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# If c is a constant and x is a variable, what is the value of c in the

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Intern
Joined: 21 Feb 2018
Posts: 23
If c is a constant and x is a variable, what is the value of c in the  [#permalink]

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20 Jul 2018, 08:57
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78% (01:10) correct 22% (01:45) wrong based on 67 sessions

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If c is a constant and x is a variable, what is the value of c in the equation x^2 + 24x + c = 0?

(1) The equation x^2 + 24x + c = 0 has exactly one distinct solution.
(2) C is less than or equal to 144
Manager
Joined: 09 Jun 2014
Posts: 248
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Re: If c is a constant and x is a variable, what is the value of c in the  [#permalink]

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20 Jul 2018, 09:30
1
My approach is as follows .

Let each root of the above quadratic equation be a.
Therefore ,sum of roots = 2a=-24/1..this implies a=-12

Now product of roots is a*a =C

We know a so we can get C wgich is equal to a^2

Statement 2: clearly insufficient

We know disriminant is always >=0
B^2 -4ac >=0

Therefore

576-4ac >=0
C<149

Many solution possible

So clearly A is the right answer .

Press Kudos if it helps !!

Posted from my mobile device
Intern
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Re: If c is a constant and x is a variable, what is the value of c in the  [#permalink]

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22 Jul 2018, 14:48
If c is a constant and x is a variable, what is the value of c in the equation x^2 +24x +c= 0?
1. The equation x^2+ 24x+ c= 0 has exactly one distinct solution.
2. 2. C is less than or equal to 144
VP
Status: Learning stage
Joined: 01 Oct 2017
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WE: Supply Chain Management (Energy and Utilities)
Re: If c is a constant and x is a variable, what is the value of c in the  [#permalink]

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22 Jul 2018, 16:58
1
franteraoka wrote:
If c is a constant and x is a variable, what is the value of c in the equation x^2 +24x +c= 0?
1. The equation x^2+ 24x+ c= 0 has exactly one distinct solution.
2. c is less than or equal to 144

Question stem:- c=?

Statemement-1:- The equation x^2+ 24x+ c= 0 has exactly one distinct solution.
For a quadratic equation of the form, $$ax^2+bx+c=0$$ to have an unique or one distinct solution, we have Discriminant is Zero or $$b^2-4ac-0$$

So, we have $$Discriminant={24}^2-4*1*c=0$$
So, the value of 'c' can be determined. (No need to solve the equation)
Sufficient.

Statement-2:- $$c\leq{144}$$

The value of 'c' can be any number with the above constraint.

Insufficient.

Ans. (A)
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Re: If c is a constant and x is a variable, what is the value of c in the  [#permalink]

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22 Jul 2018, 19:20
1
To split the middle term in an equation so that there is only 1 unique solution,
$$ax + by + c = 0$$

$$b$$ should be splitted as $$(\frac{b}{2})y + (\frac{b}{2})y$$
So c would be equal to $$(\frac{b}{2})^2$$

Here $$b = 24$$
$$(\frac{b}{2}) = 12$$
$$c = 12^2 = 144$$

Therefore, A is sufficient.
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Director
Joined: 27 May 2012
Posts: 791
Re: If c is a constant and x is a variable, what is the value of c in the  [#permalink]

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19 Aug 2018, 08:30
franteraoka wrote:
If c is a constant and x is a variable, what is the value of c in the equation x^2 +24x +c= 0?
1. The equation x^2+ 24x+ c= 0 has exactly one distinct solution.
2. 2. C is less than or equal to 144

Dear Moderator,

Came across this question, while doing DS section of Algebra, seems as though by mistake OA is visible out side the spoiler , making it futile for us to put effort into solving it. Hope you will look into this . Thank you.
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- Stne
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Posts: 123
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Re: If c is a constant and x is a variable, what is the value of c in the  [#permalink]

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19 Aug 2018, 08:55
Classic Quadratic Equation Question!
I don't see these that often, nice question.
franteraoka wrote:
If c is a constant and x is a variable, what is the value of c in the equation x^2 +24x +c= 0?
1. The equation x^2+ 24x+ c= 0 has exactly one distinct solution.
2. 2. C is less than or equal to 144

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I also invite you to critique and help me find flaws in my modus operandi. Thanks!
Director
Joined: 27 May 2012
Posts: 791
Re: If c is a constant and x is a variable, what is the value of c in the  [#permalink]

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22 Dec 2018, 12:40
franteraoka wrote:
If c is a constant and x is a variable, what is the value of c in the equation x^2 +24x +c= 0?
1. The equation x^2+ 24x+ c= 0 has exactly one distinct solution.
2. 2. C is less than or equal to 144

Dear Moderator,
Can we remove the OA which is outside the spoiler, and also format statement 2 properly, Thank you.
_________________
- Stne
Re: If c is a constant and x is a variable, what is the value of c in the   [#permalink] 22 Dec 2018, 12:40
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# If c is a constant and x is a variable, what is the value of c in the

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