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# If x, y, and z are positive integers and x < y < z, which of the follo

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Math Expert
Joined: 02 Sep 2009
Posts: 56306
If x, y, and z are positive integers and x < y < z, which of the follo  [#permalink]

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26 Mar 2018, 00:30
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35% (medium)

Question Stats:

76% (01:15) correct 24% (01:24) wrong based on 74 sessions

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If x, y, and z are positive integers and x < y < z, which of the following statements must be true?

I. y/z < y/x
II. xz > xy
III. z > x + y

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

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Joined: 04 May 2017
Posts: 15
Re: If x, y, and z are positive integers and x < y < z, which of the follo  [#permalink]

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26 Mar 2018, 00:44
Question says x<y<z

statement 1: y/z < y/x
lets take x,y,z as 1,2,3

y/z < y/x = 2/3 < 2/1 which is true. It is true for every value.

Statement 2: xz > xy
lets take x,y,z as 1,2,3

2*3 > 2*1 , true again

Statement 3:
z > x + y
lets take x,y,z as 1,2,3

3 not greater than 2+1

False.

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Status: It's near - I can see.
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Posts: 1687
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If x, y, and z are positive integers and x < y < z, which of the follo  [#permalink]

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26 Mar 2018, 09:50
2
Bunuel wrote:
If x, y, and z are positive integers and x < y < z, which of the following statements must be true?

I. y/z < y/x
II. xz > xy
III. z > x + y

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

Given : x, y, z > 0 and x < y < z

Question : Which of the following statements must be true?

I. $$\frac{y}{z} <\frac{y}{x}$$

II. $$xz > xy$$

III. $$z > x + y$$

From I. $$\frac{y}{z} <\frac{y}{x}$$

We can reduce it to $$\frac{1}{z} < \frac{1}{x}$$

Or $$x < z$$ TRUE

(B), (C), and (E) are out

From II. $$xz > xy$$

We can reduce it to $$y < z$$ (As we know x, y, and z are positive) TRUE

(A) out

Hence (D)
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If x, y, and z are positive integers and x < y < z, which of the follo   [#permalink] 26 Mar 2018, 09:50
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