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655-705 Level|   Work and Rate Problems|                           
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AbdurRakib
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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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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(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/
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AbdurRakib
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

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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I'm not sure why the question is structured so weirdly. Maybe its a problem with my understanding but can someone help with what "A lid is installed on each can that is filled and on no can that is not filled." means. BrentGMATPrepNow ScottTargetTestPrep

Thank you.
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Here's the original question...

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


ritzu
I'm not sure why the question is structured so weirdly. Maybe its a problem with my understanding but can someone help with what "A lid is installed on each can that is filled and on no can that is not filled." means. BrentGMATPrepNow ScottTargetTestPrep

Thank you.

That proviso just tells us that there aren't a bunch of Type C machines blindly installing lids on cans that are empty.

For example, without the proviso, statement 1 tells us that it could be the case that there are 12 Type A machines (to fill a total of 4800 cans) and 2 Type C machines (to install 4800 lids), OR it could be the case that there are 12 Type A machines (to fill a total of 4800 cans) and 100 Type C machines (2 of which install lids on the 4800 FILLED cans, and the remaining 98 machines install lids on a bunch of EMPTY cans).
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Going by the notion where we don't accept c=2 for granted,

let's take a step back to see all plausible explanations from 2*A + 3*B = 24
1. A=0, B=8
2. A=3, B=6
3. A=6, B=4
4. A=9, B=2
5. A=12, B=0

Now adding the C-B relation here
1. A=0, B=8, C=4
2. A=3, B=6, C=3
3. A=6, B=4, C=2
4. A=9, B=2, C=1
5. A=12, B=0, C=0

All scenarios have a total count of 12 machines.
Hence (C)
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AbdurRakib
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

ScottTargetTestPrep egmat

Question 1:
Perhaps this was a translation issue on my end by "2 Type B machines working for every Type C machine working" meant 2b=c to me? Are you only allowed to do this when you are given the exact number and not ratios (e.g., c has twice the number of machines as b vs. there are two B machines for every C machine)? So, for translation ratios, you would need to set up the ratio as you did then get to the algebraic equation?

Question 2:
When you mention "From statement one, we know that c = 2", how do you know this? Because 4,800/2400=2?
Thank you!
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woohoo921
ScottTargetTestPrep
AbdurRakib
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

ScottTargetTestPrep egmat

Question 1:
Perhaps this was a translation issue on my end by "2 Type B machines working for every Type C machine working" meant 2b=c to me? Are you only allowed to do this when you are given the exact number and not ratios (e.g., c has twice the number of machines as b vs. there are two B machines for every C machine)? So, for translation ratios, you would need to set up the ratio as you did then get to the algebraic equation?

Question 2:
When you mention "From statement one, we know that c = 2", how do you know this? Because 4,800/2400=2?
Thank you!

Regarding your first question, you got your translation backward. Because there are more b machines than c machines, it should have been b = 2c. The answer to the second question is yes.
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Perfectly summarizes every condition. We cannot take option (C) for granted unless every combination of a + b + c results in the same answer.
SudipM7
Going by the notion where we don't accept c=2 for granted,

let's take a step back to see all plausible explanations from 2*A + 3*B = 24
1. A=0, B=8
2. A=3, B=6
3. A=6, B=4
4. A=9, B=2
5. A=12, B=0

Now adding the C-B relation here
1. A=0, B=8, C=4
2. A=3, B=6, C=3
3. A=6, B=4, C=2
4. A=9, B=2, C=1
5. A=12, B=0, C=0

All scenarios have a total count of 12 machines.
Hence (C)
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