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# If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the

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Joined: 02 Sep 2009
Posts: 61283
If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the  [#permalink]

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05 Feb 2019, 01:22
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35% (medium)

Question Stats:

66% (02:10) correct 34% (02:22) wrong based on 50 sessions

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If $$mx + qy − nx − py = 0$$, $$p − q = 2$$, and $$\frac{y}{x} = -\frac{1}{3}$$, then which of the following is true?

A. n – m = 2/3

B. n – m = -2/3

C. m + n = 2/3

D. m + n = 3/2

E. m + n = -3/2

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Re: If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the  [#permalink]

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05 Feb 2019, 01:58
1
Re-arranging the terms gives, x(m-n)-y(p-q) = 0
Given p-q = 2
x(m-n) = 2y
y/x = m-n/2
-1/3 = m-n/2
m-n = -2/3
or n-m = 2/3

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Re: If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the  [#permalink]

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05 Feb 2019, 02:12
Bunuel wrote:
If $$mx + qy − nx − py = 0$$, $$p − q = 2$$, and $$y/x = -\frac{1}{3}$$, then which of the following is true?

A. n – m = 2/3

B. n – m = -2/3

C. m + n = 2/3

D. m + n = 3/2

E. m + n = -3/2

mx -nx -py +qy = 0

x(m-n) - y(p-q) = 0
x(m-n) = 2y
y/x = (m-n)/2

y/x = -1/3
m-n = -2/3
n-m = 2/3

A
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Re: If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the  [#permalink]

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24 Jan 2020, 10:14
Top Contributor
Bunuel wrote:
If $$mx + qy − nx − py = 0$$, $$p − q = 2$$, and $$\frac{y}{x} = -\frac{1}{3}$$, then which of the following is true?

A. n – m = 2/3

B. n – m = -2/3

C. m + n = 2/3

D. m + n = 3/2

E. m + n = -3/2

Tricky!!!
First notice that we can perform some factoring in parts
We'll start by rearranging the terms to get some like terms together.

Take: $$mx + qy − nx − py = 0$$
Rearrange to get: $$mx − nx + qy − py = 0$$
Factor in parts to get: $$x(m − n) + y(q - p) = 0$$
Now subtract $$y(q - p)$$ from both sides to get: $$x(m − n) = -y(q - p)$$
Rewrite the right side of the equation as follows: $$x(m − n) = y(-q + p)$$
Simplify to get: $$x(m − n) = y(p - q)$$

Divide both sides by $$x$$ to get: $$m − n = \frac{y(p - q)}{x}$$

Rewrite the right side of the equation to get: $$m − n = \frac{y}{x}(p - q)$$

Replace $$p − q$$, and $$\frac{y}{x}$$ to get: $$m − n = -\frac{1}{3}(2)$$

Simplify to get: $$m − n = -\frac{2}{3}$$

Multiply both sides by $$-1$$ to get: $$-m + n = \frac{2}{3}$$

Finally, rewrite as follows: $$n - m = \frac{2}{3}$$

Cheers,
Brent
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Re: If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the   [#permalink] 24 Jan 2020, 10:14
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