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# Is it true that x – z > y – z ? (1) xz > yz (2) x + z > y + z

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Math Expert
Joined: 02 Sep 2009
Posts: 64248
Is it true that x – z > y – z ? (1) xz > yz (2) x + z > y + z  [#permalink]

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09 Aug 2019, 01:47
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Difficulty:

45% (medium)

Question Stats:

63% (01:03) correct 38% (01:06) wrong based on 48 sessions

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Is it true that x – z > y – z ?

(1) xz > yz
(2) x + z > y + z

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Intern
Joined: 04 Jul 2018
Posts: 1
Re: Is it true that x – z > y – z ? (1) xz > yz (2) x + z > y + z  [#permalink]

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09 Aug 2019, 09:23
Original condition: x-z > y-z

adding z on both sides would give x>y so we need to find that which statement will give us.

1) not suff
2) suff

Intern
Joined: 05 Jul 2019
Posts: 24
Location: India
Schools: ISB '21
Is it true that x – z > y – z ? (1) xz > yz (2) x + z > y + z  [#permalink]

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09 Aug 2019, 09:25
Statement 1 not sufficient

Case 1 X = 5 Y=3 Z= 1
Satisfy the eq
Case 2 X=-5 Y=-3 Z=-1
Doesn't satisfy the eq

Statement2 add 2Z both the sides

Satisfy the eq

Intern
Joined: 09 Jul 2014
Posts: 22
Re: Is it true that x – z > y – z ? (1) xz > yz (2) x + z > y + z  [#permalink]

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09 Aug 2019, 09:47
Given x-z > y-z

Adding z both sides => x > y

Statement 1: xz > yz => divide by z gives us => x > y ..if z is +ve or x < y ...if z is -ve.......Hence INSUFFICIENT

Statement 2: x+z > y+z => subtract z both side => x > y....... Hence SUFFICIENT

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Joined: 18 May 2019
Posts: 811
Re: Is it true that x – z > y – z ? (1) xz > yz (2) x + z > y + z  [#permalink]

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09 Aug 2019, 14:19
Is it true that x-z>y-z?

1. xz>yz
When x=-2 and y=-1 and z=-3
Then xz=6 and yz=3
xz(6)>yz(3)
x-z=1 and y-z=2, hence can answer it is not true.
But when x=3, y=1 and z=2
Then xz=6 and yz=2, satisfying the statement that xz(6)>yz(2).
x-z=1 and y-z=—1 and the answer this time around is yes. Statement 1 is therefore insufficient.

2. x+z>y+z
This statement clearly says that x>y if we should subtract z from both sides. Once x>y, then x-z>y-z since x-z>y-z is same as x>y if z is added to both sides.

Statement alone is sufficient. The answer is B

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Joined: 30 Sep 2017
Posts: 922
GMAT 1: 720 Q49 V40
GPA: 3.8
Re: Is it true that x – z > y – z ? (1) xz > yz (2) x + z > y + z  [#permalink]

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09 Aug 2019, 15:43
Is x-z > y-z?
--> is x > y?

1) xz > yz
--> if z is +ve and we divide both sides by z, then x > y (YES)
--> if z is -ve and we divide both sides by z, then x < y (NO)
NOT SUFFICIENT

2) x+z > y+z
--> x > y
SUFFICIENT

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Re: Is it true that x – z > y – z ? (1) xz > yz (2) x + z > y + z   [#permalink] 09 Aug 2019, 15:43