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For which of the following options is the average (arithmetic mean) of

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MathRevolution
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For which of the following options is the average (arithmetic mean) of [#permalink] New post  11 Sep 2017, 00:29
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A
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D
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[GMAT math practice question]

I. 9/10, 10/11, 11/12, 12/13, 13/14
II. 10/9, 11/10, 12/11, 13/12, 14/13
III. 6/10, 7/10, 8/10, 9/10, 10/10

For which of the following options is the average (arithmetic mean) of the numbers less than the median of numbers?

A. I. only
B. II. only
C. III. only
D. II and III
E. I, II and III
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MathRevolution
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Re: For which of the following options is the average (arithmetic mean) of [#permalink] New post  13 Sep 2017, 00:16
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I. Differences between consecutive terms are 10/11 – 9/10 = 1/110, 11/12 – 10/11 = 1/132, 12/13 – 11/12 = 1/156, 13/14 – 12/13 = 1/182. The differences are getting smaller. The average is smaller than the median.

II. Difference between consecutive terms are 11/10 – 10/9 = -1/90, 12/11 – 11/10 = -1/110, 13/12 – 12/11 = -1/132, 14/13 – 13/12 = -1/156. The differences are getting bigger. The average is bigger than the media.

II Difference between consecutive terms are 7/10 – 6/10 = 1/10, 8/10 – 7/10 = 1/10, 9/10 – 8/10 = 1/10, 10/10 – 9/10 = 1/10. All differences are equal. The average is equal to the median.

Ans: A
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pushpitkc
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Re: For which of the following options is the average (arithmetic mean) of [#permalink] New post  11 Sep 2017, 03:07
Since III has a average = median = 8/10, it can be eliminated!
Hence, Option C,D and E are wrong!

So, the answer is either Option A or Option B.

Lets consider the set - 9/10, 10/11, 11/12, 12/13, 13/14
The median is 11/12 = 0.9167
The mean is 0.9 + 0.909 + 0.916 + 0.923 + 0.929 = 4.57/5 = approximately 0.9154
Here, the average is lesser than the median(Option A)
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gblessing
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Re: For which of the following options is the average (arithmetic mean) of [#permalink] New post  13 Sep 2017, 11:04
I. 9/10, 10/11, 11/12, 12/13, 13/14
II. 10/9, 11/10, 12/11, 13/12, 14/13
III. 6/10, 7/10, 8/10, 9/10, 10/10

For which of the following options is the average (arithmetic mean) of the numbers less than the median of numbers?

A. I. only
B. II. only
C. III. only
D. II and III
E. I, II and III

In the above question, I know to quickly eliminate choices C, D, and E as each references III which has an average = median.

My question: Is there an quicker way to identify between the correct answer A or B other than setting the fractions equal, adding, averaging, and then comparing against the median? I.E. How do I quickly identify the right answer between A and B so I manage time effectively?
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MathRevolution
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Re: For which of the following options is the average (arithmetic mean) of [#permalink] New post  13 Sep 2017, 11:57
Expert Reply
gblessing wrote:
I. 9/10, 10/11, 11/12, 12/13, 13/14
II. 10/9, 11/10, 12/11, 13/12, 14/13
III. 6/10, 7/10, 8/10, 9/10, 10/10

For which of the following options is the average (arithmetic mean) of the numbers less than the median of numbers?

A. I. only
B. II. only
C. III. only
D. II and III
E. I, II and III

In the above question, I know to quickly eliminate choices C, D, and E as each references III which has an average = median.

My question: Is there an quicker way to identify between the correct answer A or B other than setting the fractions equal, adding, averaging, and then comparing against the median? I.E. How do I quickly identify the right answer between A and B so I manage time effectively?


Please take a look at the above solution from Math Revolution.
We can compare the average and the median using differences between consecutive terms.

Happy Studying !!!
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Re: For which of the following options is the average (arithmetic mean) of [#permalink] New post  24 Sep 2023, 08:11
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Re: For which of the following options is the average (arithmetic mean) of [#permalink]
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