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5a3. Linear Equations: GMAT Math Tutorials

An equation is a statement that two numbers or expressions are equal. An Equation has two equal parts. Equations are useful for relating variables and numbers. Many word problems can easily be written down as equations with a little practice.


e.g., 5x + 2 = 12


When an equation has a variable, the solution to the equation is the number that makes the equation true when we replace the variable with its value. This also called as the root of the equation.


We say x = 2 is a solution to the equation 4x + 5 = 13, for replacing each occurrence of x with 2 gives us 4 × 2 + 5 = 13 ==> 8 + 5 = 13 ==> 13 = 13 which is true.


Simple Equation: Degree of an equation is the highest power of the variable used. If an equation has only one parameter with degree 1 then it is called as simple equation. Simple equations have only one variable of degree one. Hence when simplified it gives only one value as its root.


Simultaneous equations: If an equation of degree 1 has two or more than two variables then we cannot solve it to get unique value as its roots.


Averages


Arithmetic mean and Geometric mean are measures of central tendency. The other forms are mode and median, which we will be covering in statistics.


Arithmetic mean


The Average or Mean or Arithmetic Mean of a group of quantities of the same kind is their sum divided by the numbers of quantities.




Example


1. A woman is five years younger than her husband and three times as old as her daughter. If the daughter attains the age of 21 after six years, what is the present age of the father?


(A) 45 years
(B) 50 years
(C) 55 years
(D) 40 years
(E) 60 years

Solution: Husband’s age = x years. Therefore, Woman's age = x – 5 years.

Therefore Daughter's age = , Therefore -- + 6 = 21

i.e. x = 50. Hence (B) 







 
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