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

Simple Question got it wrong because i thought of magnitude and forgot about the signs....!!!!
Sill Mistakes when will I Improve....

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.

Thanks Karishma. I agree with you, I did use the numbers to confirm the solution.

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.

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!

Answer: I only

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