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If a, b, and c are consecutive integers and a < b < c,

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If a, b, and c are consecutive integers and a < b < c, [#permalink] New post 17 Oct 2005, 12:40
If a, b, and c are consecutive integers and a < b < c, which of the following must be true?
I. b - c = 1
II. abc/3 is an integer.
III. a + b + c is even

just want to know can we consider a<b<c as -1<0<1

will post the OA later
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 [#permalink] New post 17 Oct 2005, 12:44
II and III must be true.

For 1, c - b should be 1. b - c = -1.

We could consider -1, 0 & 1. I need to check out whether 0 can be treated as even.

-- Edited post --

Oops. III cannot be true as explained in the below posts. My bad :-(

Last edited by sudhagar on 17 Oct 2005, 13:01, edited 1 time in total.
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 [#permalink] New post 17 Oct 2005, 12:46
ii)

0 is not an integer. So you cannot consider it in a sequence.

i) if a,b,c -> -10,-11,-12, then b-c=-1. Not true
ii) abc/3 - Since there is atleast one odd number in the seq., abc should be divisible by 3. True
iii) a+b+c cannnot be even if there are 2 even numbers in the seq. Not true
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 [#permalink] New post 17 Oct 2005, 12:47
II...

I) Cannot be true as b<c
III) a + b + c will be even when a,c are even or b is even

Yes, you can consider -1<0<1 as the question says consecutive integers (no mention of positive integers or the likes).
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 [#permalink] New post 17 Oct 2005, 12:47
<<<deleted the wrong post>>>

Last edited by gsr on 17 Oct 2005, 12:56, edited 2 times in total.
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 [#permalink] New post 17 Oct 2005, 12:49
gsr wrote:
ii)

0 is not an integer. So you cannot consider it in a sequence.

i) if a,b,c -> -10,-11,-12, then b-c=-1. Not true
ii) abc/3 - Since there is atleast one odd number in the seq., abc should be divisible by 3. True
iii) a+b+c cannnot be even if there are 2 even numbers in the seq. Not true


gsr: 0 is very much an integer! Else why would you have it on a number line!! However, zero is neither positive nor negative.
In any case II still holds... 0 divided by any number is 0 which is an integer.
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 [#permalink] New post 17 Oct 2005, 12:55
vikramm wrote:
gsr wrote:
ii)

0 is not an integer. So you cannot consider it in a sequence.

i) if a,b,c -> -10,-11,-12, then b-c=-1. Not true
ii) abc/3 - Since there is atleast one odd number in the seq., abc should be divisible by 3. True
iii) a+b+c cannnot be even if there are 2 even numbers in the seq. Not true


gsr: 0 is very much an integer! Else why would you have it on a number line!! However, zero is neither positive nor negative.
In any case II still holds... 0 divided by any number is 0 which is an integer.


I am sorry. :oops: You are right!
I was thinking of something else and in the end confused everyone!! :x
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 [#permalink] New post 17 Oct 2005, 12:55
the OA is II

which means 0 is an integer....if we say -1<0<1 is a possibility
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 [#permalink] New post 17 Oct 2005, 13:05
sudhagar wrote:
II and III must be true.

For 1, c - b should be 1. b - c = -1.

We could consider -1, 0 & 1. I need to check out whether 0 can be treated as even.

-- Edited post --

Oops. III cannot be true as explained in the below posts. My bad :-(


0 is an even integer

II only
  [#permalink] 17 Oct 2005, 13:05
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