Manbehindthecurtain wrote:
Are x and y both positive?
(1) \(2x - 2y = 1\)
(2) \(\frac{x}{y} > 1\)
(1) \(2x - 2y = 1\)
(x - y) = 1/2
So I imagine it on the number line. x - y = 1/2 tells me that x is to the right of y, a distance of 1/2 away. They could be placed on the number line in any way.
----------------------------- 0 -------------------y --(1/2) -- x ------------
------y --(1/2) -- x ----------- 0 -------------------------
Not sufficient
(2) \(\frac{x}{y} > 1\)
x and y could be both positive or both negative.
Not sufficient.
Using both statements,
If x and y are to the right of 0 i.e. both positive, x > y and hence x/y > 1
e.g. 3/2.5 > 1
If x and y are to the left of 0 i.e. both negative, x> y but x/y < 1 (since y is negative, the inequality sign flips)
e.g. -2.5/-3 < 1
Hence, to satisfy both statements, x and y both must be positive.
Answer (C)
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