Quant question on list/ranges: Practice test 1, Quant II, Q7

[justin.lam06]

List L consists of the numbers 1, √2, x and x^2, where x > 0 and the range of numbers in List L is 4.

Quant A
x

Quant B
2

I see how x could be 5 if the bottom part of the range is 1, but can you clarify how to know for certain that the answer isn't D (or C, which is what I put)?

[n00bpron00bpron00b]

I think the answer is "A"

If x = Sqrt 5 , x^2 = 5
5 - 1 = 4

x (sqrt 5) > 2

Also, if we try to counter prove ;

If x = 2 : x^2 = 4 : Range = 4 - 1 = 3 (so "C" is out)

To prove Col A < Col B

Let us consider the max possible value for "X" - 1.9
x^2 = 3.61

3.61 - 1 not equal to 4

So "A" is greater.

What is the answer given in the book ?

[tommywallach]

Hey Justin,

X can't be 5. If x were 5, then x^2 would be 25, and the range of the data would be 24.

So the biggest x could be is rt. 5. And it turns out that's ALL that x can be. Because we can't create a range of 4 by going from 1 to -3, because there's no way for either x or x^2 to be -3 (If x is -3, then x^2 is 9, and the range is wrong; and x^2 can't be negative 3, because nothing squared can be negative).

So the answer is indeed A.

-t

P.S. Also, you seem to be mistaking range. If x is 2, then x^2 is 4, and the range of the set is actually 3.