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If x is a non-zero integer, is x prime?

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Senior Manager
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If x is a non-zero integer, is x prime?  [#permalink]

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New post 04 Apr 2019, 10:26
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If x is a non-zero integer, is x prime?

(1) The number x is at a distance less than 2 units from the number 1.5 on the number line.

(2) The sum and product of roots of a quadratic equation ax^2+bx+c are 5 and 6 respectively.
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Re: If x is a non-zero integer, is x prime?  [#permalink]

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New post 04 Apr 2019, 19:27
Lets first analyze the question without the options:
x = non-zero integer + x = prime.

Range of x = negative + positive integers + x not equal to zero

Case 1:x is at a distance of 2 ...
Range of x = [-0.5,3.5]
Integers = 1,2,3
1 = neither prime nor composite.
Option A = not sufficient

Case 2: Sum = 5 and Product =6
For a quadratic equation ax2+bx+c, sum = -b and product =6
Thus equation: (x^2)-(5x)+6=0
Roots = 2,3
X = definitely prime
Option B is sufficient
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Re: If x is a non-zero integer, is x prime?  [#permalink]

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New post 06 Apr 2019, 01:08
mangamma wrote:
If x is a non-zero integer, is x prime?

(1) The number x is at a distance less than 2 units from the number 1.5 on the number line.

(2) The sum and product of roots of a quadratic equation ax^2+bx+c are 5 and 6 respectively.



For any quadratic equation \(ax^2+bx+c\), the sum of roots is given as \(S=\frac{-b}{a}\) and the product of roots as \(P=\frac{c}{a}\)

So how come we get to know the value of 3 unknowns from 2 equations???
Please explain.
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Re: If x is a non-zero integer, is x prime?  [#permalink]

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New post 06 Apr 2019, 05:22
Ritwick91 wrote:
mangamma wrote:
If x is a non-zero integer, is x prime?

(1) The number x is at a distance less than 2 units from the number 1.5 on the number line.

(2) The sum and product of roots of a quadratic equation ax^2+bx+c are 5 and 6 respectively.



For any quadratic equation \(ax^2+bx+c\), the sum of roots is given as \(S=\frac{-b}{a}\) and the product of roots as \(P=\frac{c}{a}\)

So how come we get to know the value of 3 unknowns from 2 equations???
Please explain.


You are absolutely right is your analysis.

The point of confusion is that you are not considering the entirety of equation.
Consider the equation as: ax^{2}+bx+c=0
Now divide the complete equation by a. The resulting equation will be: x^{2}+(b/a)x+(c/a)=0
Thus in this equation:
(b/a) = -(sum of roots)
(c/a)= product of roots

Hope this explanation clears your doubt!
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Re: If x is a non-zero integer, is x prime?  [#permalink]

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New post 06 Apr 2019, 05:34
But from here we are getting (-b/a) = 5 and (c/a) =6. Please explain how we are getting the values of a,b,c from these two equations???

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Re: If x is a non-zero integer, is x prime?  [#permalink]

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New post 06 Apr 2019, 06:42
Ritwick91 wrote:
But from here we are getting (-b/a) = 5 and (c/a) =6. Please explain how we are getting the values of a,b,c from these two equations???

Posted from my mobile device


Absolutely true. We are getting values of -(b/a) and (c/a) and not the individual values.

Note that the question is to find values of x --> these values of x will help us determine if x is prime or composite.
From the second option we simplify the equation to x^2-5x+6=0. From this equation we will get the values of x. These values are sufficient to determine if x is prime or composite.

We do not require to find individual values of a,b and c.
a,b and c are given simply to confuse the test taker.

Here the main catch is that given equation can be simplified to a quadratic equation that we can solve without requiring the individual values.
Again note: Focus on what we require = values of x and not values of a,b and c

Hope that helps!
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Re: If x is a non-zero integer, is x prime?  [#permalink]

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New post 06 Apr 2019, 07:03
we can frame a quadratic equation with given sum and product of roots . this ia one of maths formula

x^2 - (sum of roots)x + product of roots = 0


hope this helps

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Re: If x is a non-zero integer, is x prime?   [#permalink] 06 Apr 2019, 07:03
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If x is a non-zero integer, is x prime?

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