model 6 operations of consecutive numbers (odd, even, square, etc.) Practice Questions Answers Test with Solutions & More Shortcuts

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: (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)

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: (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