1) If x^2 – 3x + 2 = 0. Upon solving we get x=1,2. So INSUFFICIENT
2) If x^2 – x – 2 = 0. Uppon solving we get x=-1,2. So INSUFFICIENT

1)+2) ---> We get x=1 and so understand x equals 2 which is SUFFICIENT to answer the question. So C is the answer.

1.
\(x^{2}\) - 3x +2 =0
=> \(x^{2}\) -2x -x +2=0
=> (x-1)(x-2)=0
x=1,2

Not sufficient

2. \(x^{2}\)-x-2=0
=> \(x^{2}\) -2x+x-2=0
=> (x-2)(x+1)=0
x=2,-1

Combining 1 and 2 , we get x=2 . Hence , sufficient.
Answer C

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Statement (1) on factorization
(x-2)(x-1)=0
=>x=1,2
Not Sufficient

Statement (2) on factorization
(x-2)(x+1)=0
=>x=-1,2
Not Sufficient

Combining Statement(1) and (2)
x=2
Sufficient

Answer - C
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1) has 2 solutions, x=1,2, So insufficient
2) als has 2 solutions, x=-1, 2, so insufficient.

Both gives x=2, So the answer is C.

You might wanna consider your second statement.

It should be x = 2 or x = -1

Its was the typo error.
It should be also*

OO...Yea was a typo....corrected...Thanks!

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Does x = 2?

(1) x is a number such that x^2 – 3x + 2 = 0.
(2) x is a number such that x^2 – x – 2 = 0.

There is one variable (x) from the original condition, which means we need one equation in order to match the number of variables and that of the equations. The conditions gives us two equations in total, giving us high chance that (D) is going to be our answer.
Looking at condition 1, x^2-3x+2=0, (x-2)(x-1)=0, so x=1,2, but this condition alone is insufficient as it does not give a unique answer.
Looking at condition 2, x^2-x-2=0, (x-2)(x+1)=0, so x=-1,2. This condition is insufficient as well, as it does not give a unique value of x as well.
However, combining the 2 conditions, the answer becomes x=2. The 2 conditions are sufficient only when combined together, giving a unique answer. Therefore, the answer becomes (C).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/ No. The question asks: “Does x = 2?”

Given information in the question stem or diagram: No important information is given in the question stem.

Statement 1: x^2 – 3x + 2 = 0. In this case it is best for you to “Just Do It” and see what values you get for x. Factoring the quadratic yields (x – 2 )(x – 1 ) = 0. So x = 2 or x = 1. This gives you both a “yes” and a “no” answer to the question so it is not sufficient. Eliminate choices A and D.

Statement 2: x^2 – x – 2 = 0. Factoring this quadratic gives you (x – 2) (x + 1) = 0. So x either equals 2 or -1. This statement is also not sufficient alone since those
values give a “no” and a “yes.” Eliminate choice B.

Together: When taking these statements together you need to see if there is only one value that is allowed by BOTH of the statements. x = 2 is the only value that both statements allow so the correct answer is C. Note: This is only hard if you make a mistake with the factoring or get confused about what constitutes sufficiency when considering the two statements together. This would be trickier if one statement gave two values other than 2. Then that statement would be sufficient as the answer would be a definitive NO, even if there were two possibilities from the statement. As it stands, neither alone is sufficient and the answer is C.
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1 statement:
x^2-3x+2=0
(x-2)(x-1)=0
x can be either 2 or 1. insufficient.

2 statement
x^2-x-2=0
(x-2)(x+1)=0
x can be either 2 or -1. not sufficient.

1+2, x=2.

This may be a dumb question but the fact that each has x=2 as an answer does not mean that is directly answering the question asked, thus, D is not correct?