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If the range of the six positive integers 4,3,14,7,10 and x is 14

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If the range of the six positive integers 4,3,14,7,10 and x is 14  [#permalink]

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New post 31 Dec 2018, 15:10
4
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

22% (02:03) correct 78% (01:21) wrong based on 52 sessions

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If the range of the six positive numbers 4,3,14,7,10 and x is 14, what is the difference between the greatest possible value of x and least possible value of x?

(A) 0
(B) 11
(C) 14
(D) 17
(E) 20

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If the range of the six positive integers 4,3,14,7,10 and x is 14  [#permalink]

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New post 31 Dec 2018, 21:09
Mahmoudfawzy83 wrote:
If the range of the six positive numbers 4,3,14,7,10 and x is 14, what is the difference between the greatest possible value of x and least possible value of x?

(A) 0
(B) 11
(C) 14
(D) 17
(E) 20


For all those who have answered wrong, the importance of reading the question for minor details is very important, as POSITIVE word here
The numbers can be written in an ascending order as 3,4,7,10, and 14, and X can fit in somewhere in the series..
Now the range is 14, means difference between the largest and smallest term is 14
As the range without x is 14-3=11, x will be either the largest or smallest
1) let 14 be the highest then smallest will be 14 - 14=0.
This means x is 0, but it is given that X is positive number so X>0.... Not possible
2) let 3 be the minimum, then largest will be 3+14=17
So X is 17..

Thus, the only possible way the range is 14 is 3, 4, 7, 10, 14, 17
So X can be only 17..
Minimum value of x = Maximum value of x=17

Answer = 17-17=0

A
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Re: If the range of the six positive integers 4,3,14,7,10 and x is 14  [#permalink]

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New post 02 Jan 2019, 04:19

Solution


Given:
    • Range of six positive i=numbers, {4, 3, 14, 7, 10, x} = 14

To find:
    • The difference between maximum and minimum possible values of x

Approach and Working:
    • If x > 14, then x is the maximum value of the set
    • And, range will be x – 3 = 14
      o Implies, x = 17

    • If x < 14, then 14 is the maximum value of the set
    • And, for x to be minimum, x must be the minimum value of the set. So, range will be 14 – x = 14
      o Implies, x = 0
      o But we know x is positive. So, this case is not valid

Thus, x can take only one value = 17

    • Therefore, maximum value – minimum value = 17 – 17 = 0

Hence, the correct answer is Option A

Answer: A

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Re: If the range of the six positive integers 4,3,14,7,10 and x is 14   [#permalink] 02 Jan 2019, 04:19
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If the range of the six positive integers 4,3,14,7,10 and x is 14

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