General ratio related questions

[JbhB682]

Hi

Just wanted to confirm the following on ratio's

1) if the ratio of x : y: z is 5 : - 3 : 4

Can the ratio be re-written as === -5 : 3 : -4 as well (the negative signs are now on x and z instead)

2) In order to determine the ratio of x : y : z
Ratio of X / Y and X / Z is NOT ENOUGH -- i need the ratio of Y / Z separately

[Sage Pearce-Higgins]

1) Yes, we can multiply a ratio by a "multiplier", so that the ratio 1:2 is equal to the ratio 5:10 (i.e. the "multiplier" is 5). I've never seen a case in a GMAT problem in which the multiplier is negative, but I guess it could be. Come to think of it, I've never seen a ratio in GMAT with a negative number at all. Do you have a problem in mind?

2) No. If you know the ratio x:y and the ratio x:z, you can calculate the ratio y:z. To take an example, if x:y is 1:3 and x:z is 1:4, then the ratio x:y:z is 1:3:4 and the ratio y:z is 3:4. Algebraically, if you know x/y and you know x/z, then you can simply divide the latter by the former and simplify to get y/z (try it).