At a certain factory, each of Machines A, B, and C is periodically on

Straight to point:

Note the bold and green marked words in the question stem.

So to exceed 30 units it's enough even if A and B works >>> 18+15=33 units( but don't take A +C=30: should be >30)

So now to find A n B simultaneous working LCM of A n B times>>> LCM(15,18)=90;

(it's enough if A n B works to exceed 30. No need to calculate for all 3(A, B, C) as A, B working together only makes it: now even in case u took LCM (A, B, C )=180 which is wrong in this context as A n B alone are enough to make it more than 30).



OA:C

HOPE this helps.
THANKS

Wait, why not B+C? Their sum is exactly 30

Posted from my mobile device

English is very tricky language my friend

Look below statement from question.
" The factory has a backup generator that operates only when the total power usage of the 3 machines exceeds 30 units of power."
Thus back up generator will not work if total consumption is 30units.
I hope it helps

I don't get why we used the LCM. can someone explain further

What we know

A - uses 15 units every 18th min
B - uses 18 units every 15th min
C - uses 12 units every 12th min

So, when would the power usage exceeds 30units aka >30 units of power
This can only occur when, both A and B are ON together since its the only combination of addition that results in > 30units of total power as 15+18 = 33 units. This means we have to find at what interval as in minute do they both come on together.
This question is essentially asking for the LCM (Lowest Common Multiple) of A and B.

Both A and B will be ON at LCM(18,15).
18=2*3*3
15=3*5
LCM(18,15)=2*3*3*5=90 minutes
Thus At 90 Minutes Both will be on and the Backup Generator will come on.

Ask if you have any questions

The only thing iam not able to understand here is the meaning of the last sentence. What does that last sentence exactly ask for?

Can someone please explain it in simple langauge?

Thanks in Advance!

There is a backup generator which gets switched on whenever the power usage exceeds 30 units. Now the power usage is at a specific point of time for each machine.

So we have to find when the combined power usage of the machines at a certain point exceeds 30 units and at that time the the generator will get switched on again.
Consecutive time means one after another.

I don't understand the first two lines. it say they are open for a minutes and then gets off for a fixed minutes (consecutive) so why are we not adding the time interval when its off. Can you help me break the first two lines? IanStewart Bunuel BrentGMATPrepNow

When it says events happen "periodically", that means they happen separated by a regular period, or interval. So Machine A, for example, is off for 17 minutes, then is on for 1 minute, and then is off again for 17 minutes, and on again for 1 minute. So in the 18th minute, and in the 36th minute, and so on, Machine A is on, and otherwise it is off. So Machine A is on in during each minute that is a multiple of 18, and similarly Machine B is on in any minute that is a multiple of 15, and since the total energy can only exceed 30 if Machines A and B are both on, we just need to find the Least Common Multiple of 18 and 15 to answer the question, and the answer is 90.

I hope that makes sense!

Why is nobody talking about machine C?

IMO, this is a more relatable explanation:

So, Machine A goes on the 18th minute
Machine B goes on the 15th minute
and Machine C goes on the 12th minute

Now, What combinations would actually give us a power value of over 30 ?

Machine A and B are on

AND

Machine A, B and C are on

A and C ; B and C give us a value <=30, so they are out

Now

Case1: LCM(18, 15) = 90
So, first time the power exceeds 30 units will be at 90th min

Case2: LCM(18, 15, 12)=180
So, second time the power exceeds 30 units will be at 180th min


As we are being asked the difference between the consecutive times: 180-90= 90..Ans

So, irrespective of whether we include Machine C in our calculation, (as Machine A and B are bound to use power>30 units post 90mins as discussed in Case 1), the time difference comes out to be 90mins. That's why Machine C is not paid attention to in other solutions.

But I guess as this approach may not work with different numbers, so my approach can be another way of solving such problems.


Thanks!

The question asks about when the backup generator turns on, and that only happens if the total energy usage exceeds 30. If you look at the energy usage column in the table, we have the numbers 15, 18 and 12. If you add up some or all of these numbers, and you get a total strictly larger than 30, you absolutely must be using the '15' and the '18' (whether or not you also use the 12). So the backup generator will come on any time A and B both come on, regardless of whether C also comes on, so it turns out that it doesn't matter whether C is on or off, and we don't need to think about machine C. So the solutions earlier weren't trying to "match the answer choice"; there's a good logical reason to ignore machine C here.

If the numbers in the question were slightly different, you certainly might need to consider all three machines, but with these specific numbers, you don't.

As always Ian has done a good job with his brilliant breakup of the information. But, the language in this question totally shook me to the core. Exactly the one that I need to guess and move on in the actual exam.

The question statement represents the information in a neat table. We will now carefully read this table and try to understand exactly what the question gives and what it wants.

Let’s go!


GIVEN:
We will elaborate on the case of machine A. You can then apply the same logic to machines B and C.

MACHINES:

• Machine A uses 15 units of power every 18th minute.
  
  • Machine A is OFF in the first 17 minutes and then ON in the 18th minute.
  • A is again OFF for 17 minutes after the 18th minute.
  • Then, A turns on again in the 36h minute (17 + 1 + 17 + 1), which is when it uses 15 units of power.
  • This cycle continues.
• Machine B uses 18 units of power every 15th minute.
• Machine C uses 12 units of power every 12th minute.

BACKUP:
Backup operates only when the total power usage by the three machines EXCEEDS 30 units.


TO FIND:

• The time interval between consecutive times the backup begins to operate.
  
  • Say, backup operates in the tth minute for the very first time. Since all machines are working periodically, this will happen again. Let’s say the backup will operate again in the rth minute.
  • Then, the time interval between the first time and the second time that the backup operates is (r – t) minutes. This is what we need to find.

APPROACH:
As seen above, we need to find (r – t). Now, to get this, we first need t and r. These are two consecutive times when backup operates.

When does backup operate?
Since backup operates when combined power usage exceeds 30 units and NO machine alone exceeds this usage, we will start by checking the combinations of machines, which when run together, will EXCEED 30 units of power usage.
There are only two possible combinations where the power usage is strictly GREATER than 30, and hence, only two instances when backup starts operating. These are:

- Instance 1: Machines A and B together (15 + 18 = 33).
- Instance 2: All three machines work together (15 + 18 + 12 = 45)

Observe that Instance 2 is automatically contained in Instance 1 and thus, need not be separately considered! (Since all three machines working simultaneously is just a subcase of machines A and B working simultaneously.)

[NOTE: If the combination of machines A and B did NOT consume 30 units or more, then we would have only instance 2 to work with – provided that all three consume more than 30 units!]

So, for this question, our requirement boils down to finding the time interval between consecutive times when machines A and B work simultaneously. ---- (1)


WORKING OUT:
Time interval between consecutive times when A and B work simultaneously:

- Machine A works every 18th minute. That means it works in the 18th, 36th, 54th, 72nd, 90th, 108th minutes, and so on.
- Machine B works every 15th minute. That means it works in the 15th, 30th, 45th, 60th, 75th, 90th, 105th minutes, and so on.

Observe: During the 90th minute, both the machines work simultaneously. And then again after 90 minutes, that is, in the 180th minute. So, the difference between these times is 180 – 90 = 90 minutes.

Thankfully, we don’t have to write such lists to find this final 90. Instead, 90 is the LCM of (18, 15), where 18 minutes and 15 minutes are the respective repeating times for machines A and B.

Final answer: LCM(18, 15) = 90.


Correct Answer: Choice C



Best,
Aditi Gupta,
Quant expert, e-GMAT

Bunuel chetan2u KarishmaB

Can you please help me understand the question?

I am not able to understand the first line-
'At a certain factory, each of Machines A, B, and C is periodically on for exactly 1 minute and periodically off for a fixed number of consecutive minutes.'
I did not understand the 'periodically on for exactly 1 min', 'periodically off', 'fixed no of consecutive minutes'

Can you walk me through what this would practically look like?

And when the sentence is saying 'each is periodically on', I was unable to infer 2-3 machines are working together. I thought that these machines will run separately and not together.

Looking forward to your guidance

Hi Ren
When you say each is periodically ON, it means that they are going to be ON irrespective of what is happening to the other. But there could be instances where two of them or all three of them are ON together and that is what is the requirement for us to find when total energy requirement exceeds 30.
The three have energy requirement of 18, 15 and 12. So, a combination of 18+15 or 18+15+12 will give energy requirement greater than 30.
Also, 18+15 will include the cases of 18+15+12.

Machine A……On(1)….OFF(17)……ON(1)…….OFF(17)…. So ON at 1, 18,36,54,72,90,108…
Machine B……On(1)….OFF(14)……ON(1)…….OFF(14)…. So ON at 1, 15,30,45,60,75,90,105…
Machine C……On(1)….OFF(11)……ON(1)…….OFF(11)…. So ON at 1, 12,23,34,45,56,67,78,89,90,101…

We are concerned with only the time when machine A and B are on together, and that is at 90th minute.

Why are you saying: A (min): 15,30,45...
15, 30... are the units of power, but the minutes for A are 18, 36...
I don't see why you saying that

Harsh2111s
why are we taking LCM of power instead of the time ?