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Math Expert V
Joined: 02 Sep 2009
Posts: 65829
If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 80% (01:46) correct 20% (02:10) wrong based on 59 sessions

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If $$x + y = 6t$$ and $$xy = -7t^2$$,what is the value of$$\frac{(x^2 + y^2)}{t^2}$$?

A. 20
B. 30
C. 50
D. 60
E. 90

_________________
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4999
GMAT 1: 770 Q49 V46
Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2?  [#permalink]

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Top Contributor
1
Bunuel wrote:
If $$x + y = 6t$$ and $$xy = -7t^2$$,what is the value of $$\frac{(x^2 + y^2)}{t^2}$$?

A. 20
B. 30
C. 50
D. 60
E. 90

Given: $$x + y = 6t$$
Square both sides to get: $$(x + y)^2 = (6t)^2$$
Expand and simplify: $$x^2 + 2xy + y^2 = 36t^2$$

Also given: $$xy = -7t^2$$
Multiply both sides by 2 to get: $$2xy = -14t^2$$

We now have two equations:
$$x^2 + 2xy + y^2 = 36t^2$$
$$2xy = -14t^2$$

Subtract the bottom equation from the top equation to get: $$x^2 + y^2 = 50t^2$$

Our goal is to find the value of $$\frac{(x^2 + y^2)}{t^2}$$

Replace the numerator with its equivalent value to get: $$\frac{50t^2}{t^2}$$

Simplify to get: 50

Cheers,
Brent
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If you enjoy my solutions, you'll love my GMAT prep course. GMAT Club Legend  V
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Concentration: Sustainability, Marketing
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Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2?  [#permalink]

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given
$$\frac{(x^2 + y^2)}{t^2}$$
can be re written as ;
$$\frac{(x^2 + y^2+2xy-2xy)}{t^2}$$
$$\frac{(x + y)^2-2xy}{t^2}$$
substitute given function values
IMO C

Bunuel wrote:
If $$x + y = 6t$$ and $$xy = -7t^2$$,what is the value of$$\frac{(x^2 + y^2)}{t^2}$$?

A. 20
B. 30
C. 50
D. 60
E. 90
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11407
Location: United States (CA)
Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2?  [#permalink]

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1
Bunuel wrote:
If $$x + y = 6t$$ and $$xy = -7t^2$$,what is the value of$$\frac{(x^2 + y^2)}{t^2}$$?

A. 20
B. 30
C. 50
D. 60
E. 90

Squaring the first equation, we have:

x^2 + y^2 + 2xy = 36t^2

Substituting -7t^2 for xy, we have:

x^2 + y^2 - 14t^2 = 36t^2

x^2 + y^2 = 50t^2

So, we have:

(x^2 + y^2) / t^2 = 50t^2 / t^2 = 50

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Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2?  [#permalink]

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Bunuel wrote:
If $$x + y = 6t$$ and $$xy = -7t^2$$,what is the value of$$\frac{(x^2 + y^2)}{t^2}$$?

A. 20
B. 30
C. 50
D. 60
E. 90

Asked: If $$x + y = 6t$$ and $$xy = -7t^2$$,what is the value of$$\frac{(x^2 + y^2)}{t^2}$$?

$$x^2 + y^2 = (x+y)^2 - 2xy = 36t^2 + 14t^2 = 50t^2$$

$$\frac{(x^2 + y^2)}{t^2} = 36$$

IMO C
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2?   [#permalink] 04 Aug 2020, 23:01

# If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2?   