BTGmoderatorDC wrote:If a/b < c/d & bd < 0, which of the following inequalities must be true?
I. ad -bc < 0
II. bc -ad > 0
III. ad -bc > 0
A. I only
B. II only
C. III only
D. I and II
E. II and III
In I, II and III, test the following case:
a=c=d=1 and b=-1, with the result that a/b < c/d and bd < 0.
I: ad-bc < 0
Since ad=1*1=1 and bc=-1*1=-1, we get:
1 - (-1) < 0
2 < 0
Not true.
Eliminate A and D, each of which include I.
II: bc-ad > 0
Since bc=-1*1=-1 abd ad=1*1=1, we get:
-1 - 1 > 0
-2 > 0
Not true.
Eliminate B and E, each of which include II.
The correct answer is
C.
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