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Based on the given question I guess we can have two answers
(A)8
(B)9
(C)18
(D)20
(E)80
for the F(m)=9F(V) we need to go by given answers.
either we should have product of two digits of F(m) having 9 as factor.
Only possible corresponding 'different' digits are V(M) 1(3),2(6),3(9) or 1(9) X,y,Z <> 0
Out of given choices
8 means difference only in units place
8 is possible 111 ,119 or 121 ,129 -there can be numerous examples -This is correct
9 means diff only in units place (or difference of factor of 3 each in units and tenth place which is not possible as tens digit difference would be such that total diff more than 9)
9 is not possible. Since it will leave one of the numbers zero which will make f(v)=0
18 means diff in units and tenth place.Now we cant have a difference of 9 in units or tenths place alone (as it would make function zero for either m or n)
therefore each unit and tenth place of m should have a factor of 3 more than
that of v .Only possible corresponding digits are V(M) 1(3),2(6),3(9)
clearly using these difference of 18 is not possible .Minimum diff is 22
X 33 X 11, other combination has a bigger difference eg X 3 6 X 12
Again for 20 it is clear that difference is not in units place.
It is tens place or
you can say difference of twenty in 100s and 10s place together eg 21Z and 19Z.- this is not possible as
Now we cannot have two digits with a difference of 2 if one digit is 9 times the other one
80- this is possible 111 and 191 so this is also correct
Please let me know if you have alternate views
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