What is the value of x?

Question

(1) 4x^2 – 4x + 1 = 0
(2) 4x^2 – 1 = 0

Kudos for a correct  solution .

VenoMfTw · Answer

IMO : A

St 1: 4x^2 – 4x + 1 = 0
(2x-1)^2 = 0 
(2x-1) = 0
x = 1/2
Suff

St 2: 4x^2 – 1 = 0
(2x+1)(2x-1) = 0
x = 1/2 or x = -(1/2) 
Nt suff

Hence A

ENGRTOMBA2018 · Answer

x=?

Statement 1, 4x^2 – 4x + 1 = 0 ---> (2x-1)^2 =0 ---> x =1/2 . Sufficient.

Statement 2, 4x^2 – 1 = 0 ---> x =  \pm  0.5. Not sufficient.

A is the correct answer.

GMATinsight · Answer

Question : x = ?

Statement 1 : 4x^2 – 4x + 1 = 0 
i.e. 4x^2 – 2x - 2x + 1 = 0
i.e. 2x(2x – 1) - 1(2x - 1) = 0
i.e. (2x-1)^2 = 0
i.e. 2x =1
i.e. x = 1/2
 SUFFICIENT

Statement 2 : 4x^2 – 1 = 0 
i.e. x^2 = 1/4
i.w. x =  + (1/2)
 NOT SUFFICIENT

Answer: Option A

EMPOWERgmatRichC · Answer

Hi All,

Since everyone in this thread has correctly done the math involved in this prompt, I won't rehash any of that here. Instead, I want to point out that this question is based on math rules that you probably already know (Classic Quadratics, FOIL-ing and Reverse-FOIL-ing). The GMAT is a Test that is based heavily on patterns, and at the higher levels it will test you on patterns that you know, but in ways that you're probably not used to thinking about.

This question is based entirely on 2 Classic Quadratics:

General Format:
(Y+1)^2
and
(Y+1)(Y-1)

Spotting those patterns makes dealing with this question a fairly straight-forward process. When you come across questions that look 'strange', think about what they remind you of and you'll likely find the very pattern you need to answer the question correctly.

GMAT assassins aren't born, they're made,
Rich

Mascarfi · Answer

For 1 we can use "(b^2)-4ac" to know we will have only one solution, hence sufficient.

For 2 we can easily see that there is more than one solution for X. Not sufficient.

A it is.

Bunuel · Answer

800score Official Solution:

The both statements are quadratic equations. A quadratic equation can have one solution, two distinct solutions, or no solution. Let’s solve each one.
4x² – 4x + 1 = 0
(2x)² – 2 × (2x) + 1 = 0
Now we can apply the well-known formula and get the square of the difference.
(2x – 1)² = 0
2x – 1 = 0
x = 1/2
We have the only one value as a solution. Therefore statement (1) by itself is sufficient.

4x² – 1 = 0
(2x)² = 1
2x = 1 or 2x = -1
x = 1/2 or x = -1/2
We have two distinct values as solutions. Therefore statement (2) by itself is NOT sufficient.

Statement (1) by itself is sufficient, while statement (2) by itself is not.  The correct answer is A .

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What is the value of x?

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