Try this problem from I.S.I. B.Stat TOMATO Objective Problem based on Inequations and conditions.

Inequations and Conditions (B.Stat Objective problems)


When \(x(A-x) \lt y(A-y)\) for all x,y with\(0 \lt x \lt y \lt1\), find the condition that holds

  • \(A\lt(-1)\)
  • \(A\geq2\)
  • \(A\gt2\)
  • none of these

Key Concepts


Logic

Inequations

Algebra

Check the Answer


But try the problem first…

Answer: \(A\geq2\)

Source
Suggested Reading

B.Stat Objective Problem (TOMATO) – Problem 61

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

\(x(A-x) \lt Ay-y^{2}\) then \(y^{2} – x^{2} \lt A(y-x)\) then \((y+x) \lt A\)

Second Hint

\(|x+y| \lt |x| + |y| \lt 1+1=2\) then \((x+y) \lt 2\)

Final Step

both equations hold for \( A \geq 2\).

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