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If x, y, and z are negative integers and 3x - 3y = -3z, then

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guygmat
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If x, y, and z are negative integers and 3x - 3y = -3z, then [#permalink] New post   Updated on: 13 Jul 2013, 07:14
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If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?

I. x > y
II. x > y > z
III. x = z

A. I and II
B. I only
C. II only
D. III only
E. None

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-y-and-z-are-negative-integers-and-3x-3y-3z-then-99463.html
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B

Originally posted by guygmat on 19 Jun 2011, 08:00.
Last edited by Bunuel on 13 Jul 2013, 07:14, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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fluke
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Re: Another Must Be True Problem [#permalink] New post   19 Jun 2011, 10:18
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guygmat wrote:
If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?

I. x > y
II. x > y > z
III. x = z

A)I and II
B)I only
C)II only
D)III only
E)None


3x-3y=-3z
x-y=-z
Since z<0; -z>0
x-y>0
x>y
I correct.

We can't say much about z though;

x=-5; y=-100; z=-95
II and III incorrect.

Ans: "B"
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msbinu
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Re: Another Must Be True Problem [#permalink] New post   01 Jul 2011, 23:40
3x-3y=-3z
x-y=-z
Since z<0; -z>0

Since y and y are also less than 0 ,shouldn't the equation change to
y -x =z?
(substituting -x for x ,-y for y and -z for z )
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gmatopoeia
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Re: Another Must Be True Problem [#permalink] New post   07 Sep 2011, 07:26
Quote:
If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?

I. x > y
II. x > y > z
III. x = z

A)I and II
B)I only
C)II only
D)III only
E)None


Given 3x-3y=-3z, then x+z=y.
As y<0, we know that x+z<0.

Since x<0 and z<0 and x+z =y --> y is of greater negative value (i.e. smaller) than both x and z (x>y; z>y)
Insufficient info to help us draw the direct relationship between x and z.
--> I is correct.
--> II is incorrect.
--> III cannot be determined.

Answer: B
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Re: If x, y, and z are negative integers and 3x - 3y = -3z, then [#permalink] New post   02 Jan 2017, 05:07
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guygmat wrote:
If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?

I. x > y
II. x > y > z
III. x = z

A. I and II
B. I only
C. II only
D. III only
E. None



\(3x-3y=-3z\) --> \(x-y=-z\) --> \(x+z=y\). As x, y, and z are negative integers then y is "most" negative, the least of 3 integers.

So:
I. x > y --> is always true;
II. x > y > z --> is never true, as y is less than z too;
III. x = z --> may or may not be true, we don't know how x and z are related to each other.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-y-and-z-are-negative-integers-and-3x-3y-3z-then-99463.html
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gmatclubot
Re: If x, y, and z are negative integers and 3x - 3y = -3z, then [#permalink]
02 Jan 2017, 05:07
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