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## consecutive

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### consecutive

by ruplun » Fri Mar 09, 2012 8:25 am
If m and n are two consecutive positive integers, is m \gt n ?

1. m-1 and n+1 are consecutive positive integers
2. m is an even integer

(a)let m=3 , n =4 then m-1 =2 and n+1 =5 , 2 and 5 not consecutive integers.Hence insuff
let m=6, n =7 then m-1 = 5 and n+1=8.insuff

(b)m=2,n=3
m=6,n=5.insufficient.

IMO E.Confirm.

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by gopinathhyd » Sat Mar 10, 2012 5:55 am
is M > N, we are given m and n are positive consecutive integers.

st 1. m-1 and n+1 are consecutive, this can only be true if m is > than n

we have to take the statements as true and need to prove it. Only way m-1 and n+1 are consecutive is

example : m = 4 and n = 3,

m-1 = 4-1 =3
n+1= 3+1 = 4

proved

st 2. m is even does not say any thing about n, it can be greater than m and still be consecutive number.

IMO A

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by Mike@Magoosh » Sun Mar 11, 2012 6:03 pm
Hi, there. I'll add my 2Â¢ to this conversation.

First of all, I'll make clear: I totally agree with gopinathhyd.

Prompt: If m and n are two consecutive positive integers, is m > n ?

Notice that if they are consecutive, there are only two possibilities:
(a) m > n, i.e. m = n + 1
(b) m < n, i.s. m + 1 = n

Statement #1: m-1 and n+1 are consecutive positive integers

This is a fascinating statement. I would echo gopinathhyd's caution. When analyzing the statements in DS, the purpose is to take the statement itself as God's Truth, and then see what facts you can deduce from there. It's never appropriate to consider whether the given statement is true. Scenarios inconsistent with the statement are not relevant to the discussion.

So, if m > n, then if we subtract one from m and add one to n, they will still be consecutive. This is a scenario consistent with this statement.

If n > m, then if we subtract one from m and add one to n, they will move further apart and will not be consecutive. Therefore, this is a scenario NOT under consideration, given Statement #1.

The only possibility consistent with Statement #1 is m > n, which means Statement #1 is completely sufficient for determining a definitive answer to the prompt question. Statement #1, by itself, is sufficient.

Statement #2: m is an even integer
Well, this statement, by itself, tells us nothing. If m is even, n is odd, but n could be the odd number 1 greater than m, or 1 less than m. Statement #2, by itself, is insufficient.

Again, I am full agreement with gopinathhyd's fine work.

One reason I responded to this post is that ruplun's approach seemed to indicate some misunderstanding of the structure of DS questions per se. I would like to offer some resources:

Here's a video about DS strategy, one of a series of videos we have at Magoosh.

https://gmat.magoosh.com/lessons/363-avo ... kes-part-i

Here's a blog article I wrote about DS questions:

https://magoosh.com/gmat/2012/introducti ... fficiency/

Here's another DS question about consecutive integers:

https://gmat.magoosh.com/questions/880

When you submit an answer to that question, the next page has a complete video explanation. Each of the 800+ GMAT questions we have at Magoosh has a similar video explanation of the question.

Let me know if anyone reading this has any questions about what I've said.

Mike
Magoosh GMAT Instructor
https://gmat.magoosh.com/

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