If X Is A Number Such That x^2 - 3x + 2 = 0 And x^2 - X - 2 = 0 GMAT Problem Solving

Question: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0, what is the value of x?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

“If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0“ - is a subject covered in the GMAT quantitative reasoning section. This book was taken from the book “GMAT Official Guide 2018: Quantitative Review”. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

Solutions and Explanation

Approach Solution : 1

We can write the following since both equations are set to equal 0.
x^2 - 3x + 2 = x² - x - 2

Take x^2 away from both sides to obtain, -3x + 2 = -x - 2

Add 3x to both sides to obtain, 2 = 2x - 2
Add 2 to both sides and then we get, 4 = 2x

Therefore x = 2.

Correct Answer: (E)

Approach Solution : 2

Equation - 1 :

x^2 − 3x+2=0
(x-1)(x-2)
x =1 ; x=2

Equation - 2 :

x^2 −x−2=0
(x-2)(x+1)
x =2; x =-1

Find the common value in both the x values from the two equations.

x=2 is common in both.

As a result, 2 is the value of x.

Correct Answer: (E)

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