I'm happy to help.guerrero wrote:17 , x , 35 ,12, y
Is the range of the 5 numbers in the list above less than 30 ?
1)6<=x<=20
2)y=2x
First of all, just a reminder --- range = (max) - (min). See:
https://magoosh.com/gmat/2012/common-gma ... tatistics/
Statement #1: just tells us about x, so y could be anything. Insufficient.
Statement #2:
If x = 10, y = 20, then the ordered list is {10, 12, 17, 30, 35}, with a range of 25, less than 30.
If x = 100, y = 200, then the ordered list is {12, 17, 35, 100, 200}, with a range of 190, more than 30.
Different choices consistent with this single statement lead to different answers of the prompt question, so this statement, by itself, is insufficient.
The real crux of the problem is --- what happens with combined statements?
Combined statements:
6<=x<=20 and y = 2x. Well, let's check the endpoints.
x = 6, y = 12: then then the ordered list is {6, 12, 12, 17, 35}, with a range of 29, less than 30.
From x = 6 to x = 17, the range gets smaller than this --- minimum number is larger than 6, and the maximum stays at 35. Once x > 17, the range will increase again. Let's try the other endpoint.
x = 20, y = 40: then then the ordered list is {12, 17, 20, 35, 40}, with a range of 28, less than 30.
Thus, for every value in that allowed range for x, the complete list has a range less than 30, and we can give a definitive answer of "YES" to the prompt question. Together, both statements are sufficient.
Answer = [spoiler](C)[/spoiler]
Does all this make sense?
Mike
