Kaplan Premier Prog Question

[ri2007]

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

[gabriel]

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 ..

[ri2007]

hey
thanks a lot gabriel

[samirpandeyit62]

Hey good one gabriel I too solved it like u did

200 is out directly

all nos will be of form 1xy

now we need to evalaute for each place

xy =20, 02 ,11 for avg =1

for x to be avg ,y needs to be odd except 1 we used it alredy so there are 4 possibilties

similarly for y to be avg x needs to be odd 3,5,7,9 = 4 possibilities

total =11