Skip to main content

Number Systems For CAT

Number Systems For CAT



Basic Formula
  1. (a+b)² = a² + b² + 2ab
  2. (a−b)² = a² + b²− 2ab
  3. (a+b)² − (a−b)² = 4ab
  4. (a+b)² + (a−b)² = 2(a²+b²)
  5. (a²−b²) = (a+b)(a−b)
  6. (a+b+c)² = a² + b² +c² + 2(ab+bc+ca)
  7. (a³+b³) = (a+b)(a²−ab+b²)
  8. (a³−b³) = (a−b)(a²+ab+b²)
  9. (a³+b³+c³−3abc) = (a+b+c)(a²+b²+c²−ab−bc−ca)
  10. If a+b+c=0, then a³+b³+c³ = 3abc

Type of Number

  1. Natural Number:
  2. Whole Number
  3. Integer Number
  4. Even Number
  5. Odd Number
  6. Prime Number
  7. Composite Number
  8. Co Prime Number
  9. Real Number

Remainder and Quotient

The remainder is r when number p is divided by k" means p=kq+r the integer q is called the quotient. For Example: remainder is 1 when 5 is divided by 2 means 5 = 2 x 2 + 1

Even, Odd Number 

A number n is even if the remainder is zero when n is divided by 2:n=2z+0, or n=2z.
A number n is odd if the remainder is one when n is divided by 2:n=2z+1.

The following properties for odd and even numbers are very useful - you should memorize them:
  1. even x even = even
  2. odd x odd = odd
  3. even x odd = even
  4. even + even = even
  5. odd + odd = even
  6. even + odd = odd

Divisibility of Number

Divisibility By 2
Divisibility By 3
Divisibility By 4
Divisibility By 5
Divisibility By 6
Divisibility By 7
Divisibility By 8
Divisibility By 9
Divisibility By 10

Arithmetic Progression 

If each term of a progression differs from its preceding term by a constant, then such a progression is called an arithmetical progression. This constant difference is called the common difference of the A.P.
  1. (1+2+3+....+n) = n(n+1)⁄2
  2. (l2+22+32+...+n2)=n(n+1)(2n+1)6
  3. (13+23+33+...+n3)=n2(n+1)24

Geometrical Progression

A progression of numbers in which every term bears a constant ratio with its preceding term, is called a geometrical progression. The constant ratio is called the common ratio of the G.P.

Point to Remember





Labels:

Comments

Post a Comment

Popular posts from this blog

SSC Practice Problem Solution

SSC Practice Problem Solution In this post, we will discuss solution of  SSC Practice Problem . Question 1  The efficiency of (A + B) = 100/24 = (25/6)% The efficiency of (A + B + C) = 100/8 = (25/2)% The efficiency of C = 25/2 – 25/6 = (50/6)% Hence, C can alone finish this job in = 100/(50/6) = 12 days Answer: 12 days option (1) Question 2  Original price = Rs. 6000; Price after discount = 6000 – 1200 = Rs. 4800; Price after raising service contract = 4800 + 480 = Rs. 5280 Answer: Rs. 5280 option (2) Question 3  Suppose the received money by A, B, and C is respectively 5x, 6x, and 9x. 5x = 450; => x = 90; Hence, the total money = 20x = 20*90 = Rs. 1800; Answer: Rs. 1800 option (2) Question 4 Suppose the Cost price of the bag= Rs. x; Hence, x + 0.15x = 230; => x = Rs. 200; Selling price after selling on 20% = 200 + 20% of 200 = Rs. 240 Answer: Rs. 240 option (3) Question 5  The required percentage ...
Post a Comment
Read more

Average

Average In this post, We will learn about average.  Average of any collection of data is the sum of data divide by number of data. Average = (Sum of observations /  Number of observations) Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.  problems The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u=(x+y)/2 and v=(y+z)/2. If x ≥ z, then the minimum possible value of x is (CAT 2018) As specified in the question mean of x and y and z is 80 x+y+z=3*80 mean of x, y, z,u,v is 75 x+y+z+u+v=75*5 2u=x+y 2v=y+z x+y+z+((x+y+y+z)/2)=75*5 y+3(x+y+z)=75*10 y=750-720 y=30 since x+y+z=240 y=30 so x+z=210 since x>=z so minimum value of x=210/2 = 105 Problem2: In first 5 inings sehwag has scored at average of 40. In sixth ining He had scored 52 what is His average after 6th ining. one simple approach is getting total score divided by no of inin...
Post a Comment
Read more

Trigonometry

Trigonometry The word ‘trigonometry’ means ‘triangle measurement’.It involves the ratios of the sides of right triangles and the angles. The main three ratios are called tangent, sin, and cosine. Being one of the most important topics for the  CAT exam , trigonometry requires the candidates to be well prepared with excessive practice to solve the related questions. There are some triangle questions which can be solved much faster if you can remember the trigonometric ratios involved, especially questions based on heights and distances. So, here is a detailed lesson on trigonometry for CAT topic along with various illustrations to help you understand the topic easily. There are three sides to a right-angled triangle which are named as follows depending on the angle.  Opposite Side The opposite side refers to the side opposite to the angle in question (θ). In this case, the opposite side is BC. Adjacent Side The Adjacent side is the side adjacent to angle...
Post a Comment
Read more

Complex Number

Complex Number While solving the equation of the form  a x 2 + b x + c = 0 , the roots of the equations can take three forms which are as follows: Two Distinct Real Roots Similar Root No Real roots (Complex Roots) The introduction of complex numbers in the 16th century made it possible to solve the equation  x 2 + 1 = 0 . The roots of the equation are of the form  x = ± − 1 ‾ ‾ ‾ √  and no real roots exist. Thus, with the introduction of complex numbers, we have Imaginary roots. We denote  − 1 ‾ ‾ ‾ √  with the symbol i, where i denotes Iota (Imaginary number). An equation of the form z= a+ib, where a and b are real numbers, is defined to be a complex number. The real part is denoted by Re z = a and the imaginary part is denoted by Im z = b. Algebraic Operation on Complex numbers: Addition of two complex numbers Subtraction of two complex number Multiplication of two complex number Division of two complex number Power of Iota (i) ...
Post a Comment
Read more