Tutorials

In work life and personal life often we need to learn the basics on a subject quickly. Usually it is not easy to acquire the basic concepts on any subject reliably in a short time from a concise material.

Basic concepts on any subject form the foundation, but generally we have found it is not easy to build it in a short time. Our focus here is on base concepts in a concise form that can be learned quickly and be used as a launch pad for further learning and subject specific problem solving.

Often we added a rich concept layer derived from the base concepts that helps to solve more complex problems with great ease. For us, it is a two layer concept model: Base concepts and Rich concepts derived from base concepts. Objective is efficient problem solving.

Subcategories

Basic maths: Basic concepts on maths. The content is primarily targeted for competitive test requirements.

Reasoning and logic analysis: Tutorials, problems and puzzles on competitive test reasoning and logic analysis.

How to solve a hard number system question for CAT confidently and quickly 8

Submitted by Atanu Chaudhuri on Fri, 08/01/2021 - 22:55

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The leftmost digit of a natural number at least 7 digit long is 3. When the leftmost digit is dropped, the number formed by the rest of the digits becomes $\frac{1}{5}$th of the original number. What is the product of the non-zero digits of the original number?

Hint: Solve this 8th hard number system question for CAT using the very basic concepts intelligently.

How to solve a hard number system question for CAT confidently and quickly 7

Submitted by Atanu Chaudhuri on Wed, 06/01/2021 - 22:12

thumb how to solve hard cat number system problem confidently and quickly 7

Cube of a number exceeds its product with two other numbers by 2, the cube of the second number is less than their product by 3 and the cube of the third exceeds their product by 3. Find the lowest of the three numbers.

Solve this 7th hard number system question for CAT quickly by mathematical reasoning based on indices concepts and inequality analysis.

How to solve a hard number system question for CAT confidently and quickly 6

Submitted by Atanu Chaudhuri on Tue, 05/01/2021 - 20:50

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The product of a two digit number and a second number formed by reversing the digits of the first is 2430. Find the lower number. In solving this 6th hard number system question for CAT, mathematical reasoning based on factors multiples concept provided quick systematic solution...

How to solve a hard number system question for CAT confidently and quickly 5

Submitted by Atanu Chaudhuri on Mon, 04/01/2021 - 12:24

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If 495 is subtracted from a 3-digit number with its digits reversed, result will be the original number. Sum of the digits of the number is 12 and sum of all pairwise products of its digits is 41. Find the number.

For quick solution of the 5th hard number system question for CAT, limit the possible values of the digits by identifying breakthrough conditions and enumeration using the given conditions....

How to solve a hard number system question for CAT confidently and quickly 4

Submitted by Atanu Chaudhuri on Sun, 03/01/2021 - 22:14

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The sum of thousands and tens digits in a 4 digit number is 4, the sum of hundreds and units digit is 15, and units digit is greater than the thousands digit by 7. Among all such numbers satisfying these conditions, find the number, the sum of product of whose thousands digit and units digit and hundreds digit and tens digit is the least.

For quick solution of this 4th hard number system question for CAT limit the possible values of the digits by variable linking of the conditions...

How to solve a hard number system question for CAT confidently and quickly 3

Submitted by Atanu Chaudhuri on Sun, 03/01/2021 - 16:15

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Denominator of a fraction is less than the square of the numerator by 1. If 2 is added to both, the fraction will be more than $\frac{1}{3}$. And when 3 is subtracted from both, the fraction remains positive and is smaller than $\frac{1}{10}$. Find the fraction.

For quick solution of this 3rd hard number system question for CAT, explore deeply inequality analysis and inequality algebra...

How to solve a hard number system question for CAT confidently and quickly 2

Submitted by Atanu Chaudhuri on Fri, 01/01/2021 - 18:12

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What two digit number is less than the sum of squares of its digits by 11 and exceeds their doubled product by 5?

For quick solution of the 2nd hard number system question for CAT, discover the breakthrough information from the given resources...

How to solve a hard number system question for CAT confidently and quickly 1

Submitted by Atanu Chaudhuri on Tue, 10/11/2020 - 23:41

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The first hard number system question for CAT: How many of the four digit natural numbers divisible by 24 have also 24 appearing in them? Should solve the CAT number system problem under two minutes.

Basic and Rich Geometry Concepts Part 9, Segment Relation for a Secant of a Circle

Submitted by Atanu Chaudhuri on Thu, 23/07/2020 - 01:20

thumb tangent segments and secant of a circle

The square of a tangent segment from an external point will be equal to the product of the two segments of a secant of a circle through the point. This important relation between tangent segments and secant of a circle is explored.

Basic and Rich Geometry Concepts Part 8, Internal Angle bisectors and Segment Ratios at Incentre of a triangle

Submitted by Atanu Chaudhuri on Tue, 21/07/2020 - 23:48

thumb incentre ratio of angle bisector segments and opposite side segments by angle bisector

Incentre ratio is Segmentation ratio of angle bisectors at incentre. An internal angle bisector also segments opposite side in ratio of two adjacent sides.

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