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Which of the following statements must be true about the average (arit

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Which of the following statements must be true about the average (arit  [#permalink]

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New post 20 Jun 2018, 00:23
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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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Which of the following statements must be true about the average (arit  [#permalink]

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New post 20 Jun 2018, 02:21
5

Solution



Given:
    • We are given 5 consecutive integers.

To find:
    • We need to find the average and median of 5 consecutive integers.

Approach and Working:

Let us assume that 5 consecutive numbers are: a-2, a-1, a, a+1, a+2.
    • Thus, the average of the 5 integers = \(\frac{(a-2)+ (a-1) + (a) + (a+1) + (a+2)}{5}\)= \(\frac{5a}{5}\)= a
    • And their median= a.

Thus, average and median both are the same and are one of the integers among 5 consecutive integers.

Hence, option E is the correct answer.

Answer: E
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Re: Which of the following statements must be true about the average (arit  [#permalink]

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New post 20 Jun 2018, 02:29
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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.

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Re: Which of the following statements must be true about the average (arit  [#permalink]

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New post 20 Jun 2018, 03:29
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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 (arit  [#permalink]

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New post 27 Jun 2018, 06:07
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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


There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}

Since consecutive integers are equally spaced, the average (mean) of this set of 5 integers will equals its median.
So, statement III is true
Check the answer choices.....ELIMINATE A, B and D

Also, since the set has an ODD number of values, the median will be the middle value (when the numbers are arranged in ascending order).
Since the set consists of INTEGERS only, and since the median equals the middle value, the median must be an integer
So, statement II is true
Check the answer choices.....ELIMINATE C

By the process of elimination, the correct answer must be E

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Re: Which of the following statements must be true about the average (arit  [#permalink]

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New post 27 Jun 2018, 06:17
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 (arit  [#permalink]

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New post 27 Jun 2018, 11:58
x-2,x-1,x,x+1,x+2

average=x
median=x

Answer E.
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Re: Which of the following statements must be true about the average (arit  [#permalink]

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New post 02 Jul 2018, 10:02
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.

Answer: E
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Re: Which of the following statements must be true about the average (arit  [#permalink]

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New post 11 Oct 2018, 03:12
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"?

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Re: Which of the following statements must be true about the average (arit  [#permalink]

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New post 11 Oct 2018, 03:23
1
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 (arit  [#permalink]

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New post 13 Oct 2018, 09:23
Take 2 different sets of consecutive integers.

Example: integers 1-5 and 6-10

All given statements apply to each set

Answer E
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Re: Which of the following statements must be true about the average (arit   [#permalink] 13 Oct 2018, 09:23
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