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Q #11
⏰ :

CAT Inequalities and Modulus


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Consider three distinct positive integers a, b, c all less than 100. If |a - b| + |b - c| = |c – a|, what is the maximum value possible for b?


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Q #12
⏰ :

CAT Inequalities - Integers


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Consider integers m, n such that -5 < m < 4 and -3 < n < 6. What is the maximum possible value of m2 - mn + n2?


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Q #13
⏰ :

CAT Inequalities - Integers


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Consider integers p, q, r such that |p| < |q| < |r| < 40. P + q + r = 20. What is the maximum possible value of pqr?


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Q #14
⏰ :

CAT Inequalities - Minimum Value


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What is the minimum value of f(x) = x2 – 5x + 41?


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Q #15
⏰ :

CAT Inequalities - Roots


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x4 – 4x3 + ax2 – bx = 1 = 0 has positive real roots. What is the maximum possible value of a + b?


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