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

Hi Brent,

I've gone through the integer property videos and understand the "Every nth number is divisible by n" rule for consecutive integers.

Can you point me to the videos where these two rules are? (sum of 3 consecutive integers is divisible by 3 and the product of 3 consecutive integers is divisible by 3)

In particular I've seen references to a product rule in other answers on Gmat club so I want to make sure I understand that rule. Thanks!
gmat-admin's picture

YEAH I BET THIS RIGHT AGAIN!

Just test 3 consecutive numbers and we are all set!

Both answers yield "NO", so they are both sufficient
gmat-admin's picture

Good stuff!

Hi Brent, I solved it as below and is this correct? Thanks Brent

(W+X+Y)/3 = Q(2)
Possible values of (W+X+Y): 2,5,8,11.... (Not consecutive integers and W=x=y=?)

(WXY)/3 = Q(1)
Possible values of WXY : 1,4,7,10.... (Not consecutive integers and W=x=y=?)

Therefore D.
gmat-admin's picture

I think that solution is correct.
I'm just not sure what you mean when you write "W=X=Y=?"

Thanks Brent. My bad I mean we don't know individual value of W,X,Y as "W=X=Y=?"
gmat-admin's picture

Okay thanks.
If your conclusion is that W, X and Y are definitely not consecutive integers, then your solution is fine.

Thanks Brent for confirmation..

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