Question: Are w, x and y Consecutive?

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..
gmat-admin's picture

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

Same question as the one above: A, as example, says (w+x+y)/3 has remainder 2. Your solution says (w+x+y) is divisible by 3 if they are consecutive --> this I agree with; however, they don't have a remainder of 2. Wouldn't this make the statement false? i.e. 2+3+4 = 9/3 has remainder 0, not 2. How can we say that the statement is valid then?
gmat-admin's picture

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 statement 1, the numbers are 5, 0, 0? The numbers will not be consecutive then!
gmat-admin's picture

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 3 consecutive integers is divisible by 3' another way of saying 'Every nth integer is divisible by n?'
gmat-admin's picture

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

Hi Brent, you clarified a previous question of mine where I drew on on Brunel's rule stating that "The product of n consecutive integers is always divisible by n!."

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!
gmat-admin's picture

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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