qlx wrote:
Ric123 wrote:
What is the ratio x : y: z ?
(1) x + y = 2 z
(2) 2x + 3y = z
Hi all,
I read here:
http://www.manhattangmat.com/errata-fdp-5ed.cfmabout some mistakes in the guide of
Manhattan GMAT FDPs, 5th edition.
I focused my attention on the third one: "The answer to the question as written is (E). The question should stipulate that xyz > 0".
This was the DS exercise:
Solution:
(1) INSUFFICIENT, because if you try to isolate x/y you get a variable expression.
(2) the same
(1)+(2) SUFFICIENT:
x + y = 2z &
2x+ 3y = z so
x+ y = 2(2*+ 3y)
x + y = 4x + 6y and finally you get
x/y = 5/(-3)
You can do the same to get y/z = -3
So you have x : y = -5/3 & y / z =-3/1 -> x : y : z = 5 : -3 : 1
Now, saying x:y = 1:2 or 2:4 is the same.
In the same way, I can say x:y=1:2 or -1:-2.
So, given x : y : z = 5 : -3 : 1 we may have two variables positive and one negative, or two negative and one positive, but that doesn't matter, because we are interested in the ratio (that, if wholly multiplied by -1, doesn't change its meaning).
In the Errata from the link I've posted,
Manhattan GMAT team says that we must specify xyz > 0 , that means we must specify that we want the two-variables-positive-and-one-negative case. But I believe is not necessary; in fact we do not care about the single variables, but about their ratio.
In conclusion I think that the answer to this DS is C even without the condition xyz > 0.
Someone can confirm me this?
Thank you.
Ric
Hey Ric,
Can anyone tell me why
MGMAT chose to go with xyz>0 instead of \(xyz\neq0\)
Could \(xyx\neq0\)lead to answer being C or E ?
Hi qlx,
As I wrote in the original post saying x:y=1:2 or x:y=-1:-2 is the same.
So, stated x : y : z = 5 : -3 : 1, we know that the sign of y is different from the sign of x and z, but we do not know whether we have one positive variable and two negative ones, or the opposite. However, we do not need that information, because it does not impact the value of the ratio.
xyz>0 tells us also that we are in the first case (two negative variables and one positive), but we didn't need to know that information to find the ratio. As Bunuel specified, we need to know only that none of them is zero. Note that xyz<0 would tell us that none of the variables is zero, and that one of them is negative (must be y).
I think that xyz different from zero is enough to define the required ratio, leading to C answer, even if we can't say the signs of the three variables.