CAT 2024 Inequalities Question (Hard)

Question

The number of distinct integer solutions of the equation x y x-y 2, is

Accepted Answer

Step 1 Start with the equation . Step 2 Prove the identity . Assume without loss of generality that . If and have the same sign, then and , so the sum is . If they have opposite signs, then and , so the sum is again . Since , this equals . The other case is symmetric. Step 3 Using the identity in St

CAT 2024

Quantitative

Inequalities

Hard

The number of distinct integer solutions $(x,y)$ of the equation $|x+y| + |x-y| = 2,$ is

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