 # Inequations and Conditions | ISI B.Stat TOMATO Problem

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

Answer: $A\geq2$

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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