If two distinct non-zero real variables x and y are such that (x + y) is proportional to (x − y) then the value of x/y
Options:
(A) depends on xy
(B) depends only on x and not on y
(C) depends only on y and not on x
(D) is a constant
Official Answer Key:
D
Step-by-Step Solution & Explanation
Proportionality means there exists a constant k such that:
x + y = k(x − y)
Divide throughout by y (y ≠ 0), and let t = x/y:
t + 1 = k(t − 1)
t + 1 = kt − k
t(1 − k) = −(1 + k)
t = (1 + k)/(k − 1)
The right-hand side contains only the proportionality constant k. Therefore x/y is itself a constant, independent of the individual values of x and y.
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