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Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}.

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Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}.  [#permalink]

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New post 03 Apr 2019, 02:54
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Question Stats:

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Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}. The greatest possible value of n should be how much greater than the least possible value of n, if the range of all the elements present in S is not more than 21?

    A. 12
    B. 14
    C. 15
    D. 20
    E. 21


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Re: Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}.  [#permalink]

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New post 03 Apr 2019, 10:21
Natural numbers = Positive numbers.

Range = Max value in set - Min value in set
Given, Range should not exceed 21.
Max value of n can be 22. Then range = 22-1 = 21
Min value of n can be 2 (as the numbers are distinct and 1 is already present.). Then range = 14-1 = 13.

Difference = 22-2 = 20

D is the answer.
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Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}.  [#permalink]

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New post 03 Apr 2019, 19:37
The range should not exceed 21.

Sort the elements : (1,6,7,8,12,14)---- We did not put n because n can me maximum as well as minimum so can be adjusted anywhere.

Max value of n will be 22----->>(1,6,7,8,12,14,22)---->>because then the range will be 22-1 =21 (satisfying range condition)

Min value of n will be 2-->>(Given that numbers are distinct)-->(1,2,6,7,8,12,14)--> Range 15-->(satisfying range condition)

Therefore n is 22-2=20 greater.

IMO D
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Re: Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}.  [#permalink]

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New post 04 Apr 2019, 01:29
n max= 22 ; range is 21 sufficeint
min n = 2 ;
diffrence = 22-2 ; 20
IMO D


EgmatQuantExpert wrote:
Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}. The greatest possible value of n should be how much greater than the least possible value of n, if the range of all the elements present in S is not more than 21?

    A. 12
    B. 14
    C. 15
    D. 20
    E. 21


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Re: Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}.  [#permalink]

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New post 07 Apr 2019, 06:12

Solution


Given:
In this question, we are given that
    • Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}
    • The range of all the elements present in S is not more than 21

To find:
    • The greatest possible value of n should be how much greater than the least possible value of n

Approach and Working:
Except n, we can arrange the other elements of set S, in ascending order, as 1, 6, 7, 8, 12, 14.
Now, if the range is highest possible, then the value of range = 20
    • As we already know the least value present in S is 1, if the range is 21, then it is only possible when n is the highest value element of S.
    • And the value of n = 1 + 21 = 22
    • Therefore, the highest possible value of n = 22

Again, the value of n will be least when it should be the least positive integer greater than 1.
    • Therefore, the least value of n = 2
    • Thus, the difference between the least and highest possible value of n = 22 – 2 = 20

Hence, the correct answer is option D.

Answer: D

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Re: Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}.   [#permalink] 07 Apr 2019, 06:12
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Set R contains 7 distinct natural numbers {8, 6, 14, 1, 12, n, 7}.

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