To fill an order, a manufacturer had to produce 1000 tools per day for

Hi Math experts here's my solution, would appreciate some comments.

(1) Clearly not sufficient, we only know that 3000 were produced in the first 5 days
(2) x*(n-4)+4*1500=1000n, we have two variables here. Not sufficient
(1)+(2) 3000+6000+x(n-9)=1000n, still 2 variables. Not sufficient
Answer E

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.


To fill an order, a manufacturer had to produce 1000 tools per day for n days. what is the value of n?

(1) Because of production problems, the manufacturer produced only 600 tools per day during the first 5 days
(2) Because of production problems, the manufacturer had to produce 1,500 tools per day on each of the last 4 days in order to meet the schedule


In the original condition, there are 2 variables(power, n), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2),
Since the manufacturer produced 600 tools every day for the first 5 days, they produced 3000 tools. Then the manufacturer produced 6000 tools for the next 4 days and you don’t know n. So, value of n is not unique and not sufficient. Therefore, the answer is E.


-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

Stimulus
The toal production is 1000* n

The first 5 days is pretty explanatory.

The language of statement 2 makes it a weird question.
The manufacturer had to produce 1,500 tools per day on each of the last 4 days in order to meet the schedule.
Now we don't know what the schedule is? Does he have to complete production of the tools on 9 days, 10 days , 11 days.

We don't know how many tools he has to make.
May be he has to make 18,000 tools then n will be 18. In first 5 days he will have delay . then the next 9 days he will have some other rate of production and the last 4 days 1500 tools per day.

May be he has to make 9000 tolls then n will be 9

pffff..... Kind of a weird question in my opinion

Let

O: Total amount of tools produced for that order
n: number of days until order is complete
1000: daily production rate

then: O = n * 1000

Thus were only able to determine the value of n if we can determine the value of O (the total number of tools for needed for that order)

(1) Given that 600 tools were produced on each of the first 5 days, we can only say that 5 * 600 = 3000 tools were produced on those 5 days. Nothing, however, is known about the remaining days or the total number of tools needed for the order. Insuff.

(2) Given that 1,500 tools were produced on each of the last 4 days, we can only determine that 4*1,500 = 6000 tools were produced on the last 4 days of the production period. Nothing is said about O in total. Insuff

Given (1) and (2) together, it is still not possible to determine the value of O. The only thing we know is that at least 3000 + 6000 = 9000 tools were needed to complete the order.

Hence E.

Can't we simply say that since we are given the first 4 days and the last 5 days, we can't solve since no info is given on the days "in between" the first and last? He could have worker for 10 days in between or 500 days in between, so we only have chunks of the timeline, not the whole timeline.

Yep, I drew a sketch to visualize:

1) |----3000----|-----(n-5)*rate------| = 1000n
No idea what the amt * rate is for the remaining days

2) |-----(n-4)*rate------|-----6000------| = 1000n
Same as 1)

3) |----3000----|-----(n-9)*rate------|-----6000------| = 1000n
The main point is that the amount of tools will vary with the amount of days left, and we don't know any information about either for the remaining n-9 days.

Higher level thinking again the fastest here.

\(first \ 5 \ days + x + last \ 4 \ days\)

No way to find \(x\). Done.

Why is it not C?

Here's my approach -

Number of days = n
Number of tools per day = 1000
Total tools = 1000n

Equation 1: 600 X 5 + 1000 (n-5) = 1000n
Equation 2: 1000 X (n-4) + 1500 X 4 = 1000n

Since 3000 is half of 6000 and RHS is the same that means 2 X 1000 (n-5) = 1000 (n-4)
n = 6

true, i did it with the same approach, (the answer is 9 btw). the problem here is that we know only that he did such work on the first 5 and last 4 days, we dont know if he worked 10 days with the 5th day doing nothing.

Great explanation Bunuel. Made this question click for me.

Posted from my mobile device

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.