CAT 2024 Inequalities Question (Medium)

Question

If and satisfy the equations and , then equals

Accepted Answer

We are given two equations 1. 2. We need . --- Step 1 Analyze the first equation Equation 1 x x y 15 Case A Then , so 2x y 15 quad Rightarrow quad y 15 - 2x Case B Then , so -x x y 15 quad Rightarrow quad y 15 --- Step 2 Analyze the second equation Equation 2 x y - y 20 Case A Then , so x y - y 20 q

CAT 2024

Quantitative

Inequalities

Medium

$x$

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CAT 2024

Quantitative

Inequalities

Medium

If xxx and yyy satisfy the equations ∣x∣+x+y=15|x|+x+y=15∣x∣+x+y=15 and x+∣y∣−y=20x+|y|-y=20x+∣y∣−y=20 , then (x−y)(x-y)(x−y) equals

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$x$