If y = 5 + x and y = 12 - x, and if y^2 = x^2 + k, then k equals which of the following?

A. 17
B. 25
C. 50
D. 60
E. 100
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\(12 - x = 5 + x\)

Or, \(7 = 2x\)

Or, \(x = \frac{7}{2}\)

So, \(y = 5 + \frac{7}{2}\)

Or, \(y = \frac{17}{2}\)


Given -

\(y^2 = x^2 + k\)

\(\frac{17*17}{2*2} = \frac{7*7}{2*2} + k\)

Or, \(\frac{289}{4} = \frac{49}{4} + k\)

Or, \(k = \frac{240}{4}\)

So, \(k = 60\) , answer must be (D)
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Abhishek....

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Hi everyone,

New here. Story in brief is that I'm looking for a change in career.

Anyway -

I've been using Magoosh GMAT prep and for the life of me my quant skills are teh suck. My career path took me as far away from math as possible (yes I know the GRE is less math intensive but I figured I'd use the harder prep to cover more stuff) -

Anyway - Here's a practice problem from Magoosh:

If y = x + 5 and y = 12 - x and \(y^2 = x^2 + K\) then K equals which of the following:

Choices given (A) 17, (B) 25, (C) 60, (D) 119.

How is one supposed to recognize where to even begin? In the interest of getting as many approaches as possible, I won't go into what Magoosh says to do.

Help appreciated

- ice

y = (x + 5) and y = (12 - x) => (x + 5) = (12 - x) => x =3.5, hense y=12-x=12-3.5=8.5

\(y^2 = x^2 + K\) => \(K=y^2 - x^2\) = (y-x)(y+x) =(8.5-3.5)(8.5+3.5)=5*12=60. Answer (C)

Given : y= 5+x and y=12-x
then 5+x=12-x =>x=7/2
And y^2=x^2+k=> (5+2)^2=x^2+k
=>x^2+10x+25=x^2+k
=>10(7/2)+25=k
k=60(Ans C)