Number Operations and Properties

2's complement method converts subtraction into addition by representing negative numbers in a form that allows direct addition with the minuend. Unlike 1's complement which requires an end-around carry, 2's complement handles this automatically by discarding the final carry. 10's complement is for decimal systems.

Starting with 13 = 13w/(1-w). Divide both sides by 13: 1 = w/(1-w). Multiply both sides by (1-w): 1-w = w. Add w to both sides: 1 = 2w, so w = 1/2. Now calculate (2w)² = (2 × 1/2)² = 1² = 1.

It is observable that

534 + 781 = 5 + 3 + 4 + 7 + 8 + 1 = 28 and

932 + 455 = 9 + 3 + 2 + 4 + 5 + 5 = 28

Similarly, 721 + 422 = 7 + 2 + 1 + 4 + 2 + 2 = 18, so it is a correct answer.

This question is based on the pattern of

8 + 5 = 13 => 31 and 12 + 5 = 17 => 71

Similarly, 11 + 9 = 20 => 02 = 2, so it is the correct answer.

Since the pattern is, 2 x 3 x 4 => (2 + 1) x (3 + 1) x (4 + 1) = 60, And 7 x 5 x 6 => (7 + 1) x (5 + 1) x (6 + 1) = 336, So 4 x 5 x 3 => (4 + 1) x (5 + 1) x (3 + 1) = 120, so it is a correct answer.

Options 1 and 3 both are correct. Hence, it is the most appropriate option.

Step by step: i%5 = 8%5 = 3; j-3 = 15-3 = 12; k+2 = 4+2 = 6; (j-3)/(k+2) = 12/6 = 2 (integer division); 4 + 2 = 6; (i%5) * 6 = 3*6 = 18; 2*18 = 36

2/8 = 1/4 also 8/12 = 2/3. Therefore, the equation is 1/4X + 2/3 = 3.

For two numbers x and y: AM = (x+y)/2 = 40, so x + y = 80. GM = √(xy) = 24, so xy = 576. We can find (x-y)^2 = (x+y)^2 - 4xy = 6400 - 2304 = 4096, so x-y = 64. Solving x + y = 80 and x - y = 64 gives x = 72, y = 8.

The number is x. So, x + 5 = 12 

If Z = 2, 12Z will be 12 x 2 = 24.

It is the expression for a number which is 2 less than 3 times a number x and the number so obtained is added with y + 4.

• 150, - 160, - 170, - 180 lie between - 140 and - 200.

Additive inverse of - 10 = 10 Six less than 10 is 4.

t² - 4t + 1 = 0   or t² + 1 = 4t                 t + 1/t = 4         Or (t + 1/t + 3 (t + 1/t) = 64 or t³ + 1/t³ = 64 - 3 x 4 = 52