Bunuel wrote:
If x is an integer and \(9 \lt x^2 \lt 99\), then what is the value of maximum possible value of \(x\) minus minimum possible value of \(x\)?
A. \(5\)
B. \(6\)
C. \(7\)
D. \(18\)
E. \(20\)
Hi
Bunuel,
I am not sure if I am satisfied with the explanations provided (not saying that the explanations provided here are incorrect, I am sure they are correct).
I feel I still have some gaps in clarity. I found my reasoning to correct answer as the following and please correct me if I am wrong somewhere.
So we arrive at x having the following as the values after taking the square root of all the sides
√9 = ±3 and √99 ≅ ±9.95. This produces two ranges for both sides when considering both sides independently.
-3 > x > 3 and -9.95 < x < 9.95
When we plot these two ranges on a number line then we get a maximum integer value of x = 9 and a minimum value of x = -9
So since the question asked the difference between Max and Min, hence,
(Max Value of x) - (Min Value of x) = 9 - (-9) = 9 + 9 = 18
So I have a couple of questions
1. Is my reasoning and thought process correct?
2. When we are given a question where the variable has a range on both sides like we have in this question, can I consider both sides independently and derive the range and then look at both ranges together on the number line?
Thanks,
Sud