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# What is the range of the dataset of numbers comprised entirely of {1,

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Re: What is the range of the dataset of numbers comprised entirely of {1, [#permalink]
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Bunuel wrote:
What is the range of the dataset of numbers comprised entirely of {1, 6, x, 17, 20, y} if all terms in the dataset are positive integers and xy = 18?

(A) 16
(B) 17
(C) 18
(D) 19
(E) It cannot be determined from the information given.

Let's examine the two extreme cases

Since x and y are positive integers, the SMALLEST difference between the two numbers occurs when x and y are 3 and 6.
Conversely, the GREATEST difference between the two numbers occurs when x and y are 1 and 18.

If x and y are 3 and 6, the set becomes {1, 6, 3, 17, 20, 6}, so the range = 20 - 1 = 19
If x and y are 1 and 18, the set becomes {1, 6, 1, 17, 20, 18}, so the range = 20 - 1 = 19

So the range is most definitely 19

Cheers,
Brent
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Re: What is the range of the dataset of numbers comprised entirely of {1, [#permalink]
Bunuel wrote:
What is the range of the dataset of numbers comprised entirely of {1, 6, x, 17, 20, y} if all terms in the dataset are positive integers and xy = 18?

(A) 16
(B) 17
(C) 18
(D) 19
(E) It cannot be determined from the information given.

given that xy=18 ; 1,18 ; 2,9 ; 3,6
considering all the possible values of xy ; range will be 20-1 ; 19
IMO D
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Re: What is the range of the dataset of numbers comprised entirely of {1, [#permalink]
Bunuel wrote:
What is the range of the dataset of numbers comprised entirely of {1, 6, x, 17, 20, y} if all terms in the dataset are positive integers and xy = 18?

(A) 16
(B) 17
(C) 18
(D) 19
(E) It cannot be determined from the information given.

We see that (x, y) can be (1, 18), (2, 9), (3, 6) (6, 3), (9, 2) or (18, 1). However, regardless of which ordered pair (x, y) is, the range is 20 - 1 = 19.

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Re: What is the range of the dataset of numbers comprised entirely of {1, [#permalink]
Bunuel wrote:
What is the range of the dataset of numbers comprised entirely of {1, 6, x, 17, 20, y} if all terms in the dataset are positive integers and xy = 18?

(A) 16
(B) 17
(C) 18
(D) 19
(E) It cannot be determined from the information given.

xy=18

Possible values of x and y (in any order) = (1,18) (2,9) (3,6)

In all the cases the lowest and highest value of set remains 1 and 20 resp.

Range = 20-1 =19

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Re: What is the range of the dataset of numbers comprised entirely of {1, [#permalink]
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Re: What is the range of the dataset of numbers comprised entirely of {1, [#permalink]
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