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MathRevolution
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For which of the following options is the average (arithmetic mean) of 11 Sep 2017, 00:29
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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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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A
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For which of the following options is the average (arithmetic mean) of 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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For which of the following options is the average (arithmetic mean) of 11 Sep 2017, 03:07
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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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For which of the following options is the average (arithmetic mean) of 13 Sep 2017, 11:04
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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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For which of the following options is the average (arithmetic mean) of 13 Sep 2017, 11:57
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gblessing
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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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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For which of the following options is the average (arithmetic mean) of 01 Nov 2024, 07:06
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MathRevolution
=>

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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Hello MathRevolution,

Can you please help understand the reasoning/concept behind differences getting smaller and the relation to mean and median?

Thank you!

Also, adding others experts as Mentions, if anyone can help understand this! KarishmaB Bunuel MartyMurray gmatphobia
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For which of the following options is the average (arithmetic mean) of Updated on: 02 Nov 2024, 23:04
Originally posted by KarishmaB on 02 Nov 2024, 01:02.
Last edited by KarishmaB on 02 Nov 2024, 23:04, edited 1 time in total.
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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
Show more


First look at this video: https://youtube.com/shorts/xTU-BiP5w_I?feature=shared

When we add the same positive number to both x and y of a fraction x/y, the fraction goes towards 1. As it goes towards 1, the distance between every subsequent fraction will keep decreasing (since the distance to 1 is limited)

So this is how the numbers will be placed on a number line for I. 9/10, 10/11, 11/12, 12/13, 13/14

9/10 ------------- 10/11--------- 11/12 ------ 12/13 --- 13/14 -- 1 -------

Median is 11/12 but mean cannot be 11/12 because deficit is more than the excess.
The concept of deviations from mean is useful here: https://anaprep.com/arithmetic-usefulness-of-deviations/

So mean < median


For II. 10/9, 11/10, 12/11, 13/12, 14/13, the reverse will happen

--------- 1 ---- 14/13 ----- 13/12 ------- 12/11 ---------- 11/10 ------------- 10/9

Here median is 12/11 but mean will be greater because excess is more than deficit so mean > median


and for III. 6/10, 7/10, 8/10, 9/10, 10/10 are equally spaced so mean = median


Answer (A)

Also Question 3 in this video is a very similar question: https://youtu.be/vtz0-Zbcg7M
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For which of the following options is the average (arithmetic mean) of 02 Nov 2024, 04:03
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Thank you . Soo elegant







KarishmaB
MathRevolution
[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


First look at this video: https://youtube.com/shorts/xTU-BiP5w_I?feature=shared

When we add the same positive number to both x and y of a fraction x/y, the fraction goes towards 1. As it goes towards 1, the distance between every subsequent fraction will keep decreasing (since the distance to 1 is limited)

So this is how the numbers will be placed on a number line for I. 9/10, 10/11, 11/12, 12/13, 13/14

9/10 ------------- 10/11--------- 11/12 ------ 12/13 --- 13/14 -- 1 -------

Median is 11/12 but mean cannot be 11/12 because deficit is more than the excess.
The concept of deviations from mean is useful here: https://anaprep.com/arithmetic-usefulness-of-deviations/

So mean < median


For II. 10/9, 11/10, 12/11, 13/12, 14/13, the reverse will happen

--------- 1 ---- 14/13 ----- 13/12 ------- 12/11 ---------- 11/10 ------------- 10/9

Here median is 12/11 but mean will be greater because excess is more than deficit so mean > median


and for III. 6/10, 7/10, 8/10, 9/10, 10/10 are equally spaced so mean = median


Answer (A)
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For which of the following options is the average (arithmetic mean) of 05 Nov 2025, 02:37
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