A factory assembles Product X from three components, A, B, and C. One

Question

https://gmatclub.com/forum/download/file.php?id=50470 A factory assembles Product X from three components, A, B, and C. One of each component is needed for each Product X and all three components must be available when assembly of each Product X starts. It takes two days to assemble one Product X. Assembly of each Product X starts at the beginning of one day and is finished at the end of the next day. The factory can work on at most five Product Xs at once. If components are available each day as shown in the table above, what is the largest number of Product Xs that can be assembled during the three days covered by the table? A. 3 B. 5 C. 6 D. 9 E. 10 PS56441.01 2019-09-21_1841.png

ScottTargetTestPrep · Accepted Answer

On Monday, the workers can start on only 3 products, because there are only 3 component A’s available. These 3 products will continue to be assembled all day Tuesday and be finished Tuesday night.

In the meantime, on Tuesday morning, the workers can start on only 2 new products because they are still working on the 3 (Monday) products (and their work limit is 5 products at any one time). So on Tuesday night, the 3 (Monday) products are complete, and the 2 (Tuesday) products are still in process.

On Wednesday, the workers could start on as many as 3 new products, but this is of no consequence, since they can’t finish any new products by Wednesday night. However, they will finish the 2 (Tuesday) products on Wednesday night.

Thus, they will have finished 3 products on Tuesday night and 2 more on Wednesday night, for a total of 5 completed products for the period in question.

Answer: B

itoyj · Answer

But at 1 time maximum of 5 products can be worked upon
So on Tuesday assembly of only 2 products will start as 3 are already in progress

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Archit3110 · Answer

IMO B ; 5 should be the answer of the largest assembled product 
max products during all three days if 0,1,2,3 begin assembly on Monday,we will have to consider cases and solve , i am guessing to be 5

Enrique92 · Answer

The largest number of Xs on Monday will be 3.

The largest number of Xs on Tuesday will be 3.

The largest number of Xs on Wedneday will be 3 but these ones will be done by Thursday night, then they should not be take into account.

Therefore 3+3=6

exc4libur · Answer

Factory workers can work on a max. of 5 units that takes each 2 days to complete;
Also, a unit is composed of one of each component (A,B,C) that must be available at the start of the given day.

Max. units that can start production on Monday = 3, since A = 3;
Therefore, three workers will be occupied until Tuesday, and two workers will be available;
Max. units that can start production on Tuesday = 2, since available workers = 2;
So, on Wednesday, there will be 5 units produced.

Answer (B)

sayan640 · Answer

The question states ,
"One of each component is needed for each Product X and all three components must be available when assembly of each Product X starts."
There are 3 'A' components available on Monday and so , work to assemble 3 products (x ) can start.
To complete these products 2 days will be required.
On Tuesday morning , work can start for assembling 2 more products simultaneously along with these 3 products. ( as "The factory can work on at most five Product Xs at once.")
On Tuesday evening , 3 products for which work started on Monday morning will be finished.
On Wednesday evening , 2 products for which work started on the Tuesday morning will be finished.
So , total 5 products can be assembled after the completion of Wednesday.

VeritasKarishma   GMATNinja   EgmatQuantExpert   GMATGuruNY   Bunuel

coreyander · Answer

OFFICIAL EXPLANATION

We will determine the largest number of Product Xs that can be assembled during all three days by considering separately the largest number that can be assembled if 0, 1, 2, or 3 Product Xs begin assembly on Monday.

0 Product Xs begin assembly on Monday:  In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 0 + 3 = 3 Product Xs could be assembled during the three days.

1 Product X begins assembly on Monday:  In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 1 + 3 = 4 Product Xs could be assembled during the three days.

2 Product Xs begin assembly on Monday:  In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 2 + 3 = 5 Product Xs could be assembled during the three days.
 
3 Product Xs begin assembly on Monday : In this case, at most two Product Xs can begin assembly on Tuesday (because the factory can work on at most five Product Xs at once), and hence at most 3 + 2 = 5 Product Xs could be assembled during the three days.

Therefore, the largest number of Product Xs that can be assembled during the three days is 5.

The correct answer is B.

Shobhit7 · Answer

All three components must be available + max products per day is 5

Monday= A is minimum, 3 components: work started on 3 products
Tuesday= Carry forward 3 products from Monday to completion + 2 new products started = 5 products, max capacity
Wednesday= Carry forward 2 products from Tuesday to completion + 3 new products started = 5 products, max capacity

So, at the end of Wednesday, we shall have 5 finished products and 3 unfinished products from Wednesday.

Ans 5. B

Dpkkukreja · Answer

VeritasKarishma   Bunuel   chetan2u  I understand the logic mentioned by everyone else that we can atmost make five products in one day and that's the reason we cannot start working on 3 products on Tuesday if we are working on three products on Monday.

Now, what confuses me is the official explanation given by Gmat and especially this portion " 1 Product X begins assembly on Monday:  In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 1 + 3 = 4 Product Xs could be assembled during the three days."

This says I can only start 3 products on Tuesday because only three units of product A are available on Wednesday but question stem says that all the products are supposed to be available at the start(not necessarily throughout the process)

I agree I can still start working on three products only because only three units product B are available on Tuesday but why does explanation explicitly mention about availability of product A on Wednesday?

KarishmaB · Answer

I wouldn't bother too much about the official explanations. As per the question stem, the availability on Wednesday should be irrelevant.

AdiBir · Answer

Given :  
All three components A,B,C necessary to start producing X.

It takes two days to assemble product X.

We can only work at most product Xs at any given time.

To Find:  
Maximum number of Product Xs that can be assembled in 3 days under given constraints.

Process:  
The maximum number of Product Xs we can work on a day is the minimum of (A,B,C) on a given day.

On Day 1:
min(A,B,C) = 3. So on Day 1 we start working on 3 Xs. 
These will continue till end of Day 2.
On Day 2:
We are currently working on 3 Xs from Day 1 and min(A,B,C) on Day 2 = 3.
So we can start working on 3 more Xs on Day 2, but as we can work on only 5 Xs at any time, so only two more Xs can be worked upon. 
Now total Xs in progress = 5.
On Day 3:
3 Xs were finished on Day 2, 2 Xs started on Day 2 are still in progress.
If we start any new Xs today, they won't be finishd by end of Day 3, so no point in starting.

At the end of Day 3, total 5 Product X have been produced.
Hence B is correct.

Pritishd · Answer

This is a classic example of questions were we often miss out to use the little details provided in the question stem. I marked 6 as the answer because I missed out to consider the max 5/day constraint.

You should definitely include this in your EL with the takeaway to analyze and utilize all the constraints provided in the question stem.

Hope this helps!

Fdambro294 · Answer

I really had to take a step back for a second because I thought there was some underlying trick hidden.

The hardest part with this problem is getting all the Information understood and organized.

2 Key Facts that make this question much easier:

(1) Takes from the Beginning of ONE Day ---------> to the END of NEXT Day to Finish a Product (a full 2 Days)

from this Fact, we can only finish products if we Start them on Monday or Tuesday. Otherwise, the Products will NOT be Finished by End of Work day Wednesday.

In effect, Wednesday is a throw away Day and starting projects on Wednesday will NOT help.

(2) AT MOST we can only be working on 5 of these products at ANY ONE TIME.

No matter how many components we have (even if there is beyond 5 of Each Component avialable) -----

If we Start X Products on Monday ------> it will take until END of Tuesday to finish the X Products

Therefore, at Beginning of Work on Tuesday ----> we can only Start (5 - X) Products

because the X products we Started Monday will still be on-going and we can only have a MAX of 5 products going at any one time

(I) START of DAY Monday:

Since we need All 3 Parts available on the Day we start making the product, we are limited by the 3-A parts that are available. The most products we can start on Monday morning = 3 products

(II) START of DAY Tuesday:

the components we will have to work with are -

A = 6

B = (3 not used yesterday) + 3 = 6

C = (1 not used yesterday) + 7 = 8

Even though we have enough parts to make 6 on Tuesday, we already have the 3 products in-process that we started making on Monday. These will NOT be Finished until END of Work Day Tuesday.

Therefore the MOST we can Start on Tuesday = 2 products

(III)END of Work Day Tuesday: the 3 products we started on Monday will be Finished

(IV) BEGINNING of Work Day Wednesday:
Even though we can start more products, we will NOT be able to Finish the products in time. Wednesday becomes a throw-away day.

(V)END of Work Day Wednesday: the 2 products we started on Tuesday will be Finished

5 Products will be Finished and this is the MOST we can make.

-B-

NOTE: you can try it with any amount of products started on Monday up to the MAX of 5

If we start only 1 on Monday

then when we get to Tuesday, we will only be able to Start 4 More because the Monday product will still be in-process.

And again, because it takes a full 2 Days to finish the product, we will only be able to finish 5 products by End of Work Day Wednesday

pranayeekarmakar · Answer

monday max products=3 but these will finished on Tuesday . on tuesday we can make 2 more products but these will be finished on wednesday so at the end of wednesday we have 3+2=5 products

ans B

Basshead · Answer

The key here is to note that the factory can work on at most five Product Xs at once.

On Monday, we have enough components to start making 3 Product Xs.

Tuesday, we're still working on the first 3 Product Xs, but we can take another 2 Product Xs and start working on them. At the end of Tuesday, the first 3 Product Xs are complete.

Wednesday, we can't start working on any additional Product X's because they won't be completed in time. However, the Product X's that we start working on from Tuesday will be complete.

3 + 2 = 5

Answer is B.

DrVanNostrand · Answer

Hi Scott,

Thanks for helping us out as you always do. I applied a different approach. I thought if they can't work on more than 5 products at a time, they can start working on Tuesday, starting the assembly of all five products at once and on the same day. Hence, the answer 5 products.

Is my approach correct?

Thanks in advance.

NarutoHozake · Answer

A factory assembles Product X from three components, A, B, and C. One of each component is needed for each Product X and all three components must be available when assembly of each Product X starts. It takes two days to assemble one Product X. Assembly of each Product X starts at the beginning of one day and is finished at the end of the next day. The factory can work on at most five Product Xs at once. If components are available each day as shown in the table above, what is the largest number of Product Xs that can be assembled during the three days covered by the table?

A. 3
B. 5
C. 6
D. 9
E. 10

PS56441.01

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Show Answer

Official Answer

B

A. 3
B. 5
C. 6
D. 9
E. 10

Isn't it a rational business assumption that we can carry over the products left on a particular day to the next day? 
In that case, we can start with just 1 product X on Monday and start with 5 Product X on Tuesday to make a total of 6 product X.

Vibhatu · Answer

Question asked the largest number of Product Xs!!! That means A B C have to present in order to build X. Therefore question should asked how many number of components can be made!! Not the full product!! Full product maybe just 1. Please correct it!!  Bunuel

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A factory assembles Product X from three components, A, B, and C. One

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A factory assembles Product X from three components, A, B, and C. One

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