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I.S.I. and C.M.I. Entrance

Condition checking | ISI-B.stat Entrance | Objective Problem 60

Try this beautiful problem from Inequation from TOMATO useful for ISI B.Stat Entrance based on condition checking.You may use sequential hints.

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

Source
Suggested Reading

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

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