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Set 'X' contains 9 consecutive natural numbers. If two numbers are ran

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Director
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Set 'X' contains 9 consecutive natural numbers. If two numbers are ran  [#permalink]

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New post 14 Jun 2019, 02:05
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A
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Difficulty:

  65% (hard)

Question Stats:

42% (02:00) correct 58% (01:56) wrong based on 36 sessions

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Set 'X' contains 9 consecutive natural numbers. If two numbers are randomly picked from the set, what is the probability that the average of all the numbers that are left is the same as that of Set 'X'?

A. 1/36
B. 1/18
C. 1/12
D. 1/9
E. 1/6
Director
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Re: Set 'X' contains 9 consecutive natural numbers. If two numbers are ran  [#permalink]

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New post 14 Jun 2019, 03:41
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nick1816 wrote:
Set 'X' contains 9 consecutive natural numbers. If two numbers are randomly picked from the set, what is the probability that the average of all the numbers that are left is the same as that of Set 'X'?

A. 1/36
B. 1/18
C. 1/12
D. 1/9
E. 1/6


Let’s take the set as {1, 2, 3, 4, 5, 6, 7, 8, 9}

Average = 5 [In AP series Mean = Median]

Total way of selecting 2 = 9c2 = 36

Favourable is picking 2 numbers which would add upto 10. [Only then the average of the remaining 7 terms would be 5 as 35/7 = 5]

So, favourable pairs = (1, 9), (2, 8), (3, 7), (4, 6)

Required Probability = 4/36 = 1/9

IMO Option D

Pls Hit kudos if you like the solution

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Re: Set 'X' contains 9 consecutive natural numbers. If two numbers are ran  [#permalink]

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New post 09 Aug 2019, 18:01
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To maintain the arithmetic mean, have the numbers in ascending order and take a pair equidistant from the mean.
{1, 2, 3, 4, 5, 6, 7, 8, 9}

First number can be anything other than 5
8/9

Second number must be its match, 1/8

8/9*1/8=1/9

D
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Re: Set 'X' contains 9 consecutive natural numbers. If two numbers are ran   [#permalink] 09 Aug 2019, 18:01
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Set 'X' contains 9 consecutive natural numbers. If two numbers are ran

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