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If r and s are consecutive even integers, is r greater than s?

Either s=r+2 or r=s+2. We are asked whether we have the second case: r=s+2 --> r>s.

(1) r + 2 and s - 2 are consecutive even integers --> s>r, because if r>s then r+2 and s-2 won't be consecutive even integers. Sufficient.

Or another way: stem says that the distance between r and s is 2. Now, if r>s then the distance between r+2 and s-2 would be 6 and they won't be consecutive as (1) states. Thus it must be true that r<s.

(2) r - 1 is not equal to s + 1 --> subtract 1 from both sides in r=s+2 --> r-1=s+1. Now, we are told that this is not true, hence r=s+2 is not true, which means that r>s is not true. So, s>r. Sufficient.

Re: If r and s are consecutive even integers, is r greater than [#permalink]

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03 Apr 2013, 06:30

Bunuel,

Could you help with the below confusion regarding your explanation:

In the question, it says "consecutive even integers" so those could be positive or negative, but in the answer part you have only taken into consideration the positive even integers.My doubt is the consecutive even integers could be negative also, and could possible change the final answer as E.

Could you help with the below confusion regarding your explanation:

In the question, it says "consecutive even integers" so those could be positive or negative, but in the answer part you have only taken into consideration the positive even integers.My doubt is the consecutive even integers could be negative also, and could possible change the final answer as E.

Please help to clarify.

Thanks!

In the solution above positive integers are not mentioned at all. Thus the reasoning holds true for any even r and s.
_________________

Re: If r and s are consecutive even integers, is r greater than [#permalink]

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03 Apr 2013, 06:54

Thanks, got my mistake.

In general: we should plugin both positive & negative consecutive integers if not explicitly mentioned in question, as negative consecutive integers (odd or even) are very well accepted in GMAT.

Re: If r and s are consecutive even integers, is r greater than [#permalink]

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24 Feb 2015, 11:17

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Re: If r and s are consecutive even integers, is r greater than [#permalink]

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06 Mar 2016, 07:24

Bunuel wrote:

If r and s are consecutive even integers, is r greater than s?

Either s=r+2 or r=s+2. We are asked whether we have the second case: r=s+2 --> r>s.

(1) r + 2 and s - 2 are consecutive even integers --> s>r, because if r>s then r+2 and s-2 won't be consecutive even integers. Sufficient.

Or another way: stem says that the distance between r and s is 2. Now, if r>s then the distance between r+2 and s-2 would be 6 and they won't be consecutive as (1) states. Thus it must be true that r<s.

(2) r - 1 is not equal to s + 1 --> subtract 1 from both sides in r=s+2 --> r-1=s+1. Now, we are told that this is not true, hence r=s+2 is not true, which means that r>s is not true. So, s>r. Sufficient.

If r and s are consecutive even integers, is r greater than s?

Either s=r+2 or r=s+2. We are asked whether we have the second case: r=s+2 --> r>s.

(1) r + 2 and s - 2 are consecutive even integers --> s>r, because if r>s then r+2 and s-2 won't be consecutive even integers. Sufficient.

Or another way: stem says that the distance between r and s is 2. Now, if r>s then the distance between r+2 and s-2 would be 6 and they won't be consecutive as (1) states. Thus it must be true that r<s.

(2) r - 1 is not equal to s + 1 --> subtract 1 from both sides in r=s+2 --> r-1=s+1. Now, we are told that this is not true, hence r=s+2 is not true, which means that r>s is not true. So, s>r. Sufficient.

Hi, Since you ask about Stat 1, let me concentrate on that part only.. 1) we know r and s are consecutive even integers.. Either r=s+2 or s=r+2..

2) from stat 1 r + 2 and s - 2 are consecutive even integers..

lets try two cases here.. a) r=s+2.. substitute in r+2= s+2+2= s+4.. NOW can s+4 and s-2 be consecutive even- NO so s=r+2 so s>r.. b) we can try s=r+2 too.. s-2=r+2-2=r... so s-2 and r+2 consecutive would mean r and r+2 consecutive even.. so yes s=r+2..

Re: If r and s are consecutive even integers, is r greater than [#permalink]

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06 Mar 2016, 07:58

chetan2u wrote:

smartguy595 wrote:

Bunuel wrote:

If r and s are consecutive even integers, is r greater than s?

Either s=r+2 or r=s+2. We are asked whether we have the second case: r=s+2 --> r>s.

(1) r + 2 and s - 2 are consecutive even integers --> s>r, because if r>s then r+2 and s-2 won't be consecutive even integers. Sufficient.

Or another way: stem says that the distance between r and s is 2. Now, if r>s then the distance between r+2 and s-2 would be 6 and they won't be consecutive as (1) states. Thus it must be true that r<s.

(2) r - 1 is not equal to s + 1 --> subtract 1 from both sides in r=s+2 --> r-1=s+1. Now, we are told that this is not true, hence r=s+2 is not true, which means that r>s is not true. So, s>r. Sufficient.

Hi, Since you ask about Stat 1, let me concentrate on that part only.. 1) we know r and s are consecutive even integers.. Either r=s+2 or s=r+2..

2) from stat 1 r + 2 and s - 2 are consecutive even integers..

lets try two cases here.. a) r=s+2.. substitute in r+2= s+2+2= s+4.. NOW can s+4 and s-2 be consecutive even- NO so s=r+2 so s>r.. b) we can try s=r+2 too.. s-2=r+2-2=r... so s-2 and r+2 consecutive would mean r and r+2 consecutive even.. so yes s=r+2..

Hope it helps

Thanks Chetan
_________________

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