ri2007 wrote:How many 3 digit numbers between 100 & 200 have a digit that is the average of 2 other digits.
a) 1
b)7
c) 9
d) 11
e) 13
source - Kaplan Premier Prog - CD
Ans 11
can any one show me a quick way of solving this one?
Thanks
hmm .. i don't know whether this will classify as a quick method but here goes ..
We know that the first digit will be 1 , and 1 will be average of 2 other number if the sum of the other 2 is 2, and that is possible when the numbers is 111,120,102
Now that possibility is out of the way we know that 1 will be included in the group whose average is to be found,
So the different possibilities is
(1+3)/2 = 2 .. 132,123 ( we do not consider even numbers along with 1 because then the average will not be an integer )
(1+5) /2= 3 .. 153,135
(1+7)/2= 4 .. 147,174
(1+9)/2=5 .. 195,159
So that makes 11 in all ..
