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ExpertsGlobal5
Yesterday, each bottling machine at a bottling plant was operating at below maximum output. Did any of the machines fill less than 4,000 bottles?

(1) Each machine’s maximum daily output is between 6,000 and 15,000 bottles.
(2) Each machine operated at between 50 to 70 percent of its maximum output.


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Each bottling machine was operating at levels below maximum output.

Did any of the machines fill less than 4,000 bottles? The answer can be either Yes / No.

Statement 1:

Each machine’s maximum daily output is between 6,000 and 15,000 bottles.

This statement sets the maximum daily output range, which varies from 6000 to 15000 bottles.

Since, machines operate at below max output. We cannot ascertain the exact value.

Hence, Insufficient

Statement 2:

Each machine operated at between 50 to 70 percent of its maximum output.

Without knowing the maximum output levels. We cannot determine whether they operated at levels below 4000 bottles or not.

Hence, Insufficient

Combining both Statements 1 and 2, we get

6000 and 15000 are the min and max limits of MAXIMUM daily output.

50% of these levels bring us to 3000 and 7500.

While 70% of these levels bring us to 4200 and 10500.

So, the values can fall anywhere from 3000 to 10500.

we have a 3000 to 4000 levels which gives answer NO, and above that the values give YES.

Hence, Insufficient

Option E
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ExpertsGlobal5
Yesterday, each bottling machine at a bottling plant was operating at below maximum output. Did any of the machines fill less than 4,000 bottles?

(1) Each machine’s maximum daily output is between 6,000 and 15,000 bottles.
(2) Each machine operated at between 50 to 70 percent of its maximum output.

Explanation:

The maximum output and the performance of the machines are unknown.
We need to find whether any of the machines filled less than 4,000 bottles.

Statement (1)

Each machine’s maximum daily output is between 6,000 and 15,000 bottles.

Possibility 1: If the maximum daily output of each machine is 6,500 and if each machine operates at 60 percent of its maximum output, then the number of bottles filled by each machine = 6,500 x 0.6 = 3,900 < 4,000.
Possibility 2: If the maximum daily output of each machine is 10,000 and if each machine operates at 60 percent of its maximum output, then the number of bottles filled by each machine = 10,000 x 0.6 = 6,000 > 4,000.

It is NOT possible to determine with certainty whether any of the machines filled less than 4,000 bottles. Hence, Statement (1) is insufficient.

Statement (2)

Similar reasoning as above can be applied using the same values to show that it is NOT possible to determine with certainty whether any of the machines filled less than 4,000 bottles. Hence, Statement (2) is insufficient.

As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements.

Statement (1) and Statement (2) combined

Similar reasoning as above can be applied using the same values to show that it is NOT possible to determine with certainty whether any of the machines filled less than 4,000 bottles. Hence, Statement (1) and Statement (2) combined are insufficient.

E is the correct answer choice.
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