COolguy101 wrote:
If \(x+y> y\), \(xy <x\)
Quantity A |
Quantity B |
x |
y |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
\(x + y > y\)
Subtracting \(y\) from both sides;
\(x + y - y > y - y\)
\(x > 0\)
\(xy < x\)
Since, \(x\) is positive, we can divide both sides by \(x\);
\(\frac{xy}{x} < \frac{x}{x}\)
\(y < 1\)
Now, we have no idea how big \(x\) is, or how small \(y\) is from 1 i.e. is \(y\) 0.5 or -2
Therefore we do not have enough information to compare both the quantities.
Hence, option D
Through examples;Let \(x = 2\) and \(y = 0 .5\)
\(x + y > y\)
\(2.5 > 0.5\)
\(xy < x\)
\(1 < 2\)
Here, Col. A > Col. B
Let \(x = 0.1\) and \(y = 0 .5\)
\(x + y > y\)
\(0.6 > 0.5\)
\(xy < x\)
\(0.05 < 0.1\)
Here, Col. A < Col. B