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Intern  Joined: 27 Sep 2009
Posts: 39
If a and b are consecutive negative integers, is a less than  [#permalink]

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Difficulty:   15% (low)

Question Stats: 78% (01:11) correct 22% (01:35) wrong based on 118 sessions

### HideShow timer Statistics 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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56370
If a and b are consecutive negative integers, is a less than  [#permalink]

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1
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.

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Intern  Joined: 27 Sep 2009
Posts: 39
Re: Consecutive integers- 600 level question  [#permalink]

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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.

Math Expert V
Joined: 02 Sep 2009
Posts: 56370
Re: Consecutive integers- 600 level question  [#permalink]

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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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Non-Human User Joined: 09 Sep 2013
Posts: 11749
Re: If a and b are consecutive negative integers, is a less than  [#permalink]

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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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