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

Answer: (c)

Let three consecutive natural numbers be x, x+1, x+2.

According to the question,

x + x + 1 + x + 2 = 87

3x + 3 = 87

3x = 84 ⇒ x = $84/3$ = 28

Middle number = 28 + 1 = 29 OR,$87/3$ = 29

Answer: (a)

x + x + 2 + x + 4 = 147

3 x + 6 = 147

3 x = 147 – 6 = 141

x = $141/3$ = 47

Middle Number = x + 2 = 47 + 2 = 49

Answer: (d)

The two-digit numbers are : 10, 11, 12, ..... 97, 98, 99

We know that,

1+ 2 + 3 + 4 + ..... + n = ${n(n+1)}/2$

Required sum = (1 + 2 + 3 + ......+ 99)-(1+2+ ..... + 9)

= ${99 (99 + 1)}/2 - {9(9 + 1)}/2$

= 4950 – 45 = 4905

Answer: (a)

x + x + 2 + x + 4 + x + 6 = 748

4x + 12 = 748

4x = 748 – 12 = 736

x =$736/4$ = 184

Answer: (d)

Let three consecutive even integers be 2x, 2x + 2 and 2x + 4 respectively.

2x + 2x + 2 + 2x + 4 = 54

6x + 6 = 54

6x = 54 – 6 = 48

x = 8

The least even number = 2 × 8 = 16

Answer: (c)

First 3-digit number = 100

Last 3-digit number = 999

Number of terms = 900

S = $n/2(a+l)$

= $900/2$[100 + 999]

= 450 × 1099 = 494550