joyseychow wrote:If the eleven consecutive integers are listed from least to greatest, what is the average (arithmetic mean) of eleven integers?

(1) The average of the first nine integers is 7
(2) The average of the last nine integers is 9

Looks like D


Consecutive integers ,mean=median


1. As the number are arranged in order, mean= median ¨=7 and we are talking about first nine integrs

so 7 is in the middle of 9 integers

so list is 3 4 5 6 7 8 9 10 11..and other 2 integers are 12 and 13

so complete list 3 4 5 6 7 8 9 10 11 12 13

we can now find average

sufficient

2. similarly, when The average of the last nine integers is 9

the last 9 integers would be 5 6 7 8 9 10 11 12 13

so complete list is 3 4 5 6 7 8 9 10 11 12 13

if least integer is a then we know the greatest is a + 10. We also know the average in terms of a
(1) gives us average of a through a + 6 - we can solve to get a hence sufficient
(2) same thing solve to get a so sufficient

D for me.
The key to solving this quesition is to read the Q carefully and recognize that the numbers are consecutive.

D for me too, consecutive integers clearly shows if we have average of first 9 or last 9 then we can have the other 2 numbers and hence the total average..

Consecutive integers ,mean=median

This is applicable when the consecutive is evenly spaced and the consecutive in this ques happens to be evenly spaced. If it doesn't then, what approach can I take?

joyseychow wrote:

Consecutive integers ,mean=median

This is applicable when the consecutive is evenly spaced and the consecutive in this ques happens to be evenly spaced. If it doesn't then, what approach can I take?

Each qtn tests some concept.. here the qtn was framed around consecutive integer ( with constant difference d) . so, approach varies from question to question. Specific to this question, If you say, integers are not consecutive, perhaps the answer could be something different than D, may be an E as we may not be in a position to answer the question asked..if you have a specific question and want to know approach, you can put up that question and forum users can share their strategies with you.