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There are three portions to every competitive exam. Data interpretation, verbal ability, and quantitative aptitude To answer the questions in the first two sections, there is a set pattern. What about data interpretation, though? There are a number of questions that can be asked in this section. And you must be alert to answer each and every question. Data sufficiency is one of the issues that need a lot of practice. This section’s questions are always asked in competitive exams.
Data Sufficiency
Data sufficiency encompasses a wide range of quantitative skills. A question is frequently followed by two or three statements in data sufficiency. To obtain the solution, you must decide whether any of the statements are required separately or in combination. You are not obliged to perform the computation; instead, you must determine whether the answer can be found using the data provided. There are numerous forms of data sufficiency questions. Today, we’ll talk about data sufficiency based on CI and SI.
Number System in Maths
The Number System is a technique of portraying numbers on the Number Line using symbols and rules. Digits are the symbols that range from 0 to 9. The Amount System is used to accomplish mathematical computations ranging from complex scientific calculations to simple counting of Toys for a Kid or the number of chocolates left in the box. Multiple sorts of number systems exist based on the digits’ basic value.
What is Algebra?
Algebra aids in the solution of mathematical equations and the calculation of unknown numbers such as bank interest, proportions, and percentages. We can rewrite the equations by using the variables in algebra to represent the unknown quantities that are related.
In our daily lives, we employ algebraic formulae to determine the distance and capacity of containers, as well as to calculate sales prices as needed. Algebra is useful for expressing a mathematical equation and relationship with the use of letters or other symbols to represent the entities. The equation’s unknown quantities can be solved using algebra.
Basic algebra, exponents, simplification of algebraic expressions, polynomials, quadratic equations, and other topics fall under the umbrella of algebra.
What is Mensuration?
Mensuration is defined as the act of measuring something. The world we live in is three-dimensional. In both primary and secondary school mathematics, the concept of measuring is crucial. Furthermore, measuring is directly related to our daily life. We learn to measure both 3D and 2D shapes when learning to measure objects. Both standard and nonstandard units of measurement can be used to measure objects or quantities. Handspans, for example, are a non-standard length measurement unit. You can even make an activity out of it by having youngsters use handspans to measure the length of things. Allow youngsters to observe that there is always the possibility of a discrepancy when measuring objects with non-standard units. As a result, consistent units of measurement are required. We now use units like kilometre, metre, kilogramme, gramme, litre, millilitre, and millilitre to measure length, weight, and capacity.
Examples of Number Systems
Example: To an octal number, convert (1056)16
Solution:
Given, 105616 is a hexadecimal number.
We must first convert the hexadecimal value into a decimal number.
(1056)16
= 1 × 163 + 0 × 162 + 5 × 161 + 6 × 160
= 4096 + 0 + 80 + 6
= (4182)10
We’ll now divide this decimal value by 8 repeatedly to get the appropriate octal number.
8 | 4182 | Remainder |
8 | 522 | 6 |
8 | 65 | 2 |
8 | 8 | 1 |
8 | 1 | 0 |
0 | 1 |
As a result, if we add the value of the remainder from the bottom to the top, we get:
(4182)10 = (10126)8
Therefore,
(1056)16 = (10126)8
Algebraic Examples
Example: Use the algebraic identities to expand (2x + 3y)2
Solution:
In this case, we’ll employ the algebraic identity, (a + b)2 = a2 + 2ab + b2
(2x + 3y)2 = (2x)2 + 2(2x)(3y) + (3y)2
= 4×2 + 12xy + 9y2
As a result, the solution is (2x + 3y)2 = 4×2 + 12xy + 9y2
Examples of Mensuration
• Find the surface area of a cuboid with 4 units of length, 5 units of breadth, and 6 units of height.
Solution:
Given that the cuboid’s length is 4 units, its width is 5 units, and its height is 6 units
The cuboid has a surface area of 2 (lw + wh + lh) square units.
= 2 × (lw + wh + lh)
= 2[(4 × 5) + (5 × 6) + (4 × 6)]
= 2(20 + 30 + 24)
= 2 (74)
= 148 units of measurement
As a result, the cuboid’s surface area is 148 square units.
Conclusion
It is obvious that numbers are employed to indicate quantities. A number system is created when certain symbols or digits are used to represent numbers. As a result, a number system is a method of defining a set of values that may then be used to represent a quantity.
Algebra teaches you how to solve problems by following a logical approach. As a result, you’ll have a greater knowledge of how numbers operate and interact in an equation. You’ll be better able to do any type of arithmetic if you have a deeper understanding of numbers.
It assists us in determining the volume of a 3D object, such as calculating the capacity of a water tank. It also aids us in measuring the surface areas of 3D objects, such as painting a building’s inner or outside wall. It is also beneficial in construction.
