List L consists of k consecutive integers, where k is an odd integer.

Question

List L consists of k consecutive integers, where k is an odd integer. The median of the integers in L is m. Which of the following statements must be true?

I. The sum of the integers in L is an odd integer.
II. The least integer in L is equal to  m - \frac{k−1}{2} 
III. The greatest integer in L is equal to  m+\frac{k+1}{2}

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

gmatophobia · Answer

Let's see what inferences can we make -

" List L consists of k consecutive integers " :  Inference - The list is evenly spaced; the terms are in arithmetic progression.   
  "k is an odd integer." :  Inference - The median is a member of the set   
   As the list is evenly spaced, the sum of the list = Median * Number of terms

Answer choice elimination

I. The sum of the integers in L is an odd integer.

Sum = Median * number of terms

number of terms is odd. Is the value of median odd ? Well we aren't sure.  Eliminate the option as it cannot be MUST be true.

II. The least integer in L is equal to  m - \frac{k−1}{2}

Its given there are k integers in the list. So  \frac{k-1}{2}  integers lie to the left of m and  \frac{k-1}{2}  lie to the right

-----------  \frac{k-1}{2} ----------- m-----------  \frac{k-1}{2} -----------

So the lowest term is  m - \frac{k−1}{2} .  Will keep

III. The greatest integer in L is equal to  m+\frac{k+1}{2}

With reference to the above explanation, the greatest term is  m + \frac{k−1}{2} .  Hence Eliminate

Option B

hloonker · Answer

this question is difficult to follow. i can easily eliminate option 'I'. but not sure how to go about II and III.

stne · Answer

hloonker

Try picking a small sample that replicates the criteria of the question:

Let the # of consecutive integers be  3  , now the list can start with an odd integer or an even integer, only these  2  cases.

1)   1,2,3,  here  m=2  and  k=3,  you can see that this satisfies only option  2

2)   2,3,4  here  m=3  and  k=3,  you can see that this satisfies options  1  and  2  only.

Hence we can say only option  2  must be true.

Ans B

Hope it's clear.

Fisayofalana · Answer

Easy question. But I messed up thinking that I could also test consecutive odd and even numbers, but the question only states "consecutive numbers".

List L consists of k consecutive integers, where k is an odd integer.

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List L consists of k consecutive integers, where k is an odd integer.

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