If d > 0 and 0 < 1 - c/d < 1, which of the following must be true?

I. c > 0

II. c/d < 1

III. c^2 + d^2 > 1

(A) I only

(B) II only

(C) I and II only

(D) II and III only

(E) I, II and IIISol: Given d>0 and 0 < 1 - c/d < 1---------> Eq a

Subtract from Eq a we get -1<-c/d<0

Mulitply by each term by -1 we get 1>c/d>0

Since d>0 and c/d>0 this implies c>0

also we can clearly see c/d> 1. At this stage options A,B and D can be rejected

Consider c^2+d^2> 1

If c=3 and d=5 then c^2+d^2>1

But if c=1/2 and d=3/4 then we have 1/4+9/25 or (25+36)/100 or 61 /100 which is less than 1

Ans is C

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