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

Question

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?

Lstadt · Answer

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.

Posted from my mobile device

ENAFEX · Answer

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

Bunuel · Answer

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.

ENAFEX · Answer

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

Bunuel · Answer

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.

sanjoo · Answer

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

Bunuel · Answer

"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.

sanjoo · Answer

Ok. Thanks Alot

I got it now ..

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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?

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