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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