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# Which of the following is always true? (I) The average (arithmetic me

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Which of the following is always true? (I) The average (arithmetic me  [#permalink]

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15 Nov 2016, 01:58
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Which of the following is always true?

(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.

(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.

(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.

A. I and III
B. I, II and III
C. II
D. I and II
E. None

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Which of the following is always true? (I) The average (arithmetic me  [#permalink]

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Updated on: 15 Nov 2016, 03:47
Bunuel wrote:
Which of the following is always true?

(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.

(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.

(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.

A. I and III
B. I, II and III
C. II
D. I and II
E. None

IMO B

The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(-10+-9+-8+-7+-6)/5 = -40/5 = -8 same as (-10+-6)/2 = -8 True

The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(2+3+4+5)/4 = 14/4 same as (5+2)/2 = 7/2 always true
(1+2+3+4)/4 = 10/4 same as (4+1)/2 = 5/2

The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
(3+4+5+6+7)/5 = 5 same as (7+3)/2 = 5 True

Hence B

Originally posted by Vinayak Shenoy on 15 Nov 2016, 02:32.
Last edited by Vinayak Shenoy on 15 Nov 2016, 03:47, edited 3 times in total.
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Re: Which of the following is always true? (I) The average (arithmetic me  [#permalink]

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15 Nov 2016, 03:42
Bunuel wrote:
Which of the following is always true?

(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.

(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.

(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.

A. I and III
B. I, II and III
C. II
D. I and II
E. None

Let's call 5 consecutive integers are $$k, k+1, k+2, k+3, k+4$$

(I) The average of 5 consecutive is $$\frac{k+(k+1) + (k+2)+(k+3)+(k+4)}{5}=\frac{5k+10}{5}=k+2$$
The average of the largest and the smallest is $$\frac{k+ (k+4)}{2}=\frac{2k+4}{2}=k+2$$
=> True

(II) The average of 4 consecutive is $$\frac{k+(k+1) + (k+2)+(k+3)}{4}=\frac{4k+6}{4}=k+\frac{3}{2}$$
The average of the largest and the smallest is $$\frac{k+ (k+3)}{2}=\frac{2k+3}{2}=k+\frac{3}{2}$$
=> true

(II) The average of 5 consecutive is $$\frac{k+(k+1) + (k+2)+(k+3)+(k+4)}{5}=\frac{5k+10}{5}=k+2$$
The average of the largest and the smallest is $$\frac{k+ (k+4)}{2}=\frac{2k+4}{2}=k+2$$
=> true

OA is B
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Which of the following is always true? (I) The average (arithmetic me  [#permalink]

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15 Nov 2016, 03:43
Vinayak Shenoy wrote:
Bunuel wrote:
Which of the following is always true?

(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.

(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.

(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.

A. I and III
B. I, II and III
C. II
D. I and II
E. None

IMO A

The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(-10+-9+-8+-7+-6)/5 = -40/5 = -8 same as (-10+-6)/2 = -8 True

The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(2+3+4+5)/4 = 7/4 not same as (5+2)/2 = 7/2 Not always true
(1+2+3+4)/4 = 10/4 same as (4+1)/2 = 5/2

The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
(3+4+5+6+7)/5 = 5 same as (7+3)/2 = 5 True

Hence A

(2+3+4+5)/4 = 14/4=7/2
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Re: Which of the following is always true? (I) The average (arithmetic me  [#permalink]

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15 Nov 2016, 03:47
nguyendinhtuong wrote:
Vinayak Shenoy wrote:
Bunuel wrote:
Which of the following is always true?

(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.

(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.

(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.

A. I and III
B. I, II and III
C. II
D. I and II
E. None

IMO A

The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(-10+-9+-8+-7+-6)/5 = -40/5 = -8 same as (-10+-6)/2 = -8 True

The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(2+3+4+5)/4 = 7/4 not same as (5+2)/2 = 7/2 Not always true
(1+2+3+4)/4 = 10/4 same as (4+1)/2 = 5/2

The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
(3+4+5+6+7)/5 = 5 same as (7+3)/2 = 5 True

Hence A

(2+3+4+5)/4 = 14/4=7/2

Thanks for the correction
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Which of the following is always true? (I) The average (arithmetic me  [#permalink]

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10 Apr 2017, 23:22
1
Rule: Average of consecutive integers is equal to the average of the largest and the smallest integer in the list.

This question is just trying to confuse using different terms such as positive consecutive integers, negative consecutive integers, ......
(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.

(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.

(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
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Which of the following is always true? (I) The average (arithmetic me  [#permalink]

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10 Apr 2017, 23:29
1

Shiv2016 posted above =>

For any Evenly spaced set => MEAN = MEDIAN = AVERAGE of the FIRST AND THE LAST TERM.

Evenly spaced set examples => consecutive integers,consecutive evens/odds, consecutive multiples of any integer K etc.

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