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What is the ratio x : y: z ?

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What is the ratio x : y: z ?  [#permalink]

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New post Updated on: 10 Jan 2014, 03:14
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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.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

Originally posted by Ric123 on 09 Jan 2014, 21:57.
Last edited by Bunuel on 10 Jan 2014, 03:14, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: What is the ratio x : y: z ?  [#permalink]

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New post 10 Jan 2014, 03:17
2
1
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.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.
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Re: What is the ratio x : y: z ?  [#permalink]

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New post 10 Jan 2014, 05:48
1
1
[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
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Re: What is the ratio x : y: z ?  [#permalink]

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New post 11 Jan 2014, 00:17
1
Bunuel 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.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.


Thank you, now it is clear.
I read the rules, and I will follow them from now.
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Re: What is the ratio x : y: z ?  [#permalink]

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New post 28 Jun 2014, 00:14
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.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


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 ?
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What is the ratio x : y: z ?  [#permalink]

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New post 21 Aug 2014, 09:40
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.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


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.
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Re: What is the ratio x : y: z ?  [#permalink]

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New post 02 May 2015, 13:43
Hi,
I straight away went to C Or E.
in ext 5 seconds I sensed that 3 unknown, and two equations
so came to E directly.
Its a fluke that answer was correct.
Please evaluate my approach.
Thanks
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What is the ratio x : y: z ?  [#permalink]

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New post 02 May 2015, 14:53
Celestial09 wrote:
Hi,
I straight away went to C Or E.
in ext 5 seconds I sensed that 3 unknown, and two equations
so came to E directly.
Its a fluke that answer was correct.
Please evaluate my approach.
Thanks
Celestial


Hello Celestial09
When you need to find exact values of these unknowns then it definetely E and your approach right.

But in our case you should find only ratios and this is C.
There is possible another trick when task asks about sum of two unknowns and sometimes it's possible to find even when we have three unknowns and two equations.
In this types of tasks your approach is a pitfall.

P.S. as was already said in this case was a typo about signs of this unknowns and this transform answer to the E
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Re: What is the ratio x : y: z ?  [#permalink]

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New post 14 Feb 2017, 13:24
People, is adding, subtracting the equations the right approach here? Isn't it used to find exact values for variables? Eliminate one var. and discover the other, plug in, solve, fine. But here we don't want exact values, so why are you manipulating the equations like this?..

Do I make myself clear? Thanks!
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Re: What is the ratio x : y: z ?  [#permalink]

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New post 13 Jun 2018, 07:34
niks18 gmatbusters pushpitkc amanvermagmat

Quote:
What is the ratio x : y: z ?

(1) x + y = 2 z
(2) 2x + 3y = z


How about this approach?
We have three unique linear equations to solve for x,y and z.
Since we do not have third eq, clearly (E).
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Re: What is the ratio x : y: z ? &nbs [#permalink] 13 Jun 2018, 07:34
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