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If a and b are consecutive negative integers, is a less than

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If a and b are consecutive negative integers, is a less than  [#permalink]

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New post 07 Jun 2010, 16:17
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If a and b are consecutive negative integers, is a less than b ?

(1) a + 1 and b - 1 are consecutive negative integers.
(2) a is an odd integer.
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Joined: 02 Sep 2009
Posts: 49271
If a and b are consecutive negative integers, is a less than  [#permalink]

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New post 08 Jun 2010, 07:00
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shekar123 wrote:
If a and b are consecutive negative integers, is a less than b ?

(1) a + 1 and b - 1 are consecutive negative integers.
(2) a is an odd integer.



\(a\) and \(b\) are consecutive integers means that either:
\(b=a+1\) (for example \(a=-5\) and \(b=-4\)), in this case \(a<b\);
OR:
\(a=b+1\) (for example \(a=-5\) and \(b=-6\)), in this case \(a>b\).

So the we should determine which case we have.

(1) \(a+1\) and \(b-1\)are consecutive negative integers --> again either \(a+1=b-1+1\) --> \(a+1=b\) (first case so \(a<b\)) or \(b-1=a+1+1\) --> \(b=a+3\), which is not possible as \(a\) and \(b\) are consecutive integers (difference between two consecutive integers cannot equal to 3). Sufficient.

(2) \(a\) is an odd integer. Clearly insufficient.

Answer: A.
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Re: Consecutive integers- 600 level question  [#permalink]

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New post 08 Jun 2010, 21:23
Could you please tell me as to how did u get this

\(b-1=a+1+1\) --> \(b=a+3\)

Thanks

Bunuel wrote:
shekar123 wrote:
If a and b are consecutive negative integers, is a less than b ?

(1) a + 1 and b - 1 are consecutive negative integers.
(2) a is an odd integer.



\(a\) and \(b\) are consecutive integers means that either:
\(b=a+1\) (for example \(a=-5\) and \(b=-4\)), in this case \(a<b\);
OR:
\(a=b+1\) (for example \(a=-5\) and \(b=-6\)), in this case \(a>b\).

So the we should determine which case we have.

(1) \(a+1\) and \(b-1\)are consecutive negative integers --> again either \(a+1=b-1+1\) --> \(a+1=b\) (first case so \(a<b\)) or \(b-1=a+1+1\) --> \(b=a+3\), which is not possible as \(a\) and \(b\) are consecutive integers (difference between two consecutive integers can not equal to 3). Sufficient.

(2) \(a\) is an odd integer. Clearly insufficient.

Answer: A.
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Joined: 02 Sep 2009
Posts: 49271
Re: Consecutive integers- 600 level question  [#permalink]

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New post 09 Jun 2010, 04:51
shekar123 wrote:
Could you please tell me as to how did u get this

\(b-1=a+1+1\) --> \(b=a+3\)

Thanks


Simple math:
\(b-1\) and \(a+1\) are consecutive integers --> \((b-1)=(a+1)+1\) --> \(b-1=a+2\) --> add 1 to both sides --> \(b-1+1=a+2+1\) --> \(b=a+3\).
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If a and b are consecutive negative integers, is a less than  [#permalink]

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New post 22 Aug 2018, 14:22
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Re: If a and b are consecutive negative integers, is a less than &nbs [#permalink] 22 Aug 2018, 14:22
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