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# If X > Y and Z is a positive number, which of the following relationsh

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Joined: 02 Sep 2009
Posts: 64090
If X > Y and Z is a positive number, which of the following relationsh  [#permalink]

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31 Jul 2019, 22:49
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If X > Y and Z is a positive number, which of the following relationship is not true ?

A. XZ > YZ
B. Z-X > Z-Y
C. X-Z > Y-Z
D. X/Z > Y/Z
E. X+Z > Y+Z

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Re: If X > Y and Z is a positive number, which of the following relationsh  [#permalink]

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31 Jul 2019, 23:04
2
Bunuel wrote:
If X > Y and Z is a positive number, which of the following relationship is not true ?

A. XZ > YZ
--> XZ - YZ > 0
--> Z(X - Y) > 0
--> Positive*Positive = Positive -- True

B. Z-X > Z-Y
--> 0 > Z - Y - Z + X
--> X - Y < 0
--> X < Y -- NOT True

C. X-Z > Y-Z
--> X - Z - Y + Z > 0
--> X - Y > 0
--> X > Y -- True

D. X/Z > Y/Z
--> X/Z - Y/Z > 0
--> (X - Y)/Z > 0
00> Positive/Positive = Positive -- True

E. X+Z > Y+Z
--> X > Y -- True

IMO Option B

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If X > Y and Z is a positive number, which of the following relationsh  [#permalink]

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Updated on: 31 Jul 2019, 23:49
1
If X > Y and Z is a positive number, which of the following relationship is not true ?

Try Z=2 for all answers

A. XZ > YZ
2X > 2Y --> X>Y (TRUE)

B. Z-X > Z-Y
2-X > 2-Y --> Y > X (FALSE!! The correct answer)

C. X-Z > Y-Z
X-2 > Y-2 --> X > Y (TRUE)

D. X/Z > Y/Z
X/2 > Y/2 --> X > Y (TRUE)

E. X+Z > Y+Z
X+2 > Y+2 --> X > Y (TRUE)

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Originally posted by chondro48 on 31 Jul 2019, 23:13.
Last edited by chondro48 on 31 Jul 2019, 23:49, edited 3 times in total.
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Posts: 811
Re: If X > Y and Z is a positive number, which of the following relationsh  [#permalink]

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31 Jul 2019, 23:44
x>y, and z is a positive number. Let x=4,y=3 and z=2
We are to determine the relationship that is not true.
A. xz>yz i.e. 8>6; True
B. z-x>z-y i.e. (-2)>(-1); not true.
C. x-z>y-z i.e. 2>1; true.
D. x/z>y/z i.e. 2>3/2 true.
E. x+z>y+z i.e. 6>5; true.

The answer is therefore B.

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Re: If X > Y and Z is a positive number, which of the following relationsh  [#permalink]

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06 Aug 2019, 16:47
Bunuel wrote:
If X > Y and Z is a positive number, which of the following relationship is not true ?

A. XZ > YZ
B. Z-X > Z-Y
C. X-Z > Y-Z
D. X/Z > Y/Z
E. X+Z > Y+Z

Since X > Y, then -X < -Y and hence Z - X < Z - Y. So choice B, Z - X > Z - Y, is not true.

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Re: If X > Y and Z is a positive number, which of the following relationsh   [#permalink] 06 Aug 2019, 16:47

# If X > Y and Z is a positive number, which of the following relationsh

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