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natural numbers.

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natural numbers.

by shashank.ism » Sat Feb 20, 2010 12:44 pm
Given that w, x, y and z are natural numbers such that 4w = xyz, 4x = wyz and 4z = wxy. Which of the following is a possible value of (w + x + y - z)2?

A) 25
B) 9
C) 36
D) 1
E) 49
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by ajith » Sat Feb 20, 2010 12:57 pm
shashank.ism wrote:Given that w, x, y and z are natural numbers such that 4w = xyz, 4x = wyz and 4z = wxy. Which of the following is a possible value of (w + x + y - z)2?

A) 25
B) 9
C) 36
D) 1
E) 49
4w = xyz ---(1)
4x = wyz ----(2)

dividing (1)/(2)

w/x = x/w

x^2 = w^2

4z = wxy ---(2)

(2)/3 =>
z^2 = x^2

(1)/(3) ->

(z^2) = (w)^2

Now
(w + x + y - z)

since all are natural numbers w=x=y=z

(w + x + y - z) = 2w

(2w)^2 = 4w^2

an even square - it can only be 36
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