Machines A and B each produce tablets at their respective

[krishnagmat]

Machines A and B each produce tablets at their respective constant rates. Machine A has produced 30 tablets when Machine B is turned on. Both machines continue to run until Machine B’s total production catches up to Machine A’s total production. How many tablets does Machine A produce in the time that it takes Machine B to catch up?

(1) Machine A’s rate is twice the difference between the rates of the two machines.

(2) The sum of Machine A’s rate and Machine B’s rate is five times the difference between the two rates.

Questions:
=======
It is simple if we consider that the speed of B is greater than that of A. What about the other way where the machine B cannot catchup ?

Am I missing any that derives this assumption?

OA is D
- as both alone can help to resolve the problem.
but if it is not implied (B>A) , then we can derive this from using BOTH 1& 2 , making it Option C.

[RonPurewal]

The question says "Both machines continue to run until Machine B’s total production catches up to Machine A’s total production", so you know that, at some point, Machine B’s total production catches up to Machine A’s total production.

Basically, if the question says that something happens, you can't hypothesize that it doesn't.

[krishnagmat]

Thanks for your reply.

[tim]

:)

[chiba.pawan]

Hi Ron

Can you guys tell how to interpret this questions and solve within 2 mins. I found it difficult to understand and even after i did, i was not able to solve it correctly.

Please help.

Regards
Pawan

[RonPurewal]

Hi Ron

Can you guys tell how to interpret this questions and solve within 2 mins. I found it difficult to understand and even after i did, i was not able to solve it correctly.

Please help.

Regards
Pawan

hi,
welcome to the forum (i see that this is your first post). but, remember, this forum isn't meant to be an "answer key" for random problems that people post here -- it's meant to be a place where specific questions are answered.

i.e., please don't just post a problem. instead, tell us what you've already tried.
what did you understand?
how did you try to set up the problem?
where did you get stuck?
what other methods did you try?
did you read the answer key? if so, what did (or didn't) you understand?
etc.

once you've outlined the steps you've already taken, we can give some input that will actually help you solve future problems. (if we just provide an answer key, there's very little utility in that -- and besides, the problem already has an answer key.)

[mevicks]

Hi Ron

Can you guys tell how to interpret this questions and solve within 2 mins. I found it difficult to understand and even after i did, i was not able to solve it correctly.

Please help.

Regards
Pawan

Simplify :



Consider the above scenario. Its obvious that the rate of B is faster than that of A.
Let a be the rate of A & b be the rate of B

St1: a = 2 (b - a)
a = 2b - 2a
b = (3/2) a

As we know the relationship between the rates and the number of tabs created by A in the past, we can definitely get to the point where both the machines have produced equal no. of tabs.

SUFFICIENT

St2: a + b = 5 (b - a)
6a = 4b
b = (3/2) a
Same as above.
SUFFICIENT

Answer : D

[jlucero]

Let us know if there are other questions here.

[RonPurewal]

The other thing, here, is the "2 minutes" thing. If you have a goal of solving every problem within literally 2 minutes, that's ... a bad goal.

"2 minutes per problem" is an OVERALL AVERAGE.
It's NOT a limit.

It's like an average of anything else in the world.
Say your painting crew takes on average 4 hours to paint a house. If you have to paint a huge mansion, then, obviously, you should plan for more than 4 hours. (In fact, if you finish that job within 4 hours, you've almost certainly done a shoddy job.)

If a problem has lots and lots of words, then it's perfectly ok to take longer than 2 minutes.
You shouldn't take WAY longer -- i.e., spending 5 minutes is still falling off the wagon. But viewing an average as though it were a limit is, in a word, unwise.

[rustom.hakimiyan]

The other thing, here, is the "2 minutes" thing. If you have a goal of solving every problem within literally 2 minutes, that's ... a bad goal.

"2 minutes per problem" is an OVERALL AVERAGE.
It's NOT a limit.

It's like an average of anything else in the world.
Say your painting crew takes on average 4 hours to paint a house. If you have to paint a huge mansion, then, obviously, you should plan for more than 4 hours. (In fact, if you finish that job within 4 hours, you've almost certainly done a shoddy job.)

If a problem has lots and lots of words, then it's perfectly ok to take longer than 2 minutes.
You shouldn't take WAY longer -- i.e., spending 5 minutes is still falling off the wagon. But viewing an average as though it were a limit is, in a word, unwise.

Hi Ron,

When I saw this problem, I noticed that there was a comparison between Rates for A and B and proceeded to pick D because both the statements related the two rates. I think it was a pure fluke for me to get this correct.

If I switched gears and tried solving (during the review process), I couldn't connect the dots. The CAT explanation states that:

A × t =
B × t =
B - A × t = 30 tablets

-How are they coming to the conclusion that "t" is the same in all cases? Hasn't A been running longer?

[RonPurewal]

The CAT explanation states that:

A × t =
B × t =
B - A × t = 30 tablets

-How are they coming to the conclusion that "t" is the same in all cases? Hasn't A been running longer?

I don't have the full context here, but it seems that the explanation is using "t" only for the time when both machines are running simultaneously.

According to the problem, machine B has to "catch up" to machine A"”i.e., it must produce 30 more tablets than machine A during this time. (That way, the total number of tablets produced is the same for each machine"”including the 30 produced by machine A before the calculations.)

If "t" doesn't take those first thirty tablets into account, then you need
(tablets produced by A) + 30 = (tablets produced by B)
At + 30 = Bt
which is what you have here.

I don't immediately see how you would do it without using this "t", since, at the start of the problem, there's no way to tell how long machine A has already been running.

[rustom.hakimiyan]

The CAT explanation states that:

A × t =
B × t =
B - A × t = 30 tablets

-How are they coming to the conclusion that "t" is the same in all cases? Hasn't A been running longer?

I don't have the full context here, but it seems that the explanation is using "t" only for the time when both machines are running simultaneously.

According to the problem, machine B has to "catch up" to machine A"”i.e., it must produce 30 more tablets than machine A during this time. (That way, the total number of tablets produced is the same for each machine"”including the 30 produced by machine A before the calculations.)

If "t" doesn't take those first thirty tablets into account, then you need
(tablets produced by A) + 30 = (tablets produced by B)
At + 30 = Bt
which is what you have here.

I don't immediately see how you would do it without using this "t", since, at the start of the problem, there's no way to tell how long machine A has already been running.

Right, your last statement is exactly my point. Wouldn't we need to know the individual rates to come up with the time or the difference between the two rates at least?

[RonPurewal]

That's why you don't do that approach!

By letting "t" stand for the time during which both machines are working in tandem, we eliminate that issue. Since we know the required difference in total production (in order to make the total production the same overall), we're good.

[rustom.hakimiyan]

That's why you don't do that approach!

By letting "t" stand for the time during which both machines are working in tandem, we eliminate that issue. Since we know the required difference in total production (in order to make the total production the same overall), we're good.

EDIT: Solved it.

I was trying to add their individual works instead of realizing that if I subtract their rates and times, I end up with the 30 tablets. Pretty straight forward to solve once I made that connection.

Sorry for the time drain.

[RonPurewal]

Sorry for the time drain.

No need to apologize"”that's why the forum is here in the first place.