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What is the range of the dataset of numbers comprised entirely of {1, 6, x, 17, 20, y

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by BTGModeratorVI » Sat May 16, 2020 7:26 am

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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.

Answer: D
Source: Manhattan prep
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Re: What is the range of the dataset of numbers comprised entirely of {1, 6, x, 17, 20, y

by Brent@GMATPrepNow » Sun May 17, 2020 8:13 am
BTGModeratorVI wrote: ↑
Sat May 16, 2020 7:26 am
 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.

Answer: D
Source: Manhattan prep
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

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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