In the flowchart, each rectangular box represents a distinct stage in

Question

https://gmatclub.com/forum/download/file.php?mode=view&id=17778 In the flowchart, each rectangular box represents a distinct stage in the production of a 50-kilogram batch of a specialty chemical. Decision points, which are not distinct stages, are represented by diamond shapes. The time required for each stage is indicated in minutes (min). There is no waiting time between stages. Three quarters of all batches do not require additional heating, while half of all batches require a second mixing with hydrochloric acid (HCL); none require a third. From each drop-down menu, select the option that creates the most accurate statement based on the information provided. The average time in minutes that a batch of ingredients to make it all the way through the process shown is: GRAPH_1_PLACEHOLDER The average number of stages that a batch undergoes is: GRAPH_2_PLACEHOLDER Capture.JPG

Vinit800HBS · Accepted Answer

If we don't get caught up into the traps of calculations and quarter of something and half of something else

, this one is a fairly straightforward question if followed in a logical manner. Let's assume that a batch consists of 4 units of specialty chemical (Doesn't matter if that adds up to 50 kilograms or some other number). BUT WHY 4 UNITS? Cause the information mentions that 3/4th of the batch passes through without additional heating and 1/2 of the batch requires additional HCL mixing . So to avoid getting caught up in 3/4th of 50 kilograms and deal with decimals or fractions, We can just assume 4 units in a batch. Now that it is clear, let's proceed with the question. First, if all the units (4 of them) in a batch pass through the processes without needing anything additional (no additional heating, no additional HCL mixing), then the time required is: Heating at 200K: 30 mins Sifting: 5 mins HCL mixing: 20 mins Filtration: 10 mins Drying at 150K: 60 mins Total time: 125 mins for each unit. Hence, the average time is 125 mins. But 1 unit (3/4th of the batch) requires additional heating. So it adds 20 mins to the process. And 2 units (1/2 of the batch) require additional HCL mixing. So, it adds 20 + 20 mins to the process. So, an additional 60 mins are required. Hence, an average of 60/4 = 15 mins are to be added to the 125 mins average time. Thus, the average time for the process is 140 mins . The visual representation of the same is given below. https://gmatclub.com/forum/download/file.php?id=81846 Now, we can apply the exact same process to answer the second question. Every unit must pass through: Heating at 200K Sifting HCL mixing Filtration Drying at 150K So, average number of stages is 5. But 1 unit (3/4th of the batch) requires additional heating. So it adds 1 more stage to the process. And 2 units (1/2 of the batch) require additional HCL mixing. So, it adds 2 more stages to the process. So, an additional 3 stages are required. Hence, an average of 3/4 = 0.75 stages are to be added to the 5 stages. Thus, the average number of stages for the process is 5.75 . The visual representation of the same is given below. https://gmatclub.com/forum/download/file.php?id=81847 GMAT-Club-Forum-z1uxuf97.jpeg GMAT-Club-Forum-p58rk554.jpeg

urthechange · Answer

IMO...The answers should be 140 mins and 5.75 batches...

Let's take 4 batches...

1. Total time for 4 batches will be = 120 (30*4) + 20 (3/4th do not need reheating so 20*1) + 20 (5*4) + 80 (20*4) + 40 (1/2 batches need HCL remixing so 20*2) + 40 (10*4) + 240 (60*4) = 560mins. Hence avg time is 140 mins (560/4).

2. Total stages for 4 batches will be = 4 (1*4) + 1 (3/4th do not need reheating so 1*1) + 4 (1*4) + 4 (1*4) + 2 (1/2 batches need HCL remixing so 1*2) + 4 (1*4) + 4 (1*4) = 23. Hence avg stages is 5.75 (23/4).

ptkm · Answer

If we translate the statement "Three quarters of all batches do not require additional heating" to the probability as following: 3/4 of a batch requires 0 heating and 1/4 of a batch requires 1 heating (worth 20 mins), and "half of all batches require a second mixing with hydrochloric acid, none requires the third" as 1/2 of a batch requires 1 mixing (20 mins) and 1/2 batch requires 2 mixing (40 minutes), the calculation for average time is as following: 
30 mins + (3/4*0 +1/2* 20 mins) + 5 mins + (1/2 *20 mins+1/2 * 40 mins)+10+60 = 140 mins

For the stage, we count 1 for the rectangular box, the calculation will be 1+(3/4*0+1/4*1)+1+(1/2*1+1/2*2)+1+1 = 5.75.

shauryahanda · Answer

I have a doubt, would we not be taking into account the batches moving in parallel that is while 1/4 of the batch would be re heated (taking additional 20 mins) the rest of the batch would move to next stage

What effect this would create would be that during the movement of rest of batch would be covered in the re heating times 
I.e while 1/4 of batch would be getting re heated, the rest of the batch would have finished with HCL mixing

rocky620 · Answer

shauryahanda

The processing time for a single batch will stop when it has finished the  Drying stage . So, even if there are some batches in the earlier stages, the average time required will not change.

Kimberly77 · Answer

ptkm  great explanation. Why are we only take care of 1/4 and not 2/4 as it has total 3/4? 
Could you help clarify? Thanks

DhruvBadaya · Answer

The calculations of this question was hard. It required concepts of Sets, Weighted Average and LCM. Make the denominator of all fractions to be 12 (LCM of 4 and 3 for easy calculation)

- Two twelfth of the set require ONLY additional heating
- One twelfth of the set require BOTH additional heating and additional HCl mixing
- Five twelfth of the set require ONLY additional HCl mixing
- Four twelfth of the set require NOTHING at all.

Now, use weighted average's concept to solve question 1 and 2. If you require detailed solution, mention me and I will add it here.

pearrrrrrr · Answer

my solution in the picture attached!

gclub1 · Answer

Vinit800HBS Sir Thank you for the detailed explanation. It was helpful.

Have two doubts. Could you clarify - "2 units (1/2 of the batch) require additional HCL mixing. So, it adds 20 + 20 mins to the process." - In this case, why not 2 units be processed in the same 20 mins? "2 units (1/2 of the batch) require additional HCL mixing. So, it adds 2 more stages to the process." - In this case, why not it be adds just 1 stage, as both units have the same unique stage? (Stimulus also says that half of batch requires just one second mixing). Thank you. chetan2u Sir please explain if possible.

GMATBusters · Answer

gclub1

Hi  gclub1

Even if you combine 2 lots to perform the HCL mixing operation together, it will not alter the weighted avg

Additional time will be (20 min * 2 lots + 20 min) * 1 lot /( total lot = 4) = 15 min

So, the total time is 125+15 = 140 min

Happy Learning

Adarsh_24 · Answer

I would do this way.

1) 30n + 20*(n/4) + 5n + 20n + 20(n/2)+ 10n + 60n =140n
Average = 140n/n = 140

2)n+n/4+n+n+n/2+n+n = 5n + 3n/4
Average = 5.75

Anonymous · Answer

Hi guys, I solved the graph problem using the method in the photo. What do you think of it? Was it effective and correct?

KarishmaB   Bunuel   GMATCoachBen   bb

KarishmaB · Answer

How will we calculate average time taken? Average time = Total time taken / No of batches Say we have 4 batches. Basic time taken for each of the 4 batches will be 30 + 5 + 20 + 10 + 60 = 125 mins. For 2 batches, extra 20 mins will be required (1/2 batches need second mixing of HCl) and for 1 batch, additional 20 mins will be needed for additional heating (a quarter of all batches) So Average time = Total time taken / No of batches = (4*125 + 2*20 + 1* 20)/4 = 140 Similarly, average number of stages = Total no of stages / No of batches Of 4 batches, basic stages are 5, 2 batches need an additional stage of HCl mixing and 1 batch needs additional stage of Heating. So Average number of stages = Total number of stages / No of batches = (4*5 + 2*1 + 1* 1)/4 = 5.75 Select 140 and 5.75 Here is a discussion on another Flowchart question: https://youtu.be/EwWZUiKLAZk Gmatguy007 - From what I can figure out, this is pretty much what you have done too.

Sanoshmishra · Answer

How the hell is one supposed to solve this question under 3 minutes? Imagine getting this as the first question...You'll be cooked

tabishjaved · Answer

Q1: Normal = 30+5+20+10+60 = 125 mins
Additional fixes: 125 +   = 140 mins

Q2: Normal = 5 steps
Additional fixes: 5 +   = 5.75 steps

carcass · Answer

Is this a GMAT prep, therefore offical question, or manhattan ?

Bunuel

I do know is the second one so the tag would be wrong

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