Try this beautiful problem Based on Condition checking, useful for ISI B.Stat Entrance.
Let \(x, y,z,w\) be positive real numbers ,which satisfy the two conditions that
i)if x>y then z>w and
ii)if x>z then y<w
Then one of the statements given below is a valid conclusion.which one is it?
But try the problem first...
Answer: (d) If x>y+z then z>y
TOMATO, Problem 60
Challenges and Thrills in Pre College Mathematics
At first we have to check the options which are given with proper condition. Option (a) and (b) cannot be true because there is no such statement that the vice versa will be true, because in the question given that \(x>y\) and \(x>z\). So we neglect option (a) and (b). Can you check for the option (c) and (d)
Can you now finish the problem ..........
Option (c) cannot be true as if x > y and x > z then x > y + z but z > w > y
can you finish the problem........
Now for option (d),if If x>y+z then w>y \(\Rightarrow \) z>w so z>y.
Therefore option (d) is the correct