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Robots X, Y, and Z each assemble components at their respect [#permalink]
24 Sep 2012, 04:16

Expert's post

00:00

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Difficulty:

25% (low)

Question Stats:

69% (02:23) correct
30% (01:23) wrong based on 103 sessions

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

Practice Questions Question: 47 Page: 279 Difficulty: 600

Re: Robots X, Y, and Z each assemble components at their respect [#permalink]
24 Sep 2012, 04:16

3

This post received KUDOS

Expert's post

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.

Re: Robots X, Y, and Z each assemble components at their respect [#permalink]
24 Sep 2012, 07:23

1

This post received KUDOS

Robots X, Y, and Z each assemble components at their respective constant rates. If is the ratio of Robot X's constant rate to Robot Z's constant rate and 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) INSUFF X/z < Y/z this does not allow us to pin point anything to do with z (2) INSUFF y/z<1 again, not enough, y could make 1 an hour and z could make 2 an hour or 2,000 per hour. However, we don't know anything about X Together, SUFF X/z < y/z < 1 We know that z is faster than Y and we know that Y is faster than X - the question is true
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Re: Robots X, Y, and Z each assemble components at their respect [#permalink]
24 Sep 2012, 08:02

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?

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

(1) Since r_x and r_y are RATIO of rates of X and Y wrt to Z respectively, if we compare these two the rate of Z will cancel out from both sides and we will be left with X < Y. Nothing is know about Z. Not sufficient

(2) Here, ration of rate of Y to Z is lesser than 1. Thus Y < Z. Nothing is known about X. So not sufficient.

combining (1) and (2), X < Y < Z, Z has greatest rate.

Re: Robots X, Y, and Z each assemble components at their respect [#permalink]
28 Sep 2012, 04:12

Expert's post

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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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