Quantitative Aptitude Notes Part 16(INEQUALITY)

INEQUALITY

 

What is Variables?
An element, a feature, or a factor that is liable to vary or change to find any equation and represent by x, y, z etc.

  • Example: 3x + 27y = 40 is variable
  • Example: 2y + 5x = 12 is variable.

 

What is Constant?
A constant is special number or a real number usually or whose value is fixed in the context of use is called a constant.

  • Example: 5x – 3y + 2z = 24 here is 5, 3, 2, 24 are constant value.
  • Example: 4y + 7y – 9z = 53 here is 4, 7, 9, 53 are constant value.

 

Example:

6x2 +11x + 3 = 0

Answer:
Shortcut tricks :
This equation +6 is coefficient of x2
+ 11 is coefficient of x
+3 is constant term
Step 1: we multiply (+6) x (+3) = +18
Step 2 : we break + 18 in two parts such that addition between them is 11.
So,  +18 = 9 + 2 = 11 . and product of both factors is 18 . So, +9 and +2 = Sum of is +11

Step 3: Change the sign of both the factors, So +9 = -9 and +2 = -2
and divide by coefficient of x2 , So we get -9 / 6 = -3 / 2 and -2 / 6 = – 1 / 3 .

 

Example:
4y2 + 12y + 8 = 0

Answer:
Shortcut tricks:
4  x 8 = +32
we break + 32 in two parts such that addition between them is 12.
+32 = (+8) + (+ 4) = +12 .
Change sign of both factor and divide by coefficient of y2 ,
So – 8 / 4 = – 2 .
– 4 / 4 = -1

  1. e . – 2, – 1  .

Relation between two variables

  1. x>y
  2. x>y
  3. x<y
  4. x<y
  5. x = y relation cannot be determined.
  • 5x2 + 11x + 6 = 0
  • 4y2+ 10y + 6 = 0

In equation one multiply 5 and 6 get the result is 30 separate 30 as 5 and 6 which is addition of 5+6=11.
In equation one multiply 4 and 6 get the result is 24 separate 24 as 4 and 6 which is addition of 4+6=10.

and switch the sign in to negative and divide by coefficient of x2. -5 / 5 = -5 and -6 / 5 = -6 / 5.
and the second equation is do same that is -4 / 4 = -1 and -6 / 4 = -3 / 2.

Now we get the solution is for x = -5 and -6 / 5.
Now we get the solution is for y = -1 and -3 / 2.

Example:
7x + 3y = 15……. Equation 1
10x + 5y = 10……. Equation 2

Answer:
At first we multiply the equation by 5 & 3
7x + 3y = 15……. Equation 1            (Multiply by  5 )
10x + 5y = 10……. Equation 2          (Multiply by  3 )

35x + 15y = 75……. Equation 1        (Multiply by  5 )
30x + 15y = 30……. Equation 2        (Multiply by  3 )

5x = 45 .
x = 9 .

We apply value of x in any equation to obtain y value
we apply in equation 1
7 x 9 + 3y = 15
63 + 3y = 15
3y = 65 – 15
y =  17  Approx

So , x = 9 and y = 17

 

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