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

BTGmoderatorDC 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

OA D

Source: Official Guide

Already replied: https://www.beatthegmat.com/og-17-probl ... 94147.html

Hope this helps!

-Jay
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BTGmoderatorDC 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

OA D

Source: Official Guide

If we examine the KNOWN values in ascending order, we have {3, 4, 7, 10, 14}
These numbers have a range of 11 (since 14 - 3 = 11)

In order the set to have a range of 12, there are two possible values for x:

case a: x = 2, in which case the set is {2, 3, 4, 7, 10, 14}
case b: x = 15, in which case the set is {3, 4, 7, 10, 14, 15}

So, the difference in x-values = 15 - 2 = 13

Answer: D

RELATED VIDEO
- Range and Standard Deviation: https://www.gmatprepnow.com/module/gmat ... /video/806

Cheers,
Brent

BTGmoderatorDC 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

OA D

Source: Official Guide

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 12 = x - 3 , or x = 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 - x = 12, so x = 2.

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

Answer: D