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x, y, z are three distinct positive numbers. Which is the greatest num

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x, y, z are three distinct positive numbers. Which is the greatest num  [#permalink]

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17 Mar 2018, 00:02
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x, y, z are three distinct positive numbers. Which is the greatest number among x, y, z?

(1) z - x < y - x

(2) x/y = y/z
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Joined: 29 Jun 2014
Posts: 32
Re: x, y, z are three distinct positive numbers. Which is the greatest num  [#permalink]

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17 Mar 2018, 00:24
amanvermagmat wrote:
X, Y, Z are three distinct positive numbers. Which is the greatest number among X, Y, Z?

(1) Z - X < Y - X

(2) X/Y = Y/Z

1).div both sides by X...z/x -1< y/x -1....(z-y)/x<0...
Z<Y..not suff.
2) X/Y= Y/Z ..not suff.
1)+)2)... we know from 1..that...Y/Z>1...so...X>Y
So...x>y..y>z..
C

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Re: x, y, z are three distinct positive numbers. Which is the greatest num  [#permalink]

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23 Mar 2018, 01:39
amanvermagmat wrote:
X, Y, Z are three distinct positive numbers. Which is the greatest number among X, Y, Z?

(1) Z - X < Y - X

(2) X/Y = Y/Z

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Posts: 58364
Re: X, Y, Z are three positive numbers. Which is the greatest number among  [#permalink]

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23 Mar 2018, 01:48
x, y, z are three distinct positive numbers. Which is the greatest number among x, y, z?

(1) z - x < y - x. Cancel -x on both sides: z < y. No info about x. Not sufficient.

(2) x/y = y/z. Consider x = 1, y = 2 and z = 4 OR x = 4, y = 1 and z = 1/4. Not sufficient.

(1)+(2) Since from (2) z < y, then y/z > 1. Thus, from (2) x/y > 1, which gives x > y. So we have that x > y > z. Sufficient.

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Re: x, y, z are three distinct positive numbers. Which is the greatest num  [#permalink]

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23 Mar 2018, 01:59
1. When re-written this statement gives us Y > Z.
However, we have no information about the relationship between X,Y, and Z.
We can't clearly tell which is the greatest number among X,Y,Z (Insufficient)

2. This statement can be re-written as Y^2 = XZ
Case 1: Y = 2, X = 1, Z = 4(Here, Z is the greatest number possible)
Case 2: Y = 2, X = 4, Z = 1(Here, X is the greatest number possible)
We can't clearly say which of the numbers if the greatest (Insufficient)

On combining the information in both the statements, since Y > Z
the only possibility is when X > Y > Z(Case 1 is invalid here)

Here, X is the greatest number (Sufficient - Option C)
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Re: x, y, z are three distinct positive numbers. Which is the greatest num   [#permalink] 23 Mar 2018, 01:59
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