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Source - GMAT Math Bible - Nova - Equations

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by shanice » Tue Sep 04, 2012 6:44 pm
Hi guys,

Please help me with the following:-

1) If (x - 2y)(x + 2y) = 5 and (2x - y)(2x + y) = 35, then x^2-y^2 / x^2+y^2

(A) -8/5
(B) -4/5
(C) 0
(D) 4/5
(E) 7/5

2)If l/m+n=m/n+1=n/l+m=k,where k is a real number, then which one of the following does k equal?
(A) 1/3
(B) 1/2
(C) 1
(D) 2
(E) 3

Please help.

Thank you.
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by everything's eventual » Tue Sep 04, 2012 7:25 pm
For question 1), you can solve as following :

After expanding the two equation given in the problem, you get the following :

x^2 - 4y^2 = 5 .....(i)

4x^2 - y^2 = 35.....(ii)

Add the two equations and you get following :

5x^2 - 5y^2 = 40

Therefore, x^2 - y^2 = 8.... (a)

Now subtract (i) from (ii)

3x^2 + 3y^2 = 30

Therefore, x^2 + y^2 = 10.....(b)

Divide (a) by (b) and you get = 8/10 = 4/5

Answer is [spoiler](d)[/spoiler]
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by everything's eventual » Tue Sep 04, 2012 7:31 pm
For question 2)

L/m+n = k

therefore, L/k = m+n

Similarly, m/k = n+L

n/k = L+m

Add all three equations :

1/k (m+n+L) = 2(m+n+L)

Therefore k = 1/2

Answer = B
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by Anurag@Gurome » Tue Sep 04, 2012 7:36 pm
shanice wrote:Hi guys,

Please help me with the following:-

1) If (x - 2y)(x + 2y) = 5 and (2x - y)(2x + y) = 35, then x^2-y^2 / x^2+y^2

(A) -8/5
(B) -4/5
(C) 0
(D) 4/5
(E) 7/5

Please help.

Thank you.
(x - 2y)(x + 2y) = 5 and (2x - y)(2x + y) = 35, then (x² - y²) / (x² + y²)
(x - 2y)(x + 2y) = 5 implies x² - 4y² = 5 ... Equation (1)
(2x - y)(2x + y) = 35 implies 4x² - y² = 35 ... Equation (2)
Adding equations (1) and (2), 5x² - 5y = 40 or x² - y² = 8
Subtracting equation (1) from equation (2), 3x² + 3y² = 30 or x² + y² = 10

Therefore, (x² - y²) / (x² + y²) = 8/10 or [spoiler]4/5[/spoiler]

The correct answer is D.
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by coolhabhi » Wed Sep 05, 2012 3:04 am
shanice wrote: 2)If l/m+n=m/n+1=n/l+m=k,where k is a real number, then which one of the following does k equal?
(A) 1/3
(B) 1/2
(C) 1
(D) 2
(E) 3
quote]

l
------ = k
(m+n)

=> l = k(m+n)
Similarly
m = k(n+l)
n = k(l+m)

Now add all the above three equations
l+m+n = k(m+n) + k(n+l) + k(l+m)
l+m+n = 2k(l+m+n)
1 = 2k
k = 1/2
Answer = B
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