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

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

OG Q 2017(Book Question: 236)

(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

ID: 700105

ScottTargetTestPrep · Accepted Answer

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

saiesta · Answer

(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.

Divyadisha · Answer

(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

ashwini86 · Answer

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

saswata4s · Answer

(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 .

deddex · Answer

Video Solution of the above OG Problem by GMAT Quantum https://gmatquantum.com/2017-gmat-quant ... nt-review/

BrentGMATPrepNow · Answer

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

aishu0091 · Answer

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.

Thank you.

BrentGMATPrepNow · Answer

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

OG Q 2017(Book Question: 236)

(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

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).

SudipM7 · Answer

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)

woohoo921 · Answer

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!

ScottTargetTestPrep · Answer

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.

ShubhadeepB · Answer

Perfectly summarizes every condition. We cannot take option (C) for granted unless every combination of a + b + c results in the same answer.

HarshavardhanR · Answer

GMAT-Club-Forum-un2hgczs.png Harsha

egmat · Answer

So, in this question, you've got three different machine types all working together, and you need to figure out exactly how many machines are running. Let's break this down step by step.

Understanding What We're Looking For

You need to find the  total number of machines working . Here's what we know:
- Type A: fills 400 cans/minute
- Type B: fills 600 cans/minute 
- Type C: installs 2,400 lids/minute

The key constraint that many students miss:  Every filled can gets exactly one lid . This means:
 	ext{Number of cans filled} = 	ext{Number of lids installed}

Analyzing Statement (1)

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

Let's think about this... We know the total production, but not how it's distributed. Notice how we could achieve 4,800 cans in different ways:

- Using only Type A machines:  12 	imes 400 = 4,800  cans
 → Need 2 Type C machines for lids:  2 	imes 2,400 = 4,800  lids
 → Total: 12 + 0 + 2 =  14 machines

- Using only Type B machines:  8 	imes 600 = 4,800  cans
 → Still need 2 Type C machines
 → Total: 0 + 8 + 2 =  10 machines

Since we get different totals, Statement (1) is  NOT sufficient .

Analyzing Statement (2)

"There are 2 Type B machines for every Type C machine"

Here's what you need to see - this gives us a ratio  B = 2C , but without knowing the actual number of C machines, we can't pin down the total. The ratio could scale up or down while maintaining the 2:1 relationship.

Statement (2) alone is  NOT sufficient .

Combining Both Statements

Now here's where it gets interesting! When you combine both statements:

From Statement 1: We need exactly 4,800 lids for 4,800 cans
→ Number of Type C machines:  \frac{4,800}{2,400} = 2  machines

From Statement 2 with C = 2: 
→ Type B machines:  2 	imes 2 = 4  machines

Type B produces:  4 	imes 600 = 2,400  cans
Remaining cans needed:  4,800 - 2,400 = 2,400 
Type A machines:  \frac{2,400}{400} = 6  machines

Total: 6 + 4 + 2 =  12 machines

Answer: C  - Both statements together are sufficient, but neither alone is sufficient.

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You can check out the  step-by-step solution on Neuron by e-GMAT  to master the systematic framework for solving production balance problems quickly. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice  here  - they show you exactly how to spot the patterns that save time on test day!

nbharti · Answer

A lid is installed on each can that is filled and on no can that is not filled --> Although we can get to the total number of machines as 12 by combining both statements. It is written nowhere that all the machines should be working simultaneously. What i mean by that is, It is possible that Machines A and Machine B can keep on bottling and Machine C starts operating after one minute. Nowhere the question stem says that when the bottles are filled at the same time, the lids should be placed.

Am I understanding something incorrectly in this question?

Am I understanding something incorrectly in this question?

FrozenDragon · Answer

Hey there,  You’re assuming the machines can work at different times, but the phrase “for a particular minute” means everything happens in the same minute.
 
 So cans filled and lids installed must match within that minute, which forces all machines to be working simultaneously.

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

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