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Algebra

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by yellowho » Thu Jan 20, 2011 2:36 am
For all numbers a and b, the operation & is defined by a&b= a/(a+b)
If x&y=6, then y&x=?

(A) -5
(B) -2
(C) 1
(D) 4
(E) 7

I just made up some numbers that will satisfy the first condition and then flipped it for the second. Is that a valid method? The algebra is not hard but time consuming.
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by Anurag@Gurome » Thu Jan 20, 2011 3:21 am
yellowho wrote:For all numbers a and b, the operation & is defined by a&b= a/(a+b)
If x&y=6, then y&x=?

(A) -5
(B) -2
(C) 1
(D) 4
(E) 7
Algebra is not always about solving an equation.
There is a much better algebraic method to solve this problem.

Note that, x&y + y&x = x/(x + y) + y/(x + y) = (x + y)/(x + y) = 1

Thus, y&x = 1 - x&y = 1 - 6 = -5

The correct answer is A.
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by Everest » Thu Jan 20, 2011 1:44 pm
If x&y=6, then y&x=?

x&y = x/x+y = 6 => y = -5x/6

y&x = y/y+x => -5x/6/ -5x/6+x = -5
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