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# What is the ratio x : y: z ?

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Intern
Joined: 25 Nov 2013
Posts: 14
Location: Italy
GMAT 1: 720 Q49 V38
What is the ratio x : y: z ? [#permalink]

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Updated on: 10 Jan 2014, 03:14
4
13
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Difficulty:

95% (hard)

Question Stats:

39% (01:01) correct 61% (01:09) wrong based on 273 sessions

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What is the ratio x : y: z ?

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

Hi all,

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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Posts: 47064
Re: What is the ratio x : y: z ? [#permalink]

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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,

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.

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Joined: 20 Dec 2013
Posts: 123
Re: What is the ratio x : y: z ? [#permalink]

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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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Intern
Joined: 25 Nov 2013
Posts: 14
Location: Italy
GMAT 1: 720 Q49 V38
Re: What is the ratio x : y: z ? [#permalink]

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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,

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.

Thank you, now it is clear.
Manager
Joined: 17 Mar 2014
Posts: 68
Re: What is the ratio x : y: z ? [#permalink]

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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,

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 ?
Intern
Joined: 25 Nov 2013
Posts: 14
Location: Italy
GMAT 1: 720 Q49 V38
What is the ratio x : y: z ? [#permalink]

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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,

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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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.
Thanks
Celestial
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Posts: 1248
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
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What is the ratio x : y: z ? [#permalink]

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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.
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.

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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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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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

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 ?   [#permalink] 13 Jun 2018, 07:34
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