CAT Algebra questions with solutions

103 previous year CAT questions on Algebra, taken from the QA section, each with the correct answer and a full explanation. Work through them in order or jump to a specific paper.

#028Distinct integer solutions of modulus equationQATITAEasy
#029Condition for no solution in system of linear equationsQAMCQEasy
#043Product of exponents in chain of equationsQATITAEasy
#044Sum of reciprocal terms in recurrence sequenceQAMCQHard
#045Number of solutions to max-min modulus equationQATITAMedium
#047Sum of solutions to functional equationQAMCQMedium
#049Sum of real roots of exponential equationQAMCQEasy
#051System of Absolute Value EquationsQAMCQMedium
#057Sum of Infinite SeriesQAMCQMedium
#058Logarithmic Equation and Maximum IntegerQATITAHard
#062Equation Involving Square Roots of SurdsQATITAEasy
#065Symmetric Expression of Quadratic RootsQAMCQMedium
#069Solving Rational InequalityQAMCQMedium
#070Minimization/Sum of Squares in Real VariablesQATITAMedium
#120System of absolute value equationsQAMCQHard
#125Pairs of integers satisfying absolute inequalitiesQATITAMedium
#251Number of Integer PairsQATITAMedium
#252Logarithmic Value RangeQAMCQHard
#253Smallest Value in Geometric ProgressionQAMCQHard
#254Minimum Value of Algebraic ExpressionQATITAHard
#257Maximum Value for Real xQAMCQMedium
#259Maximum Value of 2x + yQATITAEasy
#261Smallest Possible Value of bQAMCQMedium
#264Number of Integers Satisfying Exponential EqualityQAMCQEasy
#265Absolute Value Equation PairsQAMCQHard
#271Pencils and SharpenersQAMCQHard
#470Ratio of sides of rectangleQAMCQEasy
#476Product bound from sum of squaresQAMCQEasy
#627Ratio of Squares of Integers of Opposite SignsQAMCQHard
#636Expression Evaluation from Quadratic RelationQAMCQHard
#642Minimum Value of Sum of SquaresQATITAHard
#693Arithmetic Progression with LogarithmsQAMCQMedium
#695Infinitely Many Solutions for System of Linear EquationsQAMCQMedium
#696Algebraic Identity ExpansionQAMCQMedium
#697Properties of Roots of Quadratic EquationQATITAMedium
#699Inequalities with Exponential FunctionsQATITAHard
#712Sum of Infinite SeriesQAMCQMedium
#713Common Terms in Arithmetic ProgressionsQAMCQEasy
#714Functional Equation with Two VariablesQATITAMedium
#716Sum of values of x in exponential equationQAMCQMedium
#718Inequality condition for real numbersQAMCQMedium
#719Logarithmic equation evaluationQATITAMedium
#721Quadratic roots condition and AM-GM minimizationQATITAMedium
#729Maximum number of shirts boughtQATITAHard
#730Maximum number of persons for division of moneyQATITAMedium
#734Term of arithmetic progression with prime common differencesQAMCQMedium
#735Difference between max and min value of algebraic expressionQAMCQMedium
#736Largest three digit common term in two APsQATITAMedium
#737Logarithmic Equation SolutionQAMCQEasy
#738Algebraic Identity with Real VariablesQAMCQMedium
#739Radical Equation SimplificationQAMCQMedium
#741Absolute Value Equation Integer SolutionsQATITAMedium
#742Roots of Quadratic EquationsQATITAMedium
#743Cubic Polynomial Real Roots ConditionQATITAHard
#756Arithmetic Mean of Square Root FractionsQAMCQHard
#758Recursive Sequence GrowthQATITAMedium
#807Possible Integer Values of k for Quadratic EquationsQAMCQMedium
#808Minimum Value of Expression with Domain RestrictionQAMCQEasy
#812Functional Equation ConditionQAMCQMedium
#817Exponential Equations and VariablesQATITAMedium
#820Irrational Roots of Quadratic Equations with Integer CoefficientsQAMCQHard
#821Range of Algebraic ExpressionQAMCQMedium
#826Cheque Denomination OptimizationQATITAMedium
#832Average of Max and Min ValuesQAMCQEasy
#835Particle Growth SequenceQAMCQHard
#837Roots of Cubic PolynomialQAMCQMedium
#838Functional Equation and CompositionQATITAHard
#842Logarithmic Inequality Integer SolutionsQATITAHard
#843Exam Scoring OptimizationQAMCQMedium
#845Number of Integer SolutionsQATITAMedium
#847Sum of First N Terms of APQAMCQMedium
#848Quadratic Polynomial PropertiesQAMCQEasy
#865Algebraic Value of 2a + bQAMCQEasy
#887Minimum Value of Polynomial CoefficientQAMCQMedium
#888Rice Shop CustomersQAMCQMedium
#889Quadratic Function Roots and CoefficientsQASET · 2QMedium
#898Number of Distinct Terms in ExpansionQAMCQEasy
#904Sum of Square Root SeriesQAMCQHard
#1030Bounding exponential ratioQAMCQMedium
#1032Unique positive solution for system of equationsQAMCQHard
#1036Sequence recurrence relation solutionQAMCQHard
#1040Bounds on logarithmic expressionQAMCQMedium
#1048Infinite nested radical evaluationQAMCQMedium
#1049Periodicity of a functional equationQAMCQHard
#1050Cost minimization in call center hiringQAMCQHard
#1052Grid boundary vs interior tilesQAMCQMedium
#1087Continued Fraction EvaluationQAMCQMedium
#1101Number of Non-Negative Real RootsQAMCQMedium
#1104Consistency Condition for Linear EquationsQAMCQHard
#1113Sum of Infinite SeriesQAMCQHard
#1124Finding Relation Between x and yQAMCQMedium
#1126Sum of Fractional SeriesQAMCQMedium
#1129Inequality Condition for Real NumbersQAMCQEasy
#1137Parity Condition on Sequence of 1 and -1QAMCQHard
#1139Sum of Absolute ValuesQAMCQMedium
#1173Absolute Value Equations: Minimum RatioQAMCQEasy
#1193Logarithmic EquationQAMCQEasy
#1196Roots of Quadratic EquationQAMCQMedium
#1198Comparison of exponentsQAMCQEasy
#1234Algebraic SimplificationQAMCQEasy
#1265Self-Reflecting FunctionsQAMCQMedium
#1266System of Linear Equations with No SolutionQAMCQEasy
#1278Inequality EvaluationQAMCQEasy

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