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What was the median monthly number of gallons of water used by the

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Bunuel
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What was the median monthly number of gallons of water used by the [#permalink] New post   08 Aug 2023, 05:00
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What was the median monthly number of gallons of water used by the Jones family last year?

(1) The Jones family used 8,000 gallons of water during each of the first 6 months of last year.
(2) The Jones family used a total of 102,000 gallons of water last year.
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Re: What was the median monthly number of gallons of water used by the [#permalink] New post   08 Aug 2023, 06:53
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Bunuel wrote:
What was the median monthly number of gallons of water used by the Jones family last year?

(1) The Jones family used 8,000 gallons of water during each of the first 6 months of last year.
(2) The Jones family used a total of 102,000 gallons of water last year.


The median monthly number of gallons of water = Average of the water consumption of the 6th and the 7th month

Statement 1

(1) The Jones family used 8,000 gallons of water during each of the first 6 months of last year.

The statement tells that for the first six months, 8,000 gallons of water during each month. However, we don't have information on the water consumption of the family in the seventh month. Hence, this statement alone is not sufficient.

We can eliminate A and D.

Statement 2

(2) The Jones family used a total of 102,000 gallons of water last year.

To find the median, we need the consumption of water for the sixth and seventh months. The overall consumption will not help us here.
Hence, this statement alone is not sufficient. We can eliminate B.

Combined

While we know that the family consumed 8000 gallons of water in the sixth month, we cannot find how much water was consumed in the seventh month. Hence, the statements combined do not help either.

Option E
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Re: What was the median monthly number of gallons of water used by the [#permalink] New post   08 Aug 2023, 23:51
1 min on the clock.
There are 12 elements,to find the median we need average of 6 and 7.

statement 1-we are given the 6th element is 8000.we dont know 7th - insuff

Statement 2 - total water usage 102,000 gallons.Cant find median from this. -insuff

1&2 combined.
Although we can find the water usage for the last six months we dont know the specific usage from the 7th month.

So "E".
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Re: What was the median monthly number of gallons of water used by the [#permalink] New post   31 Aug 2023, 07:39
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Bunuel wrote:
What was the median monthly number of gallons of water used by the Jones family last year?

(1) The Jones family used 8,000 gallons of water during each of the first 6 months of last year.
(2) The Jones family used a total of 102,000 gallons of water last year.


n = 12 months, and we need to answer the question:

median = ?

Statement One Alone:

=> The Jones family used 8,000 gallons of water during each of the first 6 months of last year.

Let’s imagine the monthly water usages, in thousands of gallons, in chronological order.

If {8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8}, then the ascending order of the monthly usages is the same, and the median = 8 thousand gallons.

Whereas, if {8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9}, then the ascending order of the monthly usages is the same, and the median = (8 + 9)/2 = 8.5 thousand gallons, which is the mean of the two middle values.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> The Jones family used a total of 102,000 gallons of water last year.

If {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102}, then the ascending order of the monthly usages is the same, and the median = 0 thousand gallons.

If {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 91}, then the ascending order of the monthly usages is the same, and the median = 1 thousand gallons.

Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

102 – 6 × 8 = 54 thousand gallons of water was used in the last 6 months.

If {8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 14}, then the ascending order of the monthly usages is the same, and the median = 8 thousand gallons.

Whereas, if {8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9}, then the ascending order of the monthly usages is the same, and the median = (8 + 9)/2 = 8.5 thousand gallons.

The two statements together are not sufficient.

Answer: E
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Re: What was the median monthly number of gallons of water used by the [#permalink]
31 Aug 2023, 07:39
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