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Robots X, Y, and Z each assemble components at their

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Robots X, Y, and Z each assemble components at their respective constant rates. If r(x) is the ratio of robot X's constant rate to robot Z's constant rate and r(y) is the ratio of robot Y's constant rate to robot Z's constant rate, is robot Z's constant rate the greatest of the three?

(1) \(r_x<r_y\)
(2) \(r_y<1\)

Can some explain the reasoning behind this ques.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 08 Feb 2012, 05:09, edited 1 time in total.
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Robots X, Y, and Z each assemble components at their respective constant rates. If r(x) is the ratio of robot X's constant rate to robot Z's constant rate and r(y) is the ratio of robot Y's constant rate to robot Z's constant rate, is robot Z's constant rate the greatest of the three?

Let the rates of robots X, Y, and Z be x, y, and z respectively. Given: \(r_x=\frac{x}{z}\) and \(r_y=\frac{y}{z}\). Question is \(z>x\) and \(z>y\)?

(1) \(r_x<r_y\) --> \(\frac{x}{z}<\frac{y}{z}\) --> \(x<y\). Not sufficient.

(2) \(r_y<1\) --> \(\frac{y}{z}<1\) --> \(y<z\). Not sufficient.

(1)+(2) As \(x<y\) and \(y<z\) then \(x<y<z\). Sufficient.

Answer: C.
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New post 07 May 2013, 07:09
Does this equation work when plugging in numbers, opposed to looking at pure variables?
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New post 07 May 2013, 14:10
laythesmack23 wrote:
Does this equation work when plugging in numbers, opposed to looking at pure variables?


Sure. Lets say the rates are X = 5, Y = 6 and Z = 7.

Y/Z = 6/7 -> as stated in II

X/Y = 5/6 and Y/Z = 6/7 -> 5/6< 6/7 as stated in I


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Re: Robots X, Y, and Z each assemble [#permalink]

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New post 22 Oct 2013, 08:00
Bunuel wrote:
Robots X, Y, and Z each assemble components at their respective constant rates. If r(x) is the ratio of robot X's constant rate to robot Z's constant rate and r(y) is the ratio of robot Y's constant rate to robot Z's constant rate, is robot Z's constant rate the greatest of the three?

Let the rates of robots X, Y, and Z be x, y, and z respectively. Given: \(r_x=\frac{x}{z}\) and \(r_y=\frac{y}{z}\). Question is \(z>x\) and \(z>y\)?

(1) \(r_x<r_y\) --> \(\frac{x}{z}<\frac{y}{z}\) --> \(x<y\). Not sufficient.

(2) \(r_y<1\) --> \(\frac{y}{z}<1\) --> \(y<z\). Not sufficient.

(1)+(2) As \(x<y\) and \(y<z\) then \(x<y<z\). Sufficient.

Answer: C.


Bunuel,

Please help me clarify. The question says "Robots X, Y, and Z each assemble components at their respective constant rates. If r(x) is the ratio of robot X's constant rate to robot Z's constant rate", so if it is rates, why is X's constant rate not 1/X (which is the rate of completing one unit of work, and Z's rate would therefore be 1/Z. Thus r(x) would be 1/X : 1/Z? What am I misunderstanding here?
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Re: Robots X, Y, and Z each assemble [#permalink]

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New post 22 Oct 2013, 09:22
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bulletpoint wrote:
Bunuel wrote:
Robots X, Y, and Z each assemble components at their respective constant rates. If r(x) is the ratio of robot X's constant rate to robot Z's constant rate and r(y) is the ratio of robot Y's constant rate to robot Z's constant rate, is robot Z's constant rate the greatest of the three?

Let the rates of robots X, Y, and Z be x, y, and z respectively. Given: \(r_x=\frac{x}{z}\) and \(r_y=\frac{y}{z}\). Question is \(z>x\) and \(z>y\)?

(1) \(r_x<r_y\) --> \(\frac{x}{z}<\frac{y}{z}\) --> \(x<y\). Not sufficient.

(2) \(r_y<1\) --> \(\frac{y}{z}<1\) --> \(y<z\). Not sufficient.

(1)+(2) As \(x<y\) and \(y<z\) then \(x<y<z\). Sufficient.

Answer: C.


Bunuel,

Please help me clarify. The question says "Robots X, Y, and Z each assemble components at their respective constant rates. If r(x) is the ratio of robot X's constant rate to robot Z's constant rate", so if it is rates, why is X's constant rate not 1/X (which is the rate of completing one unit of work, and Z's rate would therefore be 1/Z. Thus r(x) would be 1/X : 1/Z? What am I misunderstanding here?


Because we denoted rates by x , y, and z: let the rates of robots X, Y, and Z be x, y, and z respectively.
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New post 03 Nov 2013, 08:25
Hello Everyone,
In OG 13, the question uses "rx" and "ry" in the question stem but "r_x (x in suffix)" and "r_y(y in suffix)".
Are these typos?
Or am I supposed to guess that rx and ry of question stem has been converted to r_x and r_y in the two given options?
TIA,
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drebellion wrote:
Hello Everyone,
In OG 13, the question uses "rx" and "ry" in the question stem but "r_x (x in suffix)" and "r_y(y in suffix)".
Are these typos?
Or am I supposed to guess that rx and ry of question stem has been converted to r_x and r_y in the two given options?
TIA,


It's a typo. x and y must be indexes in both stem and the statements.
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Thank you for your reply Bunuel.
Also thank you for pointing out the error/typo in Diagnostic Test Q 5 (Cylindrical tank contains 36PI f3 of water...)

At lest for the second question (Cylindrical Tank...) we will never know if its a typo or the guys who had this question in their real GMAT were unfortunate! :(

Thanks Anyway!
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New post 19 Jun 2016, 04:40
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Assume the individual rates be X, Y and Z respectively for the robots.
Given: X/Z = \(r_x\) and Y/Z = \(r_y\)
Required: Is Z the greatest?

Statement 1: \(r_x < r_y\)
Hence X/Z < Y/Z
Or, X < Y - (i)
We do not have any information about Z.
INSUFFICIENT

Statement 2: \(r_y < 1\)
Or Y/Z < 1
Hence Y < Z - (ii)
We do not know anything about X.
INSUFFICIENT

Combining both statements:
From (i) and (ii), we know that
X < Y and Y < Z
Hence X < Y < Z

SUFFICIENT

Correct Option: C
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Robots X, Y, and Z each assemble components at their   [#permalink] 19 Jun 2016, 04:40
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