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If p and q are consecutive integers, is p a multiple of 3?

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If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 01 Mar 2012, 04:47
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If p and q are consecutive integers, is p a multiple of 3?

1) q is not a multiple of 3
2) q-1 is not a multiple of 3

In consecutive integer questions like this one, is the order of the variables implied, meaning that p comes before q or could p come after q as well?
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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 01 Mar 2012, 05:16
I would recommend picking numbers.

A) it could be 4 and 5. Not enough.
B) it could be 0 and 1. Not enough.

A) and B) combined won't help either. Take 0 and 1 as a case.

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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 01 Mar 2012, 05:18
Not sure what I am getting wrong here.. Isn't the answer supposed to be B?
An Yes/No question.
According to me P and Q are consecutive and hence the order matters so p,q can be 4,5 or 5,6 or 7,8..... In all these cases P is not a multiple of 3 and hence the answer is NO.

Will wait for the experts though :D
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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 01 Mar 2012, 05:23
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BN1989 wrote:
If p and q are consecutive integers, is p a multiple of 3?

1) q is not a multiple of 3
2) q-1 is not a multiple of 3

In consecutive integer questions like this one, is the order of the variables implied, meaning that p comes before q or could p come after q as well?


No, p and q are consecutive integers does not necessarily means that they are in that order: it could be (p, q=p+1) as well as (q, p=q+1). If it were otherwise then the answer to the question would be B, not E.

If p and q are consecutive integers, is p a multiple of 3?

Out of three consecutive integers one is always multiple of 3. Now, there can be two cases.
A. (q-1, q, q+1=p)
B. (q-1=p, q, q+1)

(1) q is not a multiple of 3. Not sufficient.
(2) q-1 is not a multiple of 3. Not sufficient.

(1)+(2) Now, if we have case A, q-1 is not a multiple of 3 and q is not a multiple of 3, would mean that p=q+1 must be a multiple of 3 BUT if we have case B, then q-1=p and (2) directly says that q-1=p is not a multiple of 3. So, p may or may not be a multiple of 3. Not sufficient,

Answer: E.

Hope it's clear.
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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 01 Mar 2012, 05:41
Bunuel - Thanks for the explanation.

One question though.

For a question on consecutive integers of a set p,q,r is it necessary for the question to specify p<q<r in order to determine the order of the set? Is this a generic rule? :-0
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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 01 Mar 2012, 05:52
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ENAFEX wrote:
Bunuel - Thanks for the explanation.

One question though.

For a question on consecutive integers of a set p,q,r is it necessary for the question to specify p<q<r in order to determine the order of the set? Is this a generic rule? :-0


Yes, if we are told that p, q, and r are consecutive integers and the stem wants us to consider them in that order it would specify that p<q<r.
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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 17 Dec 2013, 11:24
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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 23 Dec 2013, 10:28
Bunuel..I have a confusion..

If a question say consecutive integers.. for example, p,q,r and s are consecutive integers, that wud also means consecutive multiples?

2,3,4,5 or we can also say sequence may go like this 3,6,9, and 12?


Thank u.

I hope u l get my question, I tried my best to explain this question :D
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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 23 Dec 2013, 10:31
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sanjoo wrote:
Bunuel..I have a confusion..

If a question say consecutive integers.. for example, p,q,r and s are consecutive integers, that wud also means consecutive multiples?

2,3,4,5 or we can also say sequence may go like this 3,6,9, and 12?


Thank u.

I hope u l get my question, I tried my best to explain this question :D


"Consecutive integers" ALWAYS mean integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, ....

For example:

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.

So, not all evenly spaced sets represent consecutive integers.
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Re: If p and q are consecutive integers, is p a multiple of 3? [#permalink] New post 23 Dec 2013, 11:44
Ok. Thanks Alot :) I got it now ..
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Re: If p and q are consecutive integers, is p a multiple of 3?   [#permalink] 23 Dec 2013, 11:44
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