If x^2 - (x-1)^2 = a, what is x in terms of a ?

Question

If  x^2 - (x - 1)^2 = a , what is  x  in terms of  a  ?

(A)  a+1

(B)  \frac{a + 1}{2}

(C)  \frac{a - 1}{2}

(D)  -\frac{a + 1}{2}

(E)  -\frac{a - 1}{2}

Bunuel · Answer

Apply  a^2 - b^2 = (a - b)(a+b) :
 
 x^2 - (x - 1)^2 = a

(x - (x - 1))(x + (x-1)) = a

(1)(2x-1) = a

2x = a+1

x = \frac{a+1}{2} 
 
Or:
 
 x^2 - (x - 1)^2 = a

x^2 - (x^2 - 2x + 1) = a

2x - 1 = a

2x = a+1

x = \frac{a+1}{2}

Answer: B.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=82775 ___ Harsha Passionate about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com GMAT-Club-Forum-51wtk593.png

GMATinsight · Answer

Since two explanations are already available, let me bring in my third one which is not any less meritorious

If x = 3 then  x^2 - (x - 1)^2 = a  would be  3^2 - (3 - 1)^2 = a = 9-4=5

i.e. for a = 5, the correct option should give me x = 3

(A)  a+1 = 5+1 = 6  WRONG

(B)  \frac{a + 1}{2} = (5 + 1)/2 = 3    CORRECT

(C)  \frac{a - 1}{2}

(D)  -\frac{a + 1}{2}

(E)  -\frac{a - 1}{2}

Answer: Option B

bumpbot · Answer

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If x^2 - (x-1)^2 = a, what is x in terms of a ?

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If x^2 - (x-1)^2 = a, what is x in terms of a ?

Prep Toolkit

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