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If x > y > z, which of the following can be true?

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Bunuel
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If x > y > z, which of the following can be true? [#permalink] New post   17 Jun 2019, 01:21
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A
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E

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Question Stats:

53% (02:12) correct 47% (02:15) wrong based on 232 sessions
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If \(x > y > z\), which of the following can be true?

I. \(\frac{x}{y} >\frac{y}{z}\)

II. \(\frac{z}{x}>\frac{y}{x}\)

III. \(\frac{z}{y}>\frac{x}{y}\)

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
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E
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Lampard42
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If x > y > z, which of the following can be true? [#permalink] New post   Updated on: 17 Jun 2019, 08:15
Bunuel wrote:
If \(x > y > z\), which of the following can be true?

I. \(\frac{x}{y} >\frac{y}{z}\)

II. \(\frac{z}{x}>\frac{y}{x}\)

III. \(\frac{z}{y}>\frac{x}{y}\)

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


I. \(\frac{x}{y} >\frac{y}{z}\) - Possible

II. \(\frac{z}{x}>\frac{y}{x}\) - Possible

III. \(\frac{z}{y}>\frac{x}{y}\) - possible

So IMO E

Originally posted by Lampard42 on 17 Jun 2019, 02:55.
Last edited by Lampard42 on 17 Jun 2019, 08:15, edited 1 time in total.
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Re: If x > y > z, which of the following can be true? [#permalink] New post   19 Oct 2019, 20:58
Bunuel wrote:
If \(x > y > z\), which of the following can be true?

I. \(\frac{x}{y} >\frac{y}{z}\)

II. \(\frac{z}{x}>\frac{y}{x}\)

III. \(\frac{z}{y}>\frac{x}{y}\)

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


Hi Bunuel
I solved this question and got E but before marking the answer, I saw the options II and III. One has an x in the denominator and one has a y in the denominator.

Can't we cancel them and then reduce
II. z>y
III. z>x

chetan2u?
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chetan2u
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Re: If x > y > z, which of the following can be true? [#permalink] New post   19 Oct 2019, 21:07
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saurabh9gupta wrote:
Bunuel wrote:
If \(x > y > z\), which of the following can be true?

I. \(\frac{x}{y} >\frac{y}{z}\)

II. \(\frac{z}{x}>\frac{y}{x}\)

III. \(\frac{z}{y}>\frac{x}{y}\)

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


Hi Bunuel
I solved this question and got E but before marking the answer, I saw the options II and III. One has an x in the denominator and one has a y in the denominator.

Can't we cancel them and then reduce
II. z>y
III. z>x

chetan2u?


No, you cannot do this..
It will depend on the sign of the variables..

II. \(\frac{z}{x}>\frac{y}{x}\)
Let z=5, y=3 and x=2...... \(\frac{5}{2}>\frac{3}{2}\) and z>y
But say z=-5, y=3 and x=-2.......\(\frac{-5}{-2}>\frac{3}{-2}.......\frac{5}{2}>-\frac{3}{2}.\) and z<y
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Re: If x > y > z, which of the following can be true? [#permalink] New post   19 Oct 2019, 21:16
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saurabh9gupta wrote:
Bunuel wrote:
If \(x > y > z\), which of the following can be true?

I. \(\frac{x}{y} >\frac{y}{z}\)

II. \(\frac{z}{x}>\frac{y}{x}\)

III. \(\frac{z}{y}>\frac{x}{y}\)

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


Hi Bunuel
I solved this question and got E but before marking the answer, I saw the options II and III. One has an x in the denominator and one has a y in the denominator.

Can't we cancel them and then reduce
II. z>y
III. z>x

chetan2u?


saurabh9gupta

If x<0 & y<0 in II & III respectively
then the conditions are possible.

-2(x)>-3(y)>-4(z)

II
z/x = 2
y/x = 1.5
z/x > y/x

III
z/y = 4/3
x/y = 2/3
z/y > x/y
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Kinshook
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If x > y > z, which of the following can be true? [#permalink] New post   19 Oct 2019, 21:19
Bunuel wrote:
If \(x > y > z\), which of the following can be true?

I. \(\frac{x}{y} >\frac{y}{z}\)

II. \(\frac{z}{x}>\frac{y}{x}\)

III. \(\frac{z}{y}>\frac{x}{y}\)

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


Asked: If \(x > y > z\), which of the following can be true?

I. \(\frac{x}{y} >\frac{y}{z}\)
4(x) > 3(y) > 2(z)
x/y = 4/3
y/x =3/2
x/y>y/z
CAN BE TRUE

II. \(\frac{z}{x}>\frac{y}{x}\)
-2(x)>-3(y)>-4(z)
z/x = 2
y/x = 1.5
z/x > y/x
CAN BE TRUE

III. \(\frac{z}{y}>\frac{x}{y}\)
-2(x)>-3(y)>-4(z)
z/y = 4/3
x/y = 2/3
z/y > x/y
CAN BE TRUE

IMO E
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Re: If x > y > z, which of the following can be true? [#permalink] New post   31 Dec 2023, 12:46
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Re: If x > y > z, which of the following can be true? [#permalink]
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