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please give me the reasoning

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please give me the reasoning

by Sharms » Wed Dec 12, 2012 8:08 pm
m just starting here... can anyone pls help wht strategy to use in this type of ques... or similar ques... m trying picking numbers...but i keep doubting myself... pls help.

If x is an integer and 9<x^2<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
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by puneetkhurana2000 » Wed Dec 12, 2012 9:13 pm
The x^2 will always be positive whether x is negative or positive, so both -9 and +9 satisfies the inequality, Max(x) - Min(x) = 9-(-9) = 18.

The other method is x^2 - 9 > 0 will result in x > 3 or x < -3

Similarly x^2 - 99 < 0 will result in x > -√99 or x < √99 ....as x is an integer we can safely write x >= -9 or x <= 9

Combining both we will get -9 <= x < -3 and 3 < x <= 9

So, Max(x) - Min(x) = 9-(-9) = 18.
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