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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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Updated on: 03 Jul 2017, 08:55
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Question Stats:

85% (02:11) correct 15% (02:28) wrong based on 99 sessions

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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, 21:36.
Last edited by bb on 03 Jul 2017, 08:55, 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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02 Jul 2017, 22:06
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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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03 Jul 2017, 08:29
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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03 Jul 2017, 17:46
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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Joined: 16 Apr 2018
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16 Apr 2018, 09:45
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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16 Apr 2018, 13:59
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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16 Apr 2018, 14:06
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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Posts: 52305
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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16 Apr 2018, 23:22
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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Joined: 26 Dec 2015
Posts: 2
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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18 Apr 2018, 10:37
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)
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, 10:37
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