Are the integers q, r and s consecutive?

Hi all,

I have following issues:
1. Can evenly spaced numbers be representated as Consecutive numbers?
0, 5, 10
2, 7, 12

Both these sets are evenly spaced but can they fall in Consecutive numbers set?

Please clarify.

1. This statement holds true for any evenly spaced set (consecutive integers are evenly spaced too). For example, let q=2; r=4; s= 6. Mean is 4=r. So, are the integers consecutive? No.

Now take q=1, r=2, s=3. Mean =2= r. So are the integers consecutive/Yes.

So we have 2 different answers from the same statement. Hence this statement alone is insufficient.

2. Even this statement holds good for all evenly spaced sets. Pick numbers to check. insufficent.

1 & 2 together: No new information.

Answer E.

Generally, it is clarified in the question if this is the case. For example, the question will mention that "the set x contains consecutive even integers" or "the sum of consecutive odd integers is 18" etc.

However, if if nothing is mentioned, i guess we have to take integers where the common difference between terms is 1.

But it will be good if someone can clarify this point! Thanks!

Are the integers q, r and s consecutive?

(1) The average (arithmetic mean) of q, r and s is r
(2) r - q = s - r


Answer : E

Statement 1

Case A:
Q=1,R=2,S=3 ..Consecutive integers and Avg=2=r
Q=10,R=20,s=30...Not consecutive integers and Avg=20=r

1 is not sufficient

Statement 2

Case B

Q=1,R=2,S=3 ..Consecutive integers r-q=s-r=1
Q=10,R=20,s=30...Not consecutive integers and r-q=s-r=10

2 is not sufficient.

Combing A+C
We have 2 set of answers , Hence not C

OA=E

(1) The average (arithmetic mean) of q, r and s is r
This could be a case of consecutive odd or even integers or any Arithmetic progression. Insufficient.


(2) r - q = s - r
This statement suggests that he numbers are in AP with a common difference. Once again, no use. Insufficient

Combining the two statements, we only understand that this is an AP with no idea about the common difference. Had the second statement been equal to r-q=s-r=1, this would have been sufficient. However, together too, both the statements are insufficient.

Hence E

We need to determine whether the integers q, r, and s are consecutive.

Statement One Alone:

The average (arithmetic mean) of q, r, and s is r.

Using the information in statement one, we can create the following equation:

r = (q + r + s)/3

3r = q + r + s

2r = q + s

r = (q + s)/2

Although we see that r is the average of q and s, we cannot determine whether q, r, and s are consecutive integers. For instance, if q = 2, r = 3, and s = 4, then the integers are consecutive. However, if q = 5, r = 9, and s = 13, then the integers are not consecutive. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

r - q = s - r

Simplifying the equation in statement two gives us:

2r = s + q

r = (s + q)/2

Since statement two provides the same information as statement one, we see that statement two is also insufficient.

Statements One and Two Together:

Since statements one and two provide the same information and are each insufficient, we do not have enough information to answer the question.

Answer: E

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