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

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Robots X, Y, and Z each assemble components at their respect [#permalink]  24 Sep 2012, 04:16
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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) $$r_y<1$$

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

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Re: Robots X, Y, and Z each assemble components at their respect [#permalink]  24 Sep 2012, 07:23
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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, 10:40
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rx = x/z and ry= y/z

1) x/z < y/z then zx < zy simplify x < y not sufficient we do not know about z

2) y/z < 1 y < z idem as 1)

1) + 2) in thew chain x < y < z ----> Z is the greatest of the 3 SUFFICIENT

Note: we can cross-multiply because we know that the rate must be positive; so we know the sign.

Good question
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Last edited by carcass on 28 Sep 2012, 05:16, edited 1 time in total.
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Re: Robots X, Y, and Z each assemble components at their respect [#permalink]  24 Sep 2012, 04:38
1) Insufficient
2) Insufficient
Both - Sufficient

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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.

Hence, both statements are required.

C
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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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: Robots X, Y, and Z each assemble components at their respect [#permalink]  23 Jun 2014, 23:35
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Re: Robots X, Y, and Z each assemble components at their respect [#permalink]  06 Oct 2014, 11:34
I took ratios for robots X, Y, Z - 1/x, 1/y and 1/z respectively.
1/y : 1/z = 1/y*z/1 = z/y
and if Ry<1 then Z is less then Y...
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Robots X, Y, and Z each assemble components at their respect [#permalink]  10 Oct 2014, 10:27
mvictor wrote:
I took ratios for robots X, Y, Z - 1/x, 1/y and 1/z respectively.
1/y : 1/z = 1/y*z/1 = z/y
and if Ry<1 then Z is less then Y...

No its alright to do so

let the rates be 1/x for X, 1/y for Y and 1/z for Z
so Rx= 1/x/1/z = z/x
and similarly
Ry= 1/y/1/z = z/y

statement 1 --> Rx<Ry
--> z/x<z/y
--> x>y (since z is constant for example z=1 , x=4 and y= 2 --> Rx<Ry --> x>y)
Nothing is said about z here so insufficient

statement 2 --> Ry<1
--> z/y<1
--> z<y (cross multiply, its okay to do so here as rates cannot be negative )

statement 1 & 2 together

z<y<x is z the greatest? clearly not

Hope it helps, if it does a Kudos will be great. Cheers!!
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Kudos [?]: 10 [0], given: 19

Re: Robots X, Y, and Z each assemble components at their respect [#permalink]  10 Oct 2014, 10:30
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.

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

Hi Bunuel,

Could you kindly check my approach?

Thanks

let the rates be 1/x for X, 1/y for Y and 1/z for Z
so Rx= 1/x/1/z = z/x
and similarly
Ry= 1/y/1/z = z/y

statement 1 --> Rx<Ry
--> z/x<z/y
--> x>y (since z is constant for example z=1 , x=4 and y= 2 --> Rx<Ry --> x>y)
Nothing is said about z here so insufficient

statement 2 --> Ry<1
--> z/y<1
--> z<y (cross multiply, its okay to do so here as rates cannot be negative )

statement 1 & 2 together

z<y<x is z the greatest? clearly not

Re: Robots X, Y, and Z each assemble components at their respect   [#permalink] 10 Oct 2014, 10:30
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