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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  [#permalink]

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New post Updated on: 03 Jul 2017, 09:55
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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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Originally posted by mkrishnabdrr on 02 Jul 2017, 22:36.
Last edited by bb on 03 Jul 2017, 09:55, edited 3 times in total.
Renamed the topic and edited the question.
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Re: If y = 5 + x and y = 12 - x, and if y^2 = x^2 + k, then k equals which  [#permalink]

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New post 02 Jul 2017, 23:06
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2
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)
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Re: If y = 5 + x and y = 12 - x, and if y^2 = x^2 + k, then k equals which  [#permalink]

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New post 03 Jul 2017, 09:29
mkrishnabdrr wrote:
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


\(12 - x = 5 + x\)

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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Re: If y = 5 + x and y = 12 - x, and if y^2 = x^2 + k, then k equals which  [#permalink]

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New post 03 Jul 2017, 18:46
Abhishek009 wrote:
mkrishnabdrr wrote:
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


\(12 - x = 5 + x\)

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)



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
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How to recognize "triggers"  [#permalink]

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New post 16 Apr 2018, 10:45
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
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How to recognize "triggers"  [#permalink]

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New post 16 Apr 2018, 14:59
icedoverfire wrote:
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


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.
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Re: How to recognize "triggers"  [#permalink]

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New post 16 Apr 2018, 15:06
icedoverfire wrote:
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)
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Re: If y = 5 + x and y = 12 - x, and if y^2 = x^2 + k, then k equals which  [#permalink]

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New post 17 Apr 2018, 00:22
icedoverfire wrote:
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


Merging topics. Please refer to the discussion above.

From my point of view, the best approach is given by pushpitkc HERE.
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Re: If y = 5 + x and y = 12 - x, and if y^2 = x^2 + k, then k equals which  [#permalink]

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New post 18 Apr 2018, 11:37
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)
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Re: If y = 5 + x and y = 12 - x, and if y^2 = x^2 + k, then k equals which &nbs [#permalink] 18 Apr 2018, 11:37
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