CAT Algebra Sectional Test 3 – with Solutions

CAT Algebra Sectional Test 3: Modulus, Logs and Functions Practice

CAT Algebra Sectional Test 3 is a Quantitative Ability topic set that mixes equation systems, nested modulus, logarithms, series and functional equations. Several questions push beyond routine formulas into comparison of large powers, coin counting and periodic functions. Aptitude360 provides a worked solution for every question.

What this CAT Algebra Test 3 checks

• Systems of linear equations with a parameter and conditions for a unique solution
• Nested modulus equations, sums of modulus functions and the location of roots in an interval
• Comparing very large powers and counting digits of a large number with logarithms
• Arithmetic and geometric sequences, including a squared geometric series
• Functional equations linking a value and its reciprocal, odd and periodic functions
• Integer solutions in coin and box problems, reciprocal polynomials and telescoping sums
• Maximum and minimum of rational expressions and of a max function

Key rules and formulas for this algebra set

• Sum of cubes: \( x^{3}+y^{3}=(x+y)^{3}-3xy(x+y) \)
• Digits in \( N \): \( \lfloor \log_{10}N \rfloor+1 \)
• Change of base: \( \log_{a}b=\dfrac{\log b}{\log a} \)
• Periodicity: \( g(x+4)=-g(x)\Rightarrow g(x+8)=g(x) \)
• Telescoping split: \( \dfrac{1}{k(k+1)}=\dfrac{1}{k}-\dfrac{1}{k+1} \)

Revision tips for harder CAT algebra

• To compare large powers, rewrite them with a common exponent and compare the bases
• In equations with the variable and its reciprocal, substitute the reciprocal and solve the pair together
• Divide a reciprocal polynomial by x squared and set a new variable equal to x plus its reciprocal

Who should take Algebra Test 3

CAT aspirants who are comfortable with basic algebra and want tougher, multi-step practice on functions and series will find this set useful.