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Last edited by Bunuel on 20 Oct 2012, 04:56, edited 1 time in total.

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)

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.

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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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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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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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:

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