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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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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
[Reveal] Spoiler: OA

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

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14 Sep 2017, 05:09
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Expert's post
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

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

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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

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

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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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16 Sep 2017, 07:29
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.

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