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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(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.

(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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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

(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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Video Solution of the above OG Problem by GMAT Quantum

https://gmatquantum.com/2017-gmat-quant ... nt-review/

Given: 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.

Target question: For a particular minute,what is the total number of machines working?

Statement 1: A total of 4,800 cans are filled that minute
Since Machine C installs 2400 lids per second, we know that there are 2 Machine C's operating during that minute.
HOWEVER, we don't know how many Machine A's and Machine B's are working.
For example, here are two possible scenarios:
Case a: There are 12 Machine A's, 0 Machine B's and 2 Machine C's. In this case, the answer to the target question is the total number of machines working = 12 + 0 + 2 = 14
Case b: There are 0 Machine A's, 8 Machine B's and 2 Machine C's. In this case, the answer to the target question is the total number of machines working = 0 + 8 + 2 = 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: For that minute,there are 2 Type B machines working for every Type C machine working
Since we are not giving any information about how many cans are filled during the minute, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 indirectly tells us that there are 2 Machine C's operating during that minute
Statement 2 indirectly tells us that there are 4 Machine B's operating during that minute (since there are 2 Type B machines working for every Type C machine working)

In one minute, 4 Machine B's can fill 2400 cans (since each Machine B can fill 600 cans per minute)
4800 - 2400 = 2400
So, the remaining 2400 cans must be filled by Machine A
Since each Machine A can fill 400 cans per minute, we'll need 6 Machine A's to fill the remaining 2400 cans.
Total number of Machines working equals = 2 + 4 + 6= 12
So, the answer to the target question is the total number of machines working = 12
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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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

We can't say for certain how many machines are working. For example, we could have those 4,800 cans all filled by type B machines, or we could have all 4,800 filled by type A machines. INSUFFICIENT.

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

We're give ratio of type B machines : type C machine, however we don't know anything about type A machines.

(1&2) There are 2 Type B machines for every Type C.

Type C installs 2,400 lids per minute. Out of the 2,400, type B accounts for 1,200 of them. The other 1,200 is accounted for by type A machines.

For every 2,400 there will be 6 machines working. Since there are 4,800 cans filled that minute, there will be 12 machines working. SUFFICIENT.
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How do we know that there is no excess capacity? Are we to assume that the machines are operating in equilibrium?

I've a question, In A option, they are saying that 48000 cans are filled but we donot know ho many cans have lid
It is not mentioned anywhere that every minute whatever the number of cans that are fill are also fitted with lid

That's why I chose E, but answer is C, how can we assume that all that cans which are filled also have lid on them??