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

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

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15 Feb 2012, 18:23
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If r and s are consecutive even integers, is r greater than s ?
(1) r + 2 and s - 2 are consecutive even integers.
(2) r - 1 is not equal to s + 1

I know why A is sufficient. Can someone please tell me how come Statement B us sufficient as well?
[Reveal] Spoiler: OA

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15 Feb 2012, 18:31
Plug in numbers.

r-1==>4-1 = 3
s+1 ==> 2+1 = 3.

Now you know S can't be smaller than R

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15 Feb 2012, 20:33
enigma123 wrote:
If r and s are consecutive even integers, is r greater than s ?
(1) r + 2 and s - 2 are consecutive even integers.
(2) r - 1 is not equal to s + 1

I know why A is sufficient. Can someone please tell me how come Statement B us sufficient as well?

Stmt1: This can happen only when s>r so is r>s no sufficient
Stmt2: This condition holds true also when s>r so again the statement is sufficient

SO ans is D

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

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15 Feb 2012, 21:28
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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.

Similar question to practice: og12-quant-2nd-ed-qn-86-consecutive-postives-126287.html

Hope it helps.
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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.

Thanks!

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

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03 Apr 2013, 06:38
gianprakash wrote:
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.

Thanks!

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

Please see if I make sense here.

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

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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.

Similar question to practice: og12-quant-2nd-ed-qn-86-consecutive-postives-126287.html

Hope it helps.

Can Someone explain Statement 1
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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, 07:38
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.

Similar question to practice: og12-quant-2nd-ed-qn-86-consecutive-postives-126287.html

Hope it helps.

Can Someone explain Statement 1

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

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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, 07:58
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.

Similar question to practice: og12-quant-2nd-ed-qn-86-consecutive-postives-126287.html

Hope it helps.

Can Someone explain Statement 1

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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Re: If r and s are consecutive even integers, is r greater than   [#permalink] 06 Mar 2016, 07:58
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