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

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Senior Manager
Joined: 30 Nov 2008
Posts: 405
Schools: Fuqua
Robots X, Y, and Z each assemble components at their  [#permalink]

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31 Mar 2009, 17:00
3
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25% (medium)

Question Stats:

75% (01:44) correct 25% (01:48) wrong based on 519 sessions

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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) $$r_y < 1$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/robots-x-y-an ... 39477.html
Math Expert
Joined: 02 Sep 2009
Posts: 59712
Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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04 Jan 2011, 03:33
4
1
ajit257 wrote:
see attachment

Can some explain the reasoning behind this ques.

Robots X, Y, and Z each assemble components at their respective constant rates. If rx is the ratio of robot X's constant rate to robot Z's constant rate and ry 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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##### General Discussion
Manager
Joined: 13 Aug 2010
Posts: 116
Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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03 Jan 2011, 21:26
1
We need both the information if the constant rate for Z is greater or not.
1. says that constant rate of Y is greater than X. x/z < x/y
2. says that constant rate of Y is smaller than Z. y/z <1

so we need both the information.
Manager
Joined: 19 Aug 2006
Posts: 157
Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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31 Mar 2009, 19:03
stmnt 1 - not suffic.
a<b => x/z < y/z => x< y

stmnt 2 - b<1 - not suffic.

let's combine - b<1 => a<b and a<1
still not sufficient, z could be >,= or < than a and/or b, and it would still satisfy stmnt 1 and 2.

I think it's E.
Intern
Joined: 30 Oct 2008
Posts: 24
Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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01 Apr 2009, 01:18
for 1 and 2
a < b < 1
x/z < y/z < 1
denominator z is greater than numerator. Hence C is answer.
Director
Joined: 04 Jan 2008
Posts: 608
Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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01 Apr 2009, 02:27
I think E
Lets take V as Robot Z's constant rate

is Robot Z's constant rate the greatest of the three?

X:Y:Z=Va:Vb:V
now to have V highest we need to know whether V is <0 or >0
V could be 2 or say, 1/2
it changes the whole picture

Robots X, Y, and Z each assemble components in their respective constant rates. If a is the ration of Robot X's constant rate to Robot Z's constant rate and b 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) a < b
2) b < 1
Current Student
Joined: 13 Jan 2009
Posts: 251
Location: India
Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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01 Apr 2009, 16:39
My take is C

X:Z=a; Y:Z=b
that means Z is bigger than Y.

1 says a<b so again Z is bigger than X.

Lets solve it by statements

Y= bZ Y is b times faster than Z if b is less than 1 then Z is faster on the similar note A can deduced.

@A Nitya .... Picture will not change as long as V is greater zero and V can not be negative as rate will always be positive.
Manager
Joined: 19 Aug 2006
Posts: 157
Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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01 Apr 2009, 18:03
hemantsood wrote:
My take is C

X:Z=a; Y:Z=b
that means Z is bigger than Y.

1 says a<b so again Z is bigger than X.

Lets solve it by statements

Y= bZ Y is b times faster than Z if b is less than 1 then Z is faster on the similar note A can deduced.

@A Nitya .... Picture will not change as long as V is greater zero and V can not be negative as rate will always be positive.

I think you reasoning is correct, the answer should be C, not E.
Math Expert
Joined: 02 Sep 2009
Posts: 59712
Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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31 Aug 2015, 07:47
mrsmarthi wrote:
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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) $$r_y < 1$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: robots-x-y-and-z-each-assemble-components-at-their-respect-139477.html
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Re: Robots X, Y, and Z each assemble components at their  [#permalink]

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25 Feb 2017, 16:16
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Re: Robots X, Y, and Z each assemble components at their   [#permalink] 25 Feb 2017, 16:16
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