MATH: aptitude 2024 (with Complete Solutions)

Base Method Multiplication correct answers 105×107 100+(5+7)|35 (5×7) =11235 97×102 =100-1 | -06 =9900-06 =9894 better to use for base 10,100,.. Units Digit Method (multiplication) correct answers This method of multiplication uses the sum of the unit's digit, provided all the other digits on the left-hand side of the unit digit are the same. 62*63= (6+0.5)x6 | (2+3) 39 | 06 3906 10^n Method (squaring) correct answers B+2x | x^2 Squaring Properties correct answers 1. n² equal to the sum of the first n odd numbers *n²=∑(2k-1)* 5² = 25 = 1 + 3 + 5 + 7 + 9. square of any number can be represented as the sum 1 + 1 + 2 + 2 +...+ n − 1 + n − 1 + n. This is the result of *adding a column and row of thickness 1 to the square graph* * 52 = 50² + 50 + 51 + 51 + 52 = 2500 + 204 = 2704*. 2. only end with digits *00, 1, 4, 6, 9, or 25* in base 10, as follows: 3. if the last digit of a number is 0, its square ends in 0 (00); preceding digits form *square* 1 or 9, its square ends in 1; preceding digit *÷4* 2 or 8, its square ends in 4; preceding digit *even* 3 or 7, its square ends in 9; preceding digit *÷4* 4 or 6, its square ends in 6; preceding digit *odd* 5, its square ends in 25 ;preceding digit 0, 2, 06, 56 4. The digital sum of any perfect square can be only *0, 1, 4, 9, and 7* graphical method for squaring correct answers 51²=50²+50+51=2500+101=2601 best for unit digit in 1 mean method for squaring correct answers 52² 54×50+2²=2704 (x+y)(x-y)=x²-y²