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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] New post 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] New post 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.

Answer: C.
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Re: Robots X, Y, and Z each assemble components at their respect [#permalink] New post 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] New post 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.

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Re: Robots X, Y, and Z each assemble components at their respect [#permalink] New post 24 Sep 2012, 04:38
1) Insufficient
2) Insufficient
Both - Sufficient

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

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Robots X, Y, and Z each assemble components at their respect [#permalink] New post 23 Jun 2014, 23:35
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Re: Robots X, Y, and Z each assemble components at their respect [#permalink] New post 06 Oct 2014, 11:34
I took ratios for robots X, Y, Z - 1/x, 1/y and 1/z respectively.
therefore I made a mistake, and answered B since
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] New post 10 Oct 2014, 10:27
mvictor wrote:
I took ratios for robots X, Y, Z - 1/x, 1/y and 1/z respectively.
therefore I made a mistake, and answered B since
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
Here's something that will help you

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 :) )
nothing about x so insufficient

statement 1 & 2 together

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

so answer is C

Hope it helps, if it does a Kudos will be great. Cheers!!
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Re: Robots X, Y, and Z each assemble components at their respect [#permalink] New post 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.

Answer: C.

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 :) )
nothing about x so insufficient

statement 1 & 2 together

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

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