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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

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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
1
2
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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Posts: 2823
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
1
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.

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

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26 Nov 2018, 10:35
I have a doubt.

In each of the cases whether we consider the value whose square root we are taking as 9, 10, or 8, can't the actual square root be either positive or negative? As a result, we cannot ascertain whether any of the values from amongst the options given (-1, 0, or +1) will for sure provide an end result that is a positive number.

Is there something I am missing here?
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Joined: 25 Jun 2017
Posts: 12
Re: The value of −3 + √(9−k) is positive for which of the following values  [#permalink]

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26 Nov 2018, 11:03
B
The number is negative when k is 0 or greater than 1.
K has to be negative.

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Re: The value of −3 + √(9−k) is positive for which of the following values   [#permalink] 26 Nov 2018, 11:03
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