Try this beautiful problem Based on Condition checking, useful for ISI B.Stat Entrance.

## Condition checking | ISI B.Stat Entrance | Problem 60

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?

- (a) if x<y then z<w
- (b) if x>y+z then z<y
- (c) if x<z then y>w
- (d) if x>y+z then z>y

**Key Concepts**

Algebra

Inequility

## Check the Answer

But try the problem first…

Answer: (d) If x>y+z then z>y

TOMATO, Problem 60

Challenges and Thrills in Pre College Mathematics

## Try with Hints

First hint

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 ……….

Second Hint

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……..

Final Step

Now for option (d),if If x>y+z then w>y \(\Rightarrow \) z>w so z>y.

Therefore option (d) is the correct

## Other useful links

- https://www.cheenta.com/integer-isi-b-stat-entrance-objective-from-tomato/
- https://www.youtube.com/watch?v=axSw4_SuKE8

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