model 6 operations of consecutive numbers (odd, even, square, etc.) Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Let the numbers be x and y.

According to the question,

x + 2y = 8 .... (i)

x – y = 2 ....... (ii)

By equation (i) – (ii),

2y + y = 8 – 2

3y = 6; y = 2

From equation (ii),

x – 2 = 2 ; x = 4

Answer: (d)

Sum of first n odd natural numbers = $n^2 = (20)^2$ = 400

Required average = $400/20$ = 20

Answer: (d)

Let the required largest number be x.

According to the question,

x + x – 5 + x – 10 = 225

3x – 15 = 225

3x = 225 + 15 = 240

x = $240/3$ = 80

Answer: (a)

$(x + 2)^2 – x^2 = 84$

or $x^2 + 4x + 4 – x^2$ = 84

4x = 84 – 4 = 80

x = $80/4$ = 20

x + 2 = 20 + 2 = 22

∴ The required sum = 20 + 22 = 42

Answer: (a)

Sum of all multiples of 3 upto 50

= 3 + 6 + ..... + 48

= 3 (1 + 2 + 3 + .... + 16)

= 3×${16(16+1)}/2$= 3 × ${272}/2$ = 408

[Since 1+2+3+…+n = ${n(n+1)}/2$]

Answer: (c)

Prime numbers upto 17⇒ 2, 3, 5, 7, 11, 13, 17

Required sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58