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# Which of the following statements must be true about the average

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Re: Which of the following statements must be true about the average [#permalink]
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Bunuel wrote:
Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.

A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III

NEW question from GMAT® Official Guide 2019

(PS00984)

Ans is E.

It is the property of consecutive number :
For every n consecutive integer, when n is an odd integer
a) The average & median is always an integer.
b) The median always equals the average.

Thanks !!
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Re: Which of the following statements must be true about the average [#permalink]
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Let 5 Consecutive integers be: 1, 2, 3, 4, 5

Mean=(1+2+3+4+5)/5=3
Median= 3
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Re: Which of the following statements must be true about the average [#permalink]
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5 consecutive integer - a, a+1, a+2, a+3, a+4
Avg = (5a+10)/5 = a+2
Median = a+2
Median = avg
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Re: Which of the following statements must be true about the average [#permalink]
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Bunuel wrote:
Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.

A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III

For a set of 5 consecutive integers, the median = average. Furthermore, both the mean and the median are one of the given integers.

For example:

1, 2, 3, 4, 5

Average = 15/5 = 3 = median.

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Re: Which of the following statements must be true about the average [#permalink]
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Hi Bunuel,
What if the consecutive numbers are both positive and negative. If we consider following case:

-1, 0, 1, 2, 3

In this case the Median 1; but the average is 2.5

How do we know that this question is asking only about "positive integers"?

Warm Regards,
FANJ
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Re: Which of the following statements must be true about the average [#permalink]
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FANewJersey wrote:
Hi Bunuel,
What if the consecutive numbers are both positive and negative. If we consider following case:

-1, 0, 1, 2, 3

In this case the Median 1; but the average is 2.5

How do we know that this question is asking only about "positive integers"?

Warm Regards,
FANJ

All options are true no matter which five consecutive integers you pick.

The average of -1, 0, 1, 2, 3 is not 2.4 it's 1: (-1 + 0 + 1 + 2 + 3)/5 = 5/5 = 1.
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Re: Which of the following statements must be true about the average [#permalink]
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: Which of the following statements must be true about the average [#permalink]
Bunuel wrote:
Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.

A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III

NEW question from GMAT® Official Guide 2019

(PS00984)

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Re: Which of the following statements must be true about the average [#permalink]
If the distribution is symmetric then the mean is equal to the median
Consecutive numbers is a symmetric distribution
The quantity of terms is odd, so the median is a number in the sample set.
As the median is equal to the mean so the mean is a number in the sample set.
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Re: Which of the following statements must be true about the average [#permalink]
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