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# Robots K, L and M assemble components at their respective constant res

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Intern
Joined: 24 Mar 2018
Posts: 7
Robots K, L and M assemble components at their respective constant res  [#permalink]

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24 Mar 2018, 07:37
7
00:00

Difficulty:

95% (hard)

Question Stats:

23% (02:48) correct 77% (02:07) wrong based on 96 sessions

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Robots K, L and M assemble components at their respective constant rates. Does robot L have the greatest constant rate of assembling among the three robots?

(1) The ratio of the constant rates of assembling of K and L is not more than that of L and M.
(2) The ratio of the constant rates of assembling K and L is not less than that of L and M.

Source: TIME (Computer Based Tests Series)
Manager
Joined: 30 Mar 2017
Posts: 123
GMAT 1: 200 Q1 V1
Robots K, L and M assemble components at their respective constant res  [#permalink]

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Updated on: 25 Mar 2018, 05:02
1
Statement 1

$$\frac{K}{L}<=\frac{L}{M}$$
$$KM<=L^2$$

We can have K=1, M=2, L=3, which makes L the greatest and the answer to the question is YES.
We can have K=1/4, M=4, L=1, which does not make L the greatest and the answer to the question is NO.
Not sufficient.

Statement 2

$$\frac{K}{L}>=\frac{L}{M}$$
$$KM>=L^2$$

L cant be greater than the greater of (K,M). E.g. if K=3 and M=6, then L cant be greater than 6 and answer to the question is NO.
Sufficient.

Originally posted by aserghe1 on 24 Mar 2018, 16:58.
Last edited by aserghe1 on 25 Mar 2018, 05:02, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 59087
Re: Robots K, L and M assemble components at their respective constant res  [#permalink]

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25 Mar 2018, 01:07
hetmavani wrote:
Robots K, L and M assemble components at their respective constant rates. Does robot L have the greatest constant rate of assembling among the three robots?

(1) The ratio of the constant rates of assembling of K and L is not more than that of L and M.
(2) The ratio of the constant rates of assembling K and L is not less than that of L and M.

Source: TIME (Computer Based Tests Series)

Similar question frop OG: https://gmatclub.com/forum/robots-x-y-a ... 39477.html
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Director
Joined: 27 May 2012
Posts: 936
Re: Robots K, L and M assemble components at their respective constant res  [#permalink]

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19 Jun 2019, 08:48
hetmavani wrote:
Robots K, L and M assemble components at their respective constant rates. Does robot L have the greatest constant rate of assembling among the three robots?

(1) The ratio of the constant rates of assembling of K and L is not more than that of L and M.
(2) The ratio of the constant rates of assembling K and L is not less than that of L and M.

Source: TIME (Computer Based Tests Series)

Let K be the number of hours it takes by K to complete the Job, similarly let L and M be the hours taken by L and M respectively.
So rate of K is 1/k , rate of L = 1/L and rate of M is 1/M

1)ratio of rates of K and L is <= ratio of rates L and M
(1/k)/(1/L) <= (1/L)(1/M)
L/K <= M/L
L^2 <= MK

2)ratio of rates rate of K and L is >=ratio of rates of L and M
(1/K)/(1/L) >=(1/L)(1/M)
L/K >= M/L
L^2 >= MK

Here the answer depends on how we choose the rate. No where in the question does it say that K, L and M are the respective rates of the robots. If it did, then the answer would be B. On the other hand if K , L and M are the number of hours taken by the respective robots to finish the job, then answer would be A.

The similar question given by Bunuel above is a better version of this question and does not offer such ambiguity.

P.S. Please feel free to let me know if I missed anything.Thank you.
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Re: Robots K, L and M assemble components at their respective constant res   [#permalink] 19 Jun 2019, 08:48
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