Section 33 - #15

can anyone please let me know how to solve this problem ?

did you type the question correctly?

Hello Nisha, yes the question is right, I did try to copy paste but statement II and III did not get printed. So I added then manually in bottom of my original query. Here is the question again:

15. If d > 0 and , which of the following must be true ?
I. c > 0
II. c/d<1
II. 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 III

OA C

Question is incomplete...

If d > 0 and, 1 < 1 - c/d < 1 which of the following must be true ?
I. c > 0
II. c/d<1
III. c^2+d^2>1

I'm not sure about the solution, but looking at the ans, here it goes...
Please comment.

Sol:

I. As given d > 0, now, If c is negative i.e. c < 0 then ans of 1 - c/d will be positive and would be greater than 1;
So c has to be positive; if it's greater than d or equal be b then ans can or can not be between 1, but that should not be considered.
Important is that c must be positive.

II. Similarly, c/d must be less than 1 so that the term 1 - c/d will be between 1.

III. Here the square of c^2 and d^2 is greater than 1, which do not say that c is positive or negative as square of positve or negative number is always positive.

Hence I & II

Ans C.