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

Question:
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.

Hi all!

GMAT Track of thought 1

Lets break this down but before that, collate the important data from the stem. X is a non zero integer. So x can be +ve or -ve.
I need a definite YES or a definite NO as an answer to, "is x prime?"

GMAT Track of thought 2

(St 1)-The number x is at a distance less than 2 units from the number 1.5 on the number line.
.......(-0.5).........0.....1..1.5.....2...3....(3.5)....4

The coloured zone is where x can lie.
But x is a non zero integer.
What values do you think I can have for x belonging to the coloured zone?
1,2,3
If x = 2 or 3, the answer to the question stem is a YES.
If x=1,then the answer to the question stem is a NO.
We dont have a definite answer.
Insufficient. Eliminate A,D.

GMAT Track of thought 3

(St 2)The sum and product of roots of a quadratic equation a\(x^2\)+bx+c are 5 and 6 respectively.
How does such an equation look like?
\(x^2\) - (sum of the roots)x + product of the roots = 0
=> \(x^2 \)- 5x+6=0
What are the roots of this equation?
x= 2 or x=3
But both of them are prime.
We have a unique answer.
Sufficient.
Correct answer for this question is option D

Hope you are clear.
Let me know if you have any questions on this.

Looking forward to help.

Devmitra Sen
GMAT Mentor