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Math Expert V
Joined: 02 Sep 2009
Posts: 60460
Which of the following statements must be true about the average (arit  [#permalink]

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16 00:00

Difficulty:   5% (low)

Question Stats: 86% (00:42) correct 14% (00:44) wrong based on 929 sessions

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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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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3203
Which of the following statements must be true about the average (arit  [#permalink]

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8

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.

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##### General Discussion
Manager  P
Joined: 01 Aug 2017
Posts: 220
Location: India
GMAT 1: 500 Q47 V15
GPA: 3.4
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Re: Which of the following statements must be true about the average (arit  [#permalink]

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1
1
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 !!
Senior Manager  P
Joined: 13 Feb 2018
Posts: 496
GMAT 1: 640 Q48 V28
Re: Which of the following statements must be true about the average (arit  [#permalink]

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2
Let 5 Consecutive integers be: 1, 2, 3, 4, 5

Mean=(1+2+3+4+5)/5=3
Median= 3
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4214
Re: Which of the following statements must be true about the average (arit  [#permalink]

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1
Top Contributor
1
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

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

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Intern  B
Joined: 08 Oct 2017
Posts: 30
Re: Which of the following statements must be true about the average (arit  [#permalink]

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1
5 consecutive integer - a, a+1, a+2, a+3, a+4
Avg = (5a+10)/5 = a+2
Median = a+2
Median = avg
Manager  S
Joined: 07 Feb 2017
Posts: 174
Re: Which of the following statements must be true about the average (arit  [#permalink]

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x-2,x-1,x,x+1,x+2

average=x
median=x

Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806
Re: Which of the following statements must be true about the average (arit  [#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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Intern  B
Joined: 01 May 2017
Posts: 33
Re: Which of the following statements must be true about the average (arit  [#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
Math Expert V
Joined: 02 Sep 2009
Posts: 60460
Re: Which of the following statements must be true about the average (arit  [#permalink]

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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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Intern  B
Joined: 14 Dec 2017
Posts: 3
Re: Which of the following statements must be true about the average (arit  [#permalink]

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Take 2 different sets of consecutive integers.

Example: integers 1-5 and 6-10

All given statements apply to each set

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_________________ Re: Which of the following statements must be true about the average (arit   [#permalink] 24 Oct 2019, 14:40
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