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# If machine J, working alone at its constant rate, takes 2 minutes to

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Math Expert
Joined: 02 Sep 2009
Posts: 50621
If machine J, working alone at its constant rate, takes 2 minutes to  [#permalink]

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08 Jul 2018, 22:20
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:04) correct 20% (00:57) wrong based on 111 sessions

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If machine J, working alone at its constant rate, takes 2 minutes to wrap 60 pieces of candy, how many minutes does it take machine K, working alone at its constant rate, to wrap 120 pieces of candy?

(1) Machine K, working alone at its constant rate, takes more than 5 minutes to wrap 60 pieces of candy.

(2) Machines J and K, working together at their respective constant rates, take 1 minute and 30 seconds to wrap 60 pieces of candy.

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If machine J, working alone at its constant rate, takes 2 minutes to  [#permalink]

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08 Jul 2018, 22:30

Solution

Given:
• Machine J, working alone at its constant rate, takes 2 minutes to wrap 60 pieces of candy

To find:
• The time machine K will take, working alone at its constant rate, to wrap 120 pieces of candy

Analysing Statement 1
• As per the information given in statement 1, machine K, working alone at its constant rate, takes more than 5 minutes to wrap 60 pieces of candy
• More than 5 minutes gives us infinite number of possibilities, and hence, does not help us in getting any specific information

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information given in statement 2, machines J and K, working together at their respective constant rates, take 1 minute and 30 seconds to wrap 60 pieces of candy
o We know the combined efficiency of J and K as well as the individual efficiency of J
o Therefore, we can find out the individual efficiency of K also

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option B.

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Re: If machine J, working alone at its constant rate, takes 2 minutes to  [#permalink]

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23 Sep 2018, 08:15
1
Bunuel wrote:
If machine J, working alone at its constant rate, takes 2 minutes to wrap 60 pieces of candy, how many minutes does it take machine K, working alone at its constant rate, to wrap 120 pieces of candy?

(1) Machine K, working alone at its constant rate, takes more than 5 minutes to wrap 60 pieces of candy.

(2) Machines J and K, working together at their respective constant rates, take 1 minute and 30 seconds to wrap 60 pieces of candy.

$$J\,\,\, - \,\,\,60\,\,{\text{candies}}\,\,\, - \,\,\,2\,\,{\text{min}}$$

$$K\,\,\, - \,\,60\,\,{\text{candies}}\,\,\left( * \right)\,\,\, - \,\,\,?\,\,\min$$

$$\left( * \right)\,\,{\text{Our}}\,\,{\text{FOCUS}}\,\,{\text{is}}\,\,{\text{half}}\,\,{\text{the}}\,\,{\text{official}}\,\,{\text{one}}!$$

$$\left( 1 \right)\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,? = 5.5\min \hfill \\ \,{\text{Take}}\,\,? = 6\min \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.$$

$$\left( 2 \right)\,\,\frac{1}{{1\frac{1}{2}}} = \frac{1}{2} + \frac{1}{?}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{1}{?}\,\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,\,?\,\,\,{\text{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.$$

(This is the "work/rate shortcut".)

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: If machine J, working alone at its constant rate, takes 2 minutes to &nbs [#permalink] 23 Sep 2018, 08:15
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