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

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Senior Manager
Joined: 25 Dec 2018
Posts: 305
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
If x is a non-zero integer, is x prime?  [#permalink]

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04 Apr 2019, 10:26
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Difficulty:

75% (hard)

Question Stats:

44% (01:59) correct 56% (02:11) wrong based on 36 sessions

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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.
Intern
Joined: 20 Oct 2018
Posts: 44
Re: If x is a non-zero integer, is x prime?  [#permalink]

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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
Manager
Joined: 24 Jul 2018
Posts: 57
Location: India
Re: If x is a non-zero integer, is x prime?  [#permalink]

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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???
Intern
Joined: 20 Oct 2018
Posts: 44
Re: If x is a non-zero integer, is x prime?  [#permalink]

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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???

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!
Manager
Joined: 24 Jul 2018
Posts: 57
Location: India
Re: If x is a non-zero integer, is x prime?  [#permalink]

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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???

Posted from my mobile device
Intern
Joined: 20 Oct 2018
Posts: 44
Re: If x is a non-zero integer, is x prime?  [#permalink]

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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!
Senior Manager
Joined: 25 Feb 2019
Posts: 285
Re: If x is a non-zero integer, is x prime?  [#permalink]

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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

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