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If the range of the six numbers 4,3,14,7,10 and x is 12, what is the

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If the range of the six numbers 4,3,14,7,10 and x is 12, what is the [#permalink]

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If the range of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?

(A) 0
(B) 2
(C) 12
(D) 13
(E) 15
[Reveal] Spoiler: OA

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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the [#permalink]

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monirjewel wrote:
If the range of the six numbers 4, 3, 14, 7, 10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15


The range of a set is the difference between the largest and smallest elements of a set.

Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.

The the difference between the greatest possible value of x and least possible value of x is 15-2=13.

Answer: D.
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the [#permalink]

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New post 13 Nov 2010, 12:16
X must either be 15 or 2 to produce a range of 12.

D. +1
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the [#permalink]

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New post 15 Nov 2010, 02:53
nice question. As in international student, the word "range" didnt say anything to me before that.

Thanks.

+1 from me.
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the [#permalink]

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monirjewel wrote:
If the range of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15


Range= Greatest value- least value

Range= 12

For the greatest value of x= 15, range will be 15-3= 12

For the least value of x= 2, the range will be 14-2= 12

so the difference between greatest and least value= 15-2= 13

D is the answer
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the [#permalink]

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monirjewel wrote:
If the range of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15


The Range of the numbers without x is 14-3 = 11......
Now x changes the range to 12....


so x can be 1 greater than largest value or 1 lesser than eth smallest value....
so Range = 11+1+1 = 13
D
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the [#permalink]

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monirjewel wrote:
If the range of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15


We are given that the range of the six numbers 4,3,14,7,10, and x is 12.

If x is the largest value in the list, then 3 would be the smallest number in the list. Since the range is 12, the largest number that x could be is 3 + 12 = 15.

If x is the smallest value in the list, then 14 would be the largest number in the list. Since the range is 12, the smallest number that x could be is 14 - 12 = 2.

Thus, the difference between the largest and smallest possible values of x is 15 - 2 = 13.

Answer: D
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the [#permalink]

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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the   [#permalink] 08 Dec 2017, 21:07
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