CAT Algebra Sectional Test 5 – with Solutions

CAT Algebra Sectional Mock 5: Logarithms, Floor Functions and Progressions

Meant for CAT aspirants already comfortable with algebra fundamentals, Sectional Test 5 is a revision-stage practice set from Aptitude360. It covers polynomial conditions, quartic curves, logarithmic equations, floor functions, progressions and functional equations. Every problem comes with a detailed written solution so you can compare methods.

What this CAT algebra set tests

• Packing and buying problems that need whole-number solutions
• Building a polynomial from known values and keeping a quartic curve above the x-axis
• Horizontal lines cutting the graph of a modulus of a quadratic
• Equations with a variable in both base and exponent, and simultaneous log equations
• Floor function equations and where a step graph meets a parabola
• Minimum values through AM-GM and constrained sums of reciprocals
• Location of roots, sums of distances, AP and infinite GP conditions, iterated and functional equations

Formulas and rules to revise for this test

• AM-GM: \( \dfrac{a+b}{2}\ge\sqrt{ab} \) for \( a,b\ge 0 \)
• Infinite GP: \( S=\dfrac{a}{1-r} \), \( |r|<1 \)
• AP term: \( a_{n}=a+(n-1)d \)
• Log power: \( \log_{a}x^{k}=k\log_{a}x \)
• \( k \) lies between the roots of \( f(x)=ax^{2}+bx+c \) if \( a\,f(k)<0 \)

How to prepare for algebra of this kind

• Take logarithms on both sides when the variable sits in the exponent and the base together.
• For a sum of several modulus terms, check values at each critical point to find where the sum changes.
• Write out the first few terms of a recurrence; many sequences repeat in a short cycle.

Who this practice set suits

Useful for CAT and OMET candidates revising Quantitative Aptitude who want harder algebra after finishing basic theory.