In this case 5, 0 and 0 are NOT consecutive.

So, the answer to the target question is "NO, the 3 integers are NOT consecutive"

ASIDE: I believe you have confused the answer to the SUFFICIENCY question with the answer to the TARGET question.

I cover this common mistake at 3:18 in the following video: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1097

Does that help?

Cheers,

Brent

## Is the rule: 'The product of

## That is also true: Every nth

That is also true: Every nth integer is divisible by n

## Hi Brent, you clarified a

In Statement one in this example, you introduce a new rule which you paraphrase as "The sum of 3 consecutive integers is divisible by 3."

Just to clarify, does this translate to the rule that "The sum of n consecutive integers is divisible by N"? (given that I have not seen this in any other of your videos so far)

I.E: We have four numbers: 1,2,3,4.

Product Rule -> 1*2*3*4="24" is divisible by N (in this case 4)

Sum Rule -> 1+2+3+4="10" which is not divisible by N (in this case 4)

As a result, I just wanted to clarify whether the sum rule only applies if N=3.

Thanks for your help and apologies if I am asking too many questions!

## Great question (keep them

Great question (keep them coming)!

You're correct; we CANNOT say that the sum of n consecutive integers is always divisible by n (as you have shown for n = 4)

However, after testing some values of n, it turns out that the rule works for all ODD values of n (e.g., n = 3, n = 5, n = 7, etc), but not for even values.

Cheers,

Brent

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