If x, y and z are non-zero numbers such that 1 = y x and xy = z, wh

Question

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

RaghavKhanna · Answer

Going through the options:
Option B states that x = 1
This is not possible since x < y < = 1

Answer: B

All other options can also be eliminated by:
E: if x > 0, y>0
=> Z > 0
=> Reject

D. if x = -2, y = 5
=> z = -10
=> x > z
=> Reject

C. If z = x
=> y = 1
=> Reject

A. y = 5, x = -1
=> z = -5
=> y > z
=> Reject

Posted from my mobile device

yashikaaggarwal · Answer

If x, y and z are non-zero numbers such that 1 >= y > x and xy = z, which of the following cannot be true?
Let Y =1 and x = 0.5
xy=0.5*1=0.5

A. y > z
1>0.5 (correct)

B. y = z
y can't be equal to z as when two distinct fractions are multiplied. its product it always closer to smaller fraction.
for ex- Let Y = 0.8 and x = 0.5
z=0.4
Y will always be greater than Z
(incorrect)

C. z = x
0.5=0.5 (Correct)

D. x > z
Let Y = 0.8 and x = 0.5
z=0.4
0.5>0.4 (correct)

E. z > 0
0.5>0 (Correct)

Answer is B

rajatchopra1994 · Answer

Explanation:

Given: 1 >= y > x and xy = z.

Option B : if y=z , then x=1
which cannot be possible, as it should be less than 1.

IMO-B

Babineaux · Answer

IMO ans is B,
Please refer to the pic uploaded.

Posted from my mobile device

alvagr · Answer

Why there is nobody who considers that any numbers given could be negative so we have a lot of options to revise but only one formula in the question given xy=z (so that x cannot be even to x) provide us with the answer immidiately

y=1 
x>0 
0<z<1

0<y<1 
x<0 
z<0

-1<y<0
-1<x<0
0<z<1

y<=-1
x<-1 
1<=z

So many possibilities 
It is unreal to reconsider every of them within 2 minutes on the real exam 
I guess there is a shortcut for solve this task  (you have to crunch first of all and formost the formula given in the question that gives you the answer at once)

philipssonicare · Answer

Don't feel other responses made it clear why B is wrong

Prompt
x,y,z≠0
x<y≤1 .˙.x≠1
xy=z

B: y=z
Substitute this into the prompt equation
xz=z
xz-z=0
z(x-1)=0
z=0 or x=1
z≠0 as x,y,z≠0
x≠1 as x<1

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If x, y and z are non-zero numbers such that 1 >= y > x and xy = z, wh

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