If (xandminus;3)(2xandminus;5)=0 and (xandminus;5/2)(xandminus;4)=0, x = ?a)-3b)-5/2c)5/2d)3e)4Correct answer is option 'C'. Can you explain this answer?

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GMAT Exam > GMAT Questions > If (x−3)(2x−5)=0 and (x−5/...

If (x−3)(2x−5)=0 and (x−5/2)(x−4)=0, x = ?

a)
-3
b)
-5/2
c)
5/2
d)
3
e)
4

Correct answer is option 'C'. Can you explain this answer?

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Verified Answer

If (x−3)(2x−5)=0 and (x−5/2)(x−4)=0, x = ?a)-...

Step 1: Question statement and Inferences

We are given two quadratic equations in x. We will solve both of them and look for a common value of x

Step 2 & 3: Finding required values and calculating the final answer

Approach:

We observe that both the given quadratic equations are already in factored form.
By putting each factor of an equation equal to zero, we can find the roots of an equation. So, we will be able to find the two roots of each equation.
The common root of both equations will be our answer

Implementing the approach:

Finding the roots of the first equation:

(x - 3)(2x - 5)

Either

x - 3 = 0

x = 3 . . . Root 1A

2x - 5 = 0

x = 5/2 . . . Root1B

Finding the roots of the second equation:

Either

x = 5/2 . . . Root 2A

x - 4 = 0

x = 4 . . . Root 2B

We observe that x=5/2

is a common root of both equations.

The value of x that satisfies both equations is x=5/2

Answer: Option (C)

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If (x−3)(2x−5)=0 and (x−5/2)(x−4)=0, x = ?a)-3b)-5/2c)5/2d)3e)4Correct answer is option 'C'. Can you explain this answer?

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