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Robots X, Y, and Z each assemble components at their [#permalink]

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03 Jan 2011, 18:30

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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?

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.

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?

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. _________________

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

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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,

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.
_________________

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

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03 Nov 2013, 12:06

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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!

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

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19 Sep 2015, 22:35

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

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01 Aug 2016, 02:23

ajit257 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?

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

Can some explain the reasoning behind this ques.

Fist of all we need to remember that rate can never be negative. this makes the question super easy to deal

(1) \(r_x<r_y\)

meaning

\(\frac{x}{z}<\frac{y}{z}\) {since neither x,y,z are rates and rate cannot be negative; therefore we can remove z from both side it easily without worrying about the sign}

so

\(x<y\)

NO info about z

INSUFFICINET

(2) \(r_y<1\)

meaning\(\frac{y}{z}\) is less than 1

No info about rate of x or rate of z

INSUFFICIENT

merge both statements

\(\frac{x}{z}<\frac{y}{z}<1\)

multiply each term with z

\(z*\frac{x}{z}<z*\frac{y}{z}<z*1\)

x<y<z

Therefore Z is greatest

SUFFICIENT ANSWER IS C
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016.

gmatclubot

Re: Robots X, Y, and Z each assemble components at their
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01 Aug 2016, 02:23

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