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Let f:N rarr N be a function that (i) ...

Let `f:N rarr N` be a function that
(i) `x-f(x)=19[x/19]-90[f(x)/90], forall x in N,` where [] denotes the greatest integer function.
(ii) `1900 lt f(1990) lt 2000.`
Find all the possible values of f(1990).

A

`1994`

B

`1924`

C

`1954`

D

`1934`

Text Solution

Verified by Experts

The correct Answer is:
A
`1990-f (1990) = 19[(1990)/(19)]-90[f(1990)/(90)]`
`because 21.11lt f(1990)/(90)lt22.22,`
`because [f(1990)/(90)]=21,22`
`implies f(1990)=1994 or 1904`
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