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

Answer: (a)

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

4x + 12 = 748

4x = 748 – 12 = 736

x =$736/4$ = 184

Answer: (a)

Let the numbers be : 3x, 3x + 3 and 3x + 6

According to the question,

3x + 3x + 3 + 3x + 6 = 45

9x + 9 = 45

9x = 45 – 9 = 36

x = $36/9$ = 4

The smallest number = 3x = 3 × 4 = 12

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: (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

Answer: (d)

We have,

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

51 + 52 + ..... + 100 = (1 + 2 + ....... 100) – (1 + 2 + ... + 50)

= ${100×101}/2 - {50×51}/2$

= 5050 – 1275 = 3775

Answer: (d)

Let the three odd consecutive natural numbers be x, x + 2 and x + 4.

According to the question

x + x + 2 + x + 4 = 87

or 3x + 6 = 87

or 3x = 81; x = 27

Smallest number = 27