pg no. 154-number properties (Q-12)

[sy14427]

Hi all,

Please help. The following question is on pg no. 154-number properties (Q-12)

Is the average of n consecutive integers equal to 1 ?

(1) n is even
(2) if S is the sum of the n consecutive integers, then 0 < S < n

Does the first option means the following:-

In option A, if we take out the average of even consecutive integers then result will be odd, for instance

0 + 2/2 =1 {-4, -2, 0, 2, 4, 6}

4 + 6/2 =5 {2, 4, 6, 8 }

6 + 8/2 = 14/2 =7 {4, 6, 8, 10}

So, in this case it is insufficient

or

option A means the following:-

the average of an even number of consecutive integers will never be an integer.

1 + 2 + 3 + 4 = 2 + 3/ 2 = 5/2

Therefore, the average of the n consecutive integers cannot equal 1. SUFFICIENT

Is there any difference between consecutive even integers and even consecutive integers ?

I am bit confused because i believe:-
consecutive even integers mean (2, 4, 6, 8,......n)
even consecutive integers mean even number of consecutive integers (1 + 2 + 3 + 4) , (5 + 6 + 7 + 8)

Please let me know if i am going on a right direction.

Thanks & Regards

[jnelson0612]

Hi there. I think your confusion is in interpreting the wording.
Notice that the question says "Is the average of n consecutive integers equal to 1?"

Statement one tells you that n is even. That means that you have an even NUMBER of consecutive integers. It does not tell you that the integers themselves are even. Think about what it means when you have an even number of consecutive integers, such as {1,2} or {1, 2, 3, 4}. Will the average of these integers ever be an integer?

[sy14427]

Thanks jnelson0612 for your reply.

I thought about it, even number of consecutive integers -

{1,2} -->There are 2 integers within the parenthesis
{1,2,3,4} --> There are 4 integers within the parenthesis

For odd number of consecutive integers -

{1,2,3} -->There are 3 integers within the parenthesis.
{1,2,3,4,5}-->There are 5 integers within the parenthesis.

But if i think about consecutive even integers then the case is different i.e {0,2,4,6,8......n}

Thanks once again your explanation really helped.

[jnelson0612]

Great, I'm happy to hear that!