At a certain factory, 4 processesA, B, C, and Dare carried out 24 ho

Question

At a certain factory, 4 processes—A, B, C, and D—are carried out 24 hours per day, 7 days per week. Process A operates on a 60-hour cycle; that is, Process A takes 60 hours to complete and immediately begins again when it is completed. Likewise, Process B operates on a 24-hour cycle, Process C operates on a 27-hour cycle, and Process D operates on a 9-hour cycle. On Monday, all 4 processes began together at 10:00 in the morning.

On the basis of the information provided, select for Processes A, B, and D the day of the week on which Processes A, B, and D will next begin together at 10:00 in the morning. Also select for All 4 processes the day of the week on which Processes A–D will next begin together at 10:00 in the morning. Make only two selections, one in each column.

ID: 700194

chetan2u · Accepted Answer

Whenever you look at a question which talks of repetition of certain activities that happen at regular interval, you are looking at LCM.

A, B and D repeat the activity after 60, 24 and 9 hour cycle. LCM(60, 24, 9) = 360hrs or 360/24 days, that is 15 days.
 15 or 14+1 days after Monday will be Tuesday.

Next, all four together, so A, B, C and D repeat the activity after 60, 24, 27 and 9 hour cycle. LCM(60, 24, 27, 9) = 360*3hrs or 360*3/24 days, that is 45 days. 45 days means 6 weeks and 3 days.
 3 days after Monday will be Thursday.

egmat · Answer

This is another one of those quant questions in the garb of TPA question format. It is a Word Problem question with LCM as the applied concept.

If you struggled with this question, then the corrective actions that you will apply will help you improve your Quant Arithmetic ability and your TPA ability. So, be sure to do a precise causal analysis here:
 
 You could not draw the inference that you need to calculate the LCM
 
 Corrective Action: Work on LCM module so that you can build your LCM ability.   
 Once you calculated the LCM, you got stuck since you did not understand how to take it to the answer needed – week day.
 
 Corrective Action: Get in the habit of ‘owning the dataset’. You need to immerse yourself in the scene so that you can make such inferences.   
 You got scared by the sheer volume of information in the dataset – 4 processes, different cycle times.
 
 Corrective Action: Read the dataset with the intention of ‘owning the dataset’

https://www.youtube.com/watch?v=XRJK-gwRNfk

Let us know which step you faltered on.
Happy Learning!
Payal

MartyMurray · Answer

At a certain factory, 4 processes—A, B, C, and D—are carried out 24 hours per day, 7 days per week. Process A operates on a 60-hour cycle; that is, Process A takes 60 hours to complete and immediately begins again when it is completed. Likewise, Process B operates on a 24-hour cycle, Process C operates on a 27-hour cycle, and Process D operates on a 9-hour cycle. On Monday, all 4 processes began together at 10:00 in the morning.

A day is 24 hours. So, a process will restart at 10 am any time the process has operated full cycles for a multiple of 24 hours.

Thus, we know the following for each process:

For A, the first multiple of 24 such that it will have operated for full cycles for a multiple of 24 hours is 2 x 60 = 120 hours. 120/24 = 5 days.

B operates a full cycle every 24 hours. So, B always starts at 10 am.

C operates for for 27 = 3 × 3 × 3 hours each cycle. 24 = 3 × 8. So, to get to a multiple of 24, C must go through 8 complete cycles or 8 × 27 = 216 hours = 9 days.

D operates for 9 hours each cycle. 24 = 3 × 8. So, to get to a multiple of 24, D must go through 8 complete cycles or 8 × 9 = 72 hours = 3 days.

On the basis of the information provided, select for Processes A, B, and D the day of the week on which Processes A, B, and D will next begin together at 10:00 in the morning.

We can ignore B since B begins at 10 in the morning every day.

A begins at 10 in the morning every 5 days, and D does every 3 days.

The least common multiple of 5 and 3 is 15. So, the three processes will next begin together after 15 days.

15 days is 2 weeks and 1 day later.

Two weeks and 1 day later than Monday is Tuesday.

For  Processes A, B, and D , select  Tuesday .

Also select for All 4 processes the day of the week on which Processes A–D will next begin together at 10:00 in the morning. Make only two selections, one in each column.

For this one, B still doesn't matter since it starts at 10 in the morning every day.

Also, we can ignore D since the cycle time of 27 hours for C is a multiple of the cycle time of 9 hours for D. So, D will always start at 10 in the morning when C does.

Thus, this question can be answered through determining when A and C will both start at 10 in the morning again.

A begins at 10 in the morning every 5 days. C does every 9 days.

The least common multiple of 5 and 9 is 45. So, they will begin together again 45 days later.

So, A and C will next begin again synch 6 weeks and 3 days later.

3 days after Monday is Thursday.

For  All four processes  select  Thursday .

Correct answer:  Tuesday, Thursday

VeeB · Answer

Very interesting question, looks complicated but follows a simple process:
First Q: Answer is Tuesday.
Logic: LCM of A, B and D is 360, that translates to the fact that these three will again process together after 360hrs which is effectively 15 days from the current Monday. Therefore the 15th day after the Monday is a Tuesday.
Second Q: Answer is Thursday
Logic is same as that of Q1, LCM of the 4 processes is 1080hrs which is 45 days that translates to a Thursday.

Posted from my mobile device

animesh45 · Answer

I made a counting mistake. Starting Monday, the next Monday is 8th day, so i chose Monday as 15th day.
Later i realised Monday 10:00 to Tuesday 10:00 counts as 1 day.
Thank you very much Sir!

acrd19 · Answer

To get the hours at which the starting point will match again, we calculate LCM of the numbers.

LCM(A,B,D) = LCM(60,24,9) = 360 hours
LCM(A,B,C,D) = 1080 hours

Days for ABD to clash = 360/24 = 15
Days for ABCD to clash = 1080/24 = 45

How many weeks and days:
15/7 = 2 weeks. 15%7 = 1 day
45/7 = 6 weeks. 45%7 = 3 days

ABD -> monday + 1 day = tuesday
ABCD -> monday + 3 days = thursday

riri3026 · Answer

akshaydesai26

Why are we dividing each of the LCMs by 24? for hours right?

chetan2u · Answer

To convert hours in days

Gemmie · Answer

A:  60 = 2^2 * 3 * 5 
B:  24 = 2^3 * 3 
C:  27 = 3^3 
D:  9 = 3^2

24h = 2^3 * 3

LCM (A, B, C, D) =  2^3 * 3^3 * 5 = 24 * 3^2 * 5 = 24 * 45 
45 = 6 * 7 + 3

LCM (A, B, D) =  2*3 * 3^2 * 5 = 24 * 3 * 5 = 24 * 15 
15 = 2 * 7 + 1

Mo___Tu___We___Th___Fr___Sa___Sun
(S).............................................
...
........(+1)
...
........(+1)...(+2)....(+3)

Therefore
A, B, D: Tuesday
A-D: Thursday

Dbrunik · Answer

okay, so this is a relatively easy question, so im not sure why so many people are getting it wrong. Although, it take take me a good amount of time, 5 minutes and 40 seconds.

Basically this is just a common denominator problem, and you just want all the exponents to match.

my only question is, how would you do this faster? i had to figure out and line up each exponent.

Siddharth26031994 · Answer

In this Question , Luckily we are given 24 hours as one machine's time, had it not been there , we would also consider 24 along with machines to find out LCM

Ex-

LCM of A,B,D,24

LCM of A,B,C,D,24

this would ensure a multiple of 24

very important point specially for who solved it

BinodBhai · Answer

yeah buddy I made the same mistake

ChiefScreen · Answer

The trick is finding the least common multiples. A, B, and D align every 180 hours, which is 7 days 12 hours, so the next 10 AM alignment is tricky to match.

At a certain factory, 4 processesA, B, C, and Dare carried out 24 ho

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

Processes A, B and D	All four processes
		Monday
		Tuesday
		Wednesday
		Thursday
		Friday
		Saturday

GMAT Two-part Analysis (TPA) Questions

At a certain factory, 4 processesA, B, C, and Dare carried out 24 ho

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia