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What is the ratio x : y: z ?
(1) x + y = 2 z
(2) 2x + 3y = z
(1) x + y = 2 z
(2) 2x + 3y = z
Hi all,
I read here:
https://www.manhattangmat.com/errata-fdp-5ed.cfm
about 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
I read here:
https://www.manhattangmat.com/errata-fdp-5ed.cfm
about 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
10 Jan 2014, 03:17
Kudos
Bookmarks
Ric123
What is the ratio x : y: z ?
(1) x + y = 2 z
(2) 2x + 3y = z
(1) x + y = 2 z
(2) 2x + 3y = z
Hi all,
I read here:
https://www.manhattangmat.com/errata-fdp-5ed.cfm
about 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
I read here:
https://www.manhattangmat.com/errata-fdp-5ed.cfm
about 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
We need xyz>0 condition to know that neither of the variables is 0. Notice that x=y=z=0, satisfy both statements and in this case x:y:z is undefined and not 5 : -3 : 1.
Hope it's clear.
P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules 2, 3, 7, and 10. Thank you.
General Discussion
10 Jan 2014, 05:48
Kudos
Bookmarks
[quote="Ric123"]What is the ratio x : y: z ?
(1) x + y = 2 z
(2) 2x + 3y = z
Statement I is insufficient:
x = 1, y = 1, z = 1
x = 3, y = 5, z = 4
Statement II is insufficient using the same concept as the first one
Combining is insufficient
x + y = 2z
4x + 6y = 2z
4x + 6y = x + y
3x = -5y
x = 5, y = -3, z = 1
x = 0, y = 0 z = 0
Hence E
(1) x + y = 2 z
(2) 2x + 3y = z
Statement I is insufficient:
x = 1, y = 1, z = 1
x = 3, y = 5, z = 4
Statement II is insufficient using the same concept as the first one
Combining is insufficient
x + y = 2z
4x + 6y = 2z
4x + 6y = x + y
3x = -5y
x = 5, y = -3, z = 1
x = 0, y = 0 z = 0
Hence E
