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

BTGmoderatorLU wrote: ↑

Tue Mar 31, 2020 1:36 am

Source: Manhattan Prep

What is the range of the dataset of numbers comprised entirely {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

The OA is D

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

BTGmoderatorLU wrote: ↑

Tue Mar 31, 2020 1:36 am

Source: Manhattan Prep

What is the range of the dataset of numbers comprised entirely {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

The OA is D

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.

Answer: D