Aptitude Day 43

Problems on Numbers

1. Three times a positive number is less than its square by 54. Find the number.

Solution:
                Let the number be x.
                x²-3x=54

                x²-9x+6x-54=0

                (x-9)(x+6)=0

                x=9, -6.

 The number is 9.

2. Twice the square of a natural number is equal to the 30 more than the four times of that number. Find the number.

Solution:

                Let the number be x.

                2x²  = 4x+30

                2x²-4x-30=0

                x²-2x-15=0

                x²-5x+3x-15=0

                (x-5)(x-5)=0

                 x=5.

The number is 5.