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

Question

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

Bunuel · Accepted Answer

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. We are just given that during the first 5 days the manufacturer produced (1,000-600)*5=2,000 fewer tools than scheduled. Not sufficient.

(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. We are just given that during the last 4 days the manufacturer produced (1,500-1,000)*4=2,000 more tools than scheduled. Not sufficient.

(1)+(2) From above we have that the least value of n is 5+4=9 and the least number of tools the manufacturer had to produce is 9,000, which is not sufficient to answer the question. For example, the manufacturer could work for n=9 days producing 600 tools per day during the first 5 days and 1,500 tools per day on each of the last 4 days OR the the manufacturer could work for n=10 days producing 600 tools per day during the first 5 days, 1,000 tools on the 6th day and 1,500 tools per day on each of the last 4 days. Not sufficient.

Answer: E.

Hope it's clear.

bangalorian2000 · Answer

1: not enough, as there is shortfall of 2000 tools which can be achieved in 1 day or any number of day. Only thing we can found from 1 is n > 5.
2: not enough, as in last four days it made 2000 tools extra to recover earlier shortfall.

Combining, there could be any number of days after first five days and last four days when manufacturer produced 1000 tools per day, hence insuffcient.

Its E.

BrainLab · Answer

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

MathRevolution · Answer

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.

LogicGuru1 · Answer

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

anairamitch1804 · Answer

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.

iliavko · Answer

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.

energetics · Answer

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.

SchruteDwight · Answer

Higher level thinking again the fastest here.

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

No way to find  x . Done.

adiz1295 · Answer

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

pier9891 · Answer

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.

MBAaustralia · Answer

Great explanation Bunuel. Made this question click for me.

Posted from my mobile device

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