princeton q

[javeedw]

If x,y and z are non-zero numbers such that 1 >= y > x and xy=z, which of the following cannot be true?

a. y>z
b. y=z
c. z=x
d. x>z
e. z>0


Please explain your answer.....I feel two of the choices could be correct.....

[chatru]

My ans is "B"

I followed the way:

1 >= Y > X

say: 0.7 > 0.6 ; z = .42
-2 > -3 ; z = 6
0.5 > -2 ; z = -1

solve and see the ans

sa

[javeedw]

I too got B but what about (d) x>z?

x != 0 , y!=0 and 1 >= y > x, implies

0<y<1 or y<0
and
x <0

So when x is negative, and y is negative , z will be postive and hence x > z CANNOT be true

When x is negative and y is postive , z will be negative but definitely greater than x. again x > z CANNOT be true
For eg.,
x = -0.5 and y = 0.5 => z = -0.25 --- z > x
x = -0.1 and y = 0.9 => z = -0.09 --- z> x

am I missing something?

[tamannaw]

can t be b

take y = 1/2 and x = 0 , z= 0

[javeedw]

can t be b

take y = 1/2 and x = 0 , z= 0

But x,y,z are non-zero numbers...

[tamannaw]

oh yes ! thanks!

[javeedw]

Official Answer given is B.....Can anyone explain why D is wrong....

[Aaragorn]

D fails when we take the following values,Y = 1/2 (or 0.5), X = 1/4 (or 0.25) and therefor Z = 1/8 (or 0.125). "D" says X is greater than Z and that is proved.

[javeedw]

D fails when we take the following values,Y = 1/2 (or 0.5), X = 1/4 (or 0.25) and therefor Z = 1/8 (or 0.125). "D" says X is greater than Z and that is proved.

Thanks guys...I realised the mistake I was making.....somehow I assumed x<0 which is incorrect....