harishsridharan wrote:
\(0< x< y< 1\)
Quantity A |
Quantity B |
\(y-x\) |
\( (x-y)^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Useful property: \(a-b = -1(b-a)\)So, \( (x-y)^2=[(-1)(y-x)]^2\)
\(=(-1)^2(y-x)^2\)
\(=(1)(y-x)^2\)
\(=(y-x)(y-x)\)
We're now ready to solve the question...
Given:
Quantity A: \(y-x\)
Quantity B: \( (x-y)^2\)
Replace Quantity B with its equivalent value:
Quantity A: \(y-x\)
Quantity B: \((y-x)(y-x)\)
Since \(0< x< y< 1\), we know that \(y - x\) is POSITIVE, which means we can safely divide both quantities by \(y - x\) to get:
Quantity A: \(1\)
Quantity B: \(y-x\)
From here, a nice way to determine which quantity is greater is to first add \(x\) to both quantities to get:
Quantity A: \(1+x\)
Quantity B: \(y\)
Since x is positive, we know that Quantity A is greater than 1.
Conversely, we are told that y < 1.
So Quantity A must be greater.
Answer: A