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If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =

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If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =  [#permalink]

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New post 07 Apr 2019, 21:33
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (02:02) correct 35% (02:17) wrong based on 23 sessions

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Re: If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =  [#permalink]

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New post 07 Apr 2019, 22:14
In ax+by+cz, substituting y(b-c)/(c-a) for x and y(a-b)/(c-a) for z,
solving gives us 0/c-a

Answer A

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Re: If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =  [#permalink]

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New post 07 Apr 2019, 22:28
From given equation we know that a, b, c can't be equal so, Let a=1,b=2,c=3,
Then the given equation will become x=-y/2=z
Now put all the values of a, b, c in ax+by+cz
=x+2y+3z
Now as x=-y/2=z
The equation will become
=-y/2+2y-3y/2
=0

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Re: If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =  [#permalink]

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New post 07 Apr 2019, 22:35
1
Another way solve it is put
X/(b-c) =Y/(c-a) =z/(a-b) =k
And put the values of x, y, z from above equation in ax+by+cz
It will become 0.
Hence A

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Re: If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =  [#permalink]

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New post 08 Apr 2019, 01:23
1
Bunuel wrote:
If a, b, and c are three different numbers and \(\frac{x}{b-c}=\frac{y}{c-a}=\frac{z}{a-b}\), then what is the value of \(ax + by + cz\) ?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4


let a=1,b=2 ,c = 3
and x=-1,y=2,z=-1
so \(ax + by + cz\)
IMO A ; 0
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Re: If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =  [#permalink]

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New post 18 Apr 2019, 14:32
aankit

Hello!

Why are we sure that we can substitute the values with any number?

Kind regards!
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Re: If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =  [#permalink]

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New post 18 Apr 2019, 18:12
jfranciscocuencag wrote:
aankit

Hello!

Why are we sure that we can substitute the values with any number?

Kind regards!


as no. of equations is less than no. of variables and if the equation is correct with one or more solution then we can take any value of a,b,c provided they are not equal, these values have to satisfy the equation.
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Re: If a, b, and c are three different numbers and x/(b - c) = y/(c - a) =   [#permalink] 18 Apr 2019, 18:12
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