A Range Question

[nareshchowdary28]

Hi Guys,

I hava a question here about ranges.

List L consists of the numbers 1, root2, x, x^2, where x>0 and the range of the list L is 4

Quantity A

x

Quantity B

2

My answer is D
but actual answer is A

I know that range = max - min which x^2-1 = 4 and x= root5

but my question is there are lists like where the elements are not in order, so you need to make it into order and find the range.

and here how do they conclude that x > 1 why not 0< x <1 in that case x^2 is even smaller than other elements. so how did they assumed that max is x^2 and min is 1..?

Please help me.

[jgabry]

Hi Naresh,

Even though we can't assume the numbers in the list are in order, in this case if x>0 and the list contains only 1, root2, x, x^2 then x must be greater than 2 if the range is 4. it would be impossible for the greatest number in the list minus the smallest number to equal 4 if x were less than or equal to 2.

if x = 2 then the largest number is x^2 = 4 and the smallest number is 1, so the range is 4 - 1 = 3. this doesn't work. if x < 2 then we have an even smaller range.

so we don't need to assume the numbers are in ascending to conclude that they are indeed in order here. but, like you said, there can definitely be other problems in which the order shown does not turn out to represent the numbers in their proper positions in the list.

i hope that helps!

[nareshchowdary28]

Thanks Man,

Yes, That helps.

[tommywallach]

Hey Guys,

Great explanation from jgabry (as usual). Oftentimes, the GRE won't be able to do something that will make the question too easy. For example, often putting a list in order will give away the question (if the question is something like "Which of these is biggest"). Similarly, geometry figures CAN'T be drawn to scale, or else you could get the answer just by looking at it.

Also, as a theoretical idea, always be wary of picking answer choice D whenever the question seems to be PUSHING you towards D. On this question, it's clear we don't know what x is, and that might make us think that we can't know whether it's bigger than 2. If I were guessing on this question, I would pick something other than D, because it seems to obvious. It may sound crazy, but you can pick up a lot of questions on this test by thinking on the meta, test-writing level like this.

Good luck!

-t