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

Question

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

pushpitkc · Accepted Answer

Given data : 
y-x = 5
y+x = 12

Since  y^2 = x^2 +k
k =  y^2  -  x^2 
k = (y+x)(y-x) = 5*12 = 60(Option D)

Abhishek009 · Answer

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)

Mkrishnabdrr · Answer

The trick to solving this question is recognizing that  y^2 - x^2 =(y+x)(y-x)
y = 5 + x
or, y-x=5

y = 12 - x
or, y+x=12

y^2  =  x^2 + k
or,  y^2 - x^2 =k
or, (y+x)(y-x)=k
or, 12 * 5 =k
i.e. k = 60

Hence, Ans is D

icedoverfire · Answer

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

mvictor · Answer

At first, you can start combining the first 2 equations.
12-x=x+5
2x=7
x=3.5
y=8.5

y^2 = x^2 +k
or y^2 - x^2 = k
now, this will be burdensome to calculate with decimals.
on another side, we can calculate (y-x)(y+x), which is basically y^2 - x^2.

now y-x and y+x is easier to calculate, and their product is easier to calculate as well.
y-x = 5
y+x = 12
5*12 = 60.
K is 60.
It takes time to form the number sense and start seeing the way you would approach this question.
the approach may vary, depending on how easy it is for you.

Hero8888 · Answer

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)

Bunuel · Answer

Merging topics. Please refer to the discussion above.

From my point of view, the best approach is given by  pushpitkc   HERE .

swatisahoo · Answer

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)

bumpbot · Answer

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards