Bunuel wrote:
Does \(|x-2| = |y-2|\)?
(1) \(x≠y\)
(2) \(x<2\) and \(y<2\)
Question:
Does \(|x-2| = |y-2|\)
Inference: Is the distance between x and 2 same as the distance between y and 2 ?Statement 1\(x≠y\)
Statement 1 gives us information regarding the value of x and y. The statement tells us that x and y do not have the same value. However, the statement does not provide any information on the relative position of x and y.
For example, x and y can be two different values which are equidistant from 2 on a number line. This can happen when x and y lie on the opposite sides of 2 as shown below
----------- x ------------ 2 ------------ y ------------
----------- y ------------ 2 ------------ x ------------
Alternatively, x and y can also be two values such the distance is not same from 2.
As we have two contradicting answers, we can rule out statement 1 and eliminate A and D
Statement 2x < 2 and y < 2
This statement provides us with information regarding x and y with respect to 2. The statement tells us that x and y both lie on the left of 2 on a number line.
However, the statement is not sufficient.
For example. If x and y have the same value (both lie to the left of 2 on a number line), the distance between x and 2 and the distance between y and 2 will be same. Alternatively if x and y are different values, the distances will be different.
Eliminate B.
CombinedThe statements combined rules out the possibility that x and y have the same value. As x and y lie on the same side of 2, the distance between x and 2 and the distance between y and 2 will NOT be the same.
The statements combined are sufficient to answer the question.
Option C