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

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Manager
Joined: 20 Nov 2009
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If x, y, and z are negative integers and 3x - 3y = -3z, then  [#permalink]

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Updated on: 20 Oct 2012, 04:56
7
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65% (hard)

Question Stats:

55% (01:53) correct 45% (01:56) wrong based on 369 sessions

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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

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Originally posted by aiming4mba on 19 Aug 2010, 23:50.
Last edited by Bunuel on 20 Oct 2012, 04:56, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 20 Feb 2009
Posts: 64
Location: chennai

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20 Aug 2010, 01:51
2
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

From the question: we infer that x-y = -z
x,y&z are negative integers .
ex: x= -4
y= -6
-4 - (-6) = -(-2). this implies x>y
here x is not equql to z (III)
z>y (II)

So (I) will be answer , SO option B)
Math Expert
Joined: 02 Sep 2009
Posts: 49968

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20 Aug 2010, 07:03
4
aiming4mba 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.

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Manager
Joined: 20 Apr 2010
Posts: 218
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21 Aug 2010, 15:55
Simple Question got it wrong because i thought of magnitude and forgot about the signs....!!!!
Sill Mistakes when will I Improve....
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15 Nov 2010, 17:34
1
3x - 3y = -3z

x-y=-z =>y=x+z

Since y=x+z, and x, y, and z are –ve integers, x and z should be greater than y. Also, it’s not mandatory that x=z
So, the answer is a) Only I
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Joined: 16 Oct 2010
Posts: 8386
Location: Pune, India

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15 Nov 2010, 20:53
1
lotus wrote:
3x - 3y = -3z

x-y=-z =>y=x+z

Since y=x+z, and x, y, and z are –ve integers, x and z should be greater than y. Also, it’s not mandatory that x=z
So, the answer is a) Only I

Your solution is great lotus. I just want to add here that when you arrive at y=x+z, and you want to find out what this relation means considering that all x, y and z are negative, take some numbers:
x = -3, z = -4, then y = -7. So this means that y is going to be smaller than both x and z. Also, x and z may or may not be the same number. Taking numbers at this stage will help you to clearly see the solution. Remember, you are not arriving at the answer using numbers (which can be useful sometimes but should be generally avoided). You are just making a clear picture in your mind.
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Intern
Joined: 02 Jul 2009
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16 Nov 2010, 14:02
Thanks Karishma. I agree with you, I did use the numbers to confirm the solution.
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Joined: 06 Nov 2010
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16 Nov 2010, 17:10
3x-3y=-3z

Dividing by -3 gives:

y-x=z

Having this in hand, I created a number line to visually identify the characteristics of each number when you subract one from the other to get a third:

+-----Y---------X-------0-----------+
--------<--Z--->

or:

+-----X---------Y-------0-----------+
--------<--Z--->

Is y greater than x or vice versa? Pick numbers to see. Start with what if y is less than x, e.g. y=-2 and x=-1.

y-x=(-2)-(-1) =-1.

We know z is negative, so this must be true. Thus, y is less than (to the left of) x.

Looking at the number line, can we learn anything else about z? Not really, since z could be anything, i.e. the numberline could look like this:

+-----Y---------X-------0-----------+
--------<--Z--->

or like this:

+-----Y-------------------------X-0-----------+
--------<----------Z----------->

Thus, we don't know anything at all about z.

Answer B is the only possible choice.
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If x, y, and z are negative integers and 3x - 3y = -3z, then whi  [#permalink]

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13 Dec 2012, 00:56
1
3x - 3y = -3z
x - y = -z
z = y - x where z < 0 thus, y-x<0 ==> y<x

I. x > y ALWAYS TRUE!

Let y=-3 and x=-2 then z=-1

II. -2 > -3 > -1 FALSE!
III. -2 = -1 FALSE!

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Re: If x, y, and z are negative integers and 3x - 3y = -3z, then  [#permalink]

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23 Sep 2017, 07:33
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Re: If x, y, and z are negative integers and 3x - 3y = -3z, then &nbs [#permalink] 23 Sep 2017, 07:33
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