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

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New post 09 Jun 2010, 04:51
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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   [#permalink] 22 Aug 2018, 14:22
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