Vishnu88 wrote: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 III
I think the OA should be E as opposed to C.
In case I am mistaken, appreciate if you could substantiate with an example [spoiler](for including excluding III)[/spoiler].
To satisfy the condition that 0 < 1- c/d < 1, c/d must be a positive fraction between 0 and 1.
Thus, II must be true.
Eliminate A.
Since d>0, in order for c/d to be a positive fraction between 0 and 1, c>0.
Thus, I must be true.
Eliminate B and D.
If c = 1/4 and d = 3/4, then c/d = (1/4)/(3/4) = 1/3, which is a positive fraction between 0 and 1.
(1/4)² + (3/4)² = 1/16 + 9/16 = 10/16 = 5/8.
Thus, III does not have to be true.
Eliminate E.
The correct answer is
C.
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