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Each type A machine fills 400 cans per minute,each Type B machine fill

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

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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

OG Q 2017(Book Question: 236)
[Reveal] Spoiler: OA

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

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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

OG Q 2017(Book Question: 236)



(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.

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

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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

OG Q 2017(Book Question: 236)


(1) A total of 4,800 cans are filled that minute

That means 2 machine C are working.

To produce 4800 cans, we can have different combinations of Machine A and B working.

Not sufficient.

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

So if 1 Machine C is working, 2 Machine B are working. But we dont know how many machine A are working.

Not Sufficient.

Combining both statements, we know that in a minute we are producing 4800 cans or lids. So 2 Machine C are working.

If 2 machine C are working, 4 Machine B are working (4 Machine B produce 2400 cans). Remaining 2400 cans are produced by 6 Machine A.

So total 12 machines are working. Sufficient.

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

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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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New post 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

OG Q 2017(Book Question: 236)


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.

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

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New post 26 Jan 2017, 07:20
(1) 400A + 600B = 4800

Now if B = 6, A = 3;
Again if B = 4, A = 6; Hence Insufficient.

(2) 400A + 600B = 2400C
if C = 1, B = 2; Therefore A = 3;
but if C = 2, B = 4, A = 6; Hence Insufficient.

(1) & (2) together: 400A + 600B = 4800
C = 2; Therefore B = 4 and A = 6; Hence Sufficient.

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

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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

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

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New post 06 Feb 2017, 19:07
Bunuel

Sir can you please confirm my solution?

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.

Kindly confirm. Thank you.

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

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New post 09 Apr 2017, 16:51
I took the same thought process as fischingforanswers.

How do we know for certain that there are 2 Type C Machines?

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

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

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New post 18 Nov 2017, 10:16
Answered it correctly simply on the logic that knowing both 1 and 2 we must arrive at some solutions anyway, is it flawed logic?

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Re: Each type A machine fills 400 cans per minute,each Type B machine fill   [#permalink] 18 Nov 2017, 10:16
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