Bunuel wrote:
The value of \(−3 + \sqrt{9−k}\) is positive for which of the following values of k ?
I. -1
II. 0
III. 1
A. None
B. I only
C. II only
D. III only
E. I and III
Given Expression = \(-3 + \sqrt{9 - k}\)
If k = 1
Given Expression = \(-3 + \sqrt{8}\)
We know that \(\sqrt{9} = 3\). So \(\sqrt{8}\) will be a little less than 3.
Given Expression = -3 + Something less than 3 = A little negative quantity
If k = 0
Given Expression = \(-3 + \sqrt{9}\)
Given Expression = \(-3 + 3\) = 0 = A non-negative non-positive quantity
If k = -1
Given Expression = \(-3 + \sqrt{10}\)
We know that \(\sqrt{9} = 3\). So \(\sqrt{10}\) will be a little more than 3.
Given Expression = -3 + Something more than 3 = A little positive quantity
It is positive only for k = -1
Answer B.
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Karishma
Veritas Prep GMAT Instructor
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