Negative Ratios

Question

Can you have negative in ratios 
eg : A : B = 2 : -4

can we extend this to A : B : C = 1 : -3 : - 4 is this possible

is there a rule for using negative ratios

thanks

l0rrie · Answer

Hmm interesting.. I didnt see it anywhere though.. Where did you see this?

KarishmaB · Answer

The following is what I think:

Ratios tell you how big the numbers are with respect to each other when they are both positive. They generally measure real quantities so the negatives don't arise. Let me give an example.

A owes the bank $2 million.
B owes the bank $1 million.

A's debt : B's debt = 2:1 which makes sense

Assuming no assets,
A's net worth : B's net worth = -2 : - 1 = 2:1 (multiplying both by -1)
Is A's net worth twice of B's net worth? Certainly not. A has more debt.

So ratios are used only when both the numbers are positive.

deeuk · Answer

sorry, I dint get the conclusion of the last part.So -ve numbers' ratio does not exist?
In ' The ratio of x to y is 7/9', should I not consider x = -7 and y=-9 too ?
Thanks in advance

Bunuel · Answer

Technically if we are told that the ratio of x to y is 7/9, then x = - 7 and y = -9 are indeed possible values but  on the GMAT, ratios always only involve positive quantities . If the question wants to allow for negative values of x and y, the word  ratio  would not be used in the question at all, but instead it would be said that the value of the fraction x/y is 7/9.

Hope it helps.

deeuk · Answer

Thank you sir/ma'm.. But the reason I looked up negative ratios is because of the solution to the 6th of the seven samurai questions of Fractions/Ratios/Decimals. The question goes like this
Is x < y ?
(1) The ratio of x to y is 7/9.
(2) xy>0
Thanks again

Bunuel · Answer

The answer to this question is E (discussed here: is-x-y-127437.html) because x=7 and y=9 as well as x=-7 and y=-9 satisfy the statements.

But again, though technically, this question is OK, the GMAT still would put the first statement as "the value of x/y is 7/9".

Anyway, the takeaway is that the real question would not use the word ratio for quantities which are not positive.

deeuk · Answer

GMAT- ratio quantities are positive, UNLESS they are expressed as a fraction. Got it.

MvArrow · Answer

Dear Bunuel,
In answering this question I picked up A just because of the word RATIO; in fact I supposed that as we are considering a ratio it is not possible to have a negative multiplier.
So you are basically telling me that my approach is correct and the question is a little bit flawed right?

Thanks a lot!

Negative Ratios

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