Problem Solving

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


OA Later.... first some discussions..

Post official answer please....

Hi,
3x - 3y = -3z => x+z = y
As, x,y,z are negative. y should be smaller than x and z.
eg: if x = -2, z=-3, y = -5.
The relation between x and z cannot be established though.
y<x and y<z

Hence, B

3x - 3y = -3z

simplify the equation first to ->> x - y = -z -->

x = -z + y ..... since the integers are negative....lets see what it would look like in real....x(-1) = -z(-1) + y(-1)

-x = z - y

x = -z + y <---- equation withouting worrying about plugging in negative numbers now.


Clearly here y > x, hence A,B is out

If the above is false, then so is D.

We are left with C and E.

C is also false because x does not = z.

IMO E

Let me know if I went wrong some where....

Yes Frank is right.. The answer is B.

@ Frank

Where did I go wrong?

Gurpinder wrote:@ Frank

Where did I go wrong?

Hi,
-x = z - y

x = -z + y <---- equation withouting worrying about plugging in negative numbers now.

Clearly here y > x, hence A,B is out
-z is positive. So, when you add a positive quantity(-z) to a negative quantity(y), the resulting number(x) will increase. So, x > y
eg. -2 = 3 + (-5). Here x = -2, z= -3, y =-5

Well this is NOT so confusing, did it in 60sec, apply it this way

3x -3y = -3z
x - y = -z
x + z = y .... This is the equation we need to evaluate.

Since all are -ve, y will always be more -ve than x and hence x > y
from equation you can easily say that II & III are not essentially true.
Bingo!! Answer is B.

Frankenstein wrote:

Gurpinder wrote:@ Frank

Where did I go wrong?

Hi,
-x = z - y

x = -z + y <---- equation withouting worrying about plugging in negative numbers now.

Clearly here y > x, hence A,B is out
-z is positive. So, when you add a positive quantity(-z) to a negative quantity(y), the resulting number(x) will increase. So, x > y
eg. -2 = 3 + (-5). Here x = -2, z= -3, y =-5

Ahh...I confused my self....

yes, y=x+z and since they are negative, x>y

thanks buddy!