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The value of −3 + √(9−k) is positive for which of the following values

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The value of −3 + √(9−k) is positive for which of the following values  [#permalink]

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New post 14 Sep 2017, 05:09
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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

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The value of −3 + √(9−k) is positive for which of the following values  [#permalink]

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New post 14 Sep 2017, 05:09
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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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The value of −3 + √(9−k) is positive for which of the following values  [#permalink]

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New post 14 Sep 2017, 06:44
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


For the expression to be positive , \(\sqrt{9−k}\) should return a value greater than 3
It will be true only when k<0
=> k=-1

Answer B
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Re: The value of −3 + √(9−k) is positive for which of the following values  [#permalink]

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New post 14 Sep 2017, 08:21
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


As per the question \(−3 + \sqrt{9−k}>0\) or \(\sqrt{9−k}>3\). Squaring both sides we get
\(9-k>9\). Hence \(k<0\). From the given values only \(-1\) satisfies this condition

Option B
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Re: The value of −3 + √(9−k) is positive for which of the following values  [#permalink]

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New post 16 Sep 2017, 07:29
1
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


We can analyze each Roman numeral:

I. -1

-3 + √(9 - (-1))

-3 + √10

-3 + 3.2 is positive.

II. 0

-3 + √(9 - 0)

-3 + √9

-3 + 3 is NOT positive.

III. 1

-3 + √(9 - 1)

-3 + √8

-3 + 2.8 is NOT positive.

Alternate Solution:

-3 + √(9 - k) > 0

√(9 - k) > 3

9 - k > 9

-k > 0

k < 0

Of the choices, only Roman numeral I, for which k = -1, satisfies the requirement for the value of k.

Answer: B
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Re: The value of −3 + √(9−k) is positive for which of the following values &nbs [#permalink] 16 Sep 2017, 07:29
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