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Each type A machine fills 400 cans per minute,each Type B machine fill [#permalink]

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24 Jun 2016, 11:36

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Each type A machine fills 400 cans per minute,each Type B machine fills 600 cans per minute,and each Type C machine installs 2,400 lids per minute.A lid is installed on each can that is filled and on no can that is not filled.For a particular minute,what is the total number of machines working?

(1) A total of 4,800 cans are filled that minute (2) For that minute,there are 2 Type B machines working for every Type C machine working

Re: Each type A machine fills 400 cans per minute,each Type B machine fill [#permalink]

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24 Jun 2016, 12:47

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AbdurRakib wrote:

Each type A machine fills 400 cans per minute,each Type B machine fills 600 cans per minute,and each Type C machine installs 2,400 lids per minute.A lid is installed on each can that is filled and on no can that is not filled.For a particular minute,what is the total number of machines working?

(1) A total of 4,800 cans are filled that minute (2) For that minute,there are 2 Type B machines working for every Type C machine working

(1) A total of 4,800 cans are filled that minute Not sufficient. There are different combinations of A and B (e.g. 12 machines A's and 0 machine B's OR 2 machine B's and 9 machine A's) that could fill 4800 cans. However, considering that a lid is to be installed on each can, we know that 2 machine C's are working.

(2) For that minute,there are 2 Type B machines working for every Type C machine working Not sufficient, this only gives us the ratio of machine B to machine C.

Combined we know that 4800 cans are filled in a minute, meaning that 2 machine C's are working and therefore (see statement 2) 4 machine B's are working. If 4 machine B's can produce 2400 cans meaning that 6 machine A's produce the remaining 2400 cans. Total number of machines are therefore, 12.

Re: Each type A machine fills 400 cans per minute,each Type B machine fill [#permalink]

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24 Jun 2016, 13:36

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AbdurRakib wrote:

Each type A machine fills 400 cans per minute,each Type B machine fills 600 cans per minute,and each Type C machine installs 2,400 lids per minute.A lid is installed on each can that is filled and on no can that is not filled.For a particular minute,what is the total number of machines working?

(1) A total of 4,800 cans are filled that minute (2) For that minute,there are 2 Type B machines working for every Type C machine working

Re: Each type A machine fills 400 cans per minute,each Type B machine fill [#permalink]

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24 Jun 2016, 19:28

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C ...

Answer choice B might tempt to use it as alone since we have the 3:2:1 ratio , but that could lead tp any number of machines , combining with A we get the exact figures
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Re: Each type A machine fills 400 cans per minute,each Type B machine fill [#permalink]

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25 Jan 2017, 19:07

AbdurRakib wrote:

Each type A machine fills 400 cans per minute,each Type B machine fills 600 cans per minute,and each Type C machine installs 2,400 lids per minute.A lid is installed on each can that is filled and on no can that is not filled.For a particular minute,what is the total number of machines working?

(1) A total of 4,800 cans are filled that minute (2) For that minute,there are 2 Type B machines working for every Type C machine working

The question indicates that "a lid is installed on each can that is filled." Isn't it possible that there are more than 2 Type C machines working, and that only 2 were utilized to fill cans? The constraint here is the amount of cans being filled, not necessarily the amount of lids that are put on the cans. I put E, but clearly I thought too much into this.

Each type A machine fills 400 cans per minute,each Type B machine fills 600 cans per minute,and each Type C machine installs 2,400 lids per minute.A lid is installed on each can that is filled and on no can that is not filled.For a particular minute,what is the total number of machines working?

(1) A total of 4,800 cans are filled that minute (2) For that minute,there are 2 Type B machines working for every Type C machine working

We are given that each Type A machine fills 400 cans per minute, each Type B machine fills 600 cans per minute, and each Type C machine installs 2,400 lids per minute.

We need to determine the total number of machines working for a particular minute. If we let a = the number of Type A machines needed, b = the number of Type B machines needed, and c = the number of Type C machines needed, we need to determine the value of a + b + c.

Statement One Alone:

A total of 4,800 cans are filled that minute.

Since a Type C machine installs 2,400 lids per minute, we know that we need 2 Type C machines (i.e., c = 2) to install 4,800 lids after the 4,800 cans are filled in that minute.

Since each Type A machine fills 400 cans per minute and each Type B machine fills 600 cans per minute, we have:

400a + 600b = 4,800

4a + 6b = 48

2a + 3b = 24

However, since we only have one equation but we have two variables, the values of a and b are not unique. For example, a = 12 and b = 0 OR a = 0 and b = 8.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

For that minute, there are 2 Type B machines working for every Type C machine working.

Thus, b/c = 2/1, i.e., b = 2c; however we still cannot determine a + b + c. Statement two alone is not sufficient.

Statements One and Two Together:

From statement one, we know that c = 2 and 2a + 3b = 24, and from statement two, we know that b = 2c. Since c = 2 and b = 2c, we see that b = 4.

Next we can substitute 4 for b in the equation 2a + 3b = 24:

2a + 3(4) = 24

2a + 12 = 24

2a = 12

a = 6

Thus a + b + c = 6 + 4 + 2 = 12. We need 12 machines for that particular minute.

Answer: C
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I opted for option C. In that minute, 4800 cans are filled. From the question I inferred that even if the producer makes more and more of Lids/minute, he fill only certain number of cans based on working rates of Machine A and B.

Trial 1 C=2. L=2*2400=4800 B=4[Given: B=2C] CansB=4*600=2400 A=Balance=2400 Cans. Therefore 2400/400=6 Machine A Total Number of Machines=2+4+6=12

Trial 2 C=3 Lids=3*2400=7200. But we need to focus on only 4800 as total Cans produced are 4800. B=2C=6 CansB=6*600=3600 A=Balance=1200 cans. So, Number of A machines=1200/400=3 Total Number of machines working=3+6+3=12

Trial 3 C=4 Lids=4*2400=9600. But we need to focus on only 4800 lids as total number of cans filled are 4800. B=2C=8 CansB=8*600=4800 A=Balance=0 No need of Machine A as we have already achieved 4800 cans filled by machine B. Total Machines=4+8=12

Trial 4 C=8 Lids=19200 B=2C=16 CansB=16*6=9600. This trial is wrong as total number of cans in that minute is exceeding 4800 as given in Statement 1.

So, based on above 3 Trials, we have 12 answer consistent for every trial. Hence, we can say that total machines employed in that hour are 12. Are my 3 trials appropriate? Or that one had to do only C=2 B=4 and A=6 trial only? I think we cannot take only this scenario as statement B says Number of Bs are double the number of Cs. It doesn't say that C=2.

Each type A machine fills 400 cans per minute,each Type B machine fill [#permalink]

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25 Apr 2017, 09:23

Though I got it rgiht, I think the wording of this question can be improved. "C machine installs 2,400 lids per minute.A lid is installed on each can that is filled and on no can that is not filled".

isn't it clearer to say: "C machine installs 2,400 lids per minute. A Lid is installed on each can that is filled." ?? "......on no can that is not filled" looks weird and not necessary.
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