If x y and 1/x

Question

If  x > y  and  \frac{1}{x} < \frac{1}{y} , which of the following could be true:

I.  0 < x < 1  and  0 < y < 1 
II.  xy < 0 
III.  -1 < x < 0  and  -1 < y < 0

A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III

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chetan2u · Accepted Answer

A very straight forward answer will be x > y and \frac{1}{x} < \frac{1}{y} , that is cross-multiplication is NOT changing the sign. MEANS both x and y have SAME sign or xy>0. I. 0 < x < 1 and 0 < y < 1 ...xy>0..YES II. xy < 0 ...NO III. -1 < x < 0 and -1 < y < 0 ...xy>0..YES I and III D OR Choose values... I. 0 < x < 1 and 0 < y < 1 ..........x=0.9 and y=0.3...0.9>0.3 and \frac{1}{0.3}>\frac{1}{0.9} .. \frac{10}{3}>\frac{10}{9} ...YES II. xy < 0 ....x=2 and y=-1...2>-1 but 1/2>1/-1...Eliminate III. -1 < x < 0 and -1 < y < 0 ....x=-0.3 and y=-0.9...-0.3>-0.9 and -\frac{1}{0.3}>-\frac{1}{0.9} .. \frac{10}{3}>\frac{10}{9} ...YES

Archit3110 · Answer

for given condition 
  x > y  and  \frac{1}{x} < \frac{1}{y}

we can test with integers and fractions ; ( 2,3) ( 1/2,1/3) & ( -1/2,-1/3)
 0 < x < 1  and  0 < y < 1 
 -1 < x < 0  and  -1 < y < 0 
true
IMO D;

metalhead2593 · Answer

1/x<1/y So (y-x)/xy <0 We know that x>y, so y-x <0. xy must be positive (>0). So, either x,y >0 or x,y <0 I. Yes II. NO III. Yes IMO D.

Kinshook · Answer

If x > y and \frac{1}{x} < \frac{1}{y} , which of the following could be true: x>y 1/y -1/x > 0 (x-y)/xy>0 Since x-y>0 xy>0 I. 0 < x < 1 and 0 < y < 1 xy>0; COULD BE TRUE II. xy < 0 MUST NOT BE TRUE III. -1 < x < 0 and -1 < y < 0 xy>0; COULD BE TRUE IMO D

Biplob12345 · Answer

Given that xy>0 and x>y, which of the followingmust be true? 
A.x+y>0
B.x^2+y^2>xy
C.x^2-y^2>0
seeking Detail solution Thank you

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If x > y and 1/x < 1/y, which of the following could be true:

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