Model 2 Average Of Consecutive Numbers Practice Questions Answers Test With Solutions & More Shortcuts

Answer: (b)

Using Rule 1,

Average of numbers = ${x_1+x_2+…+x_n}/n$

Average of first five odd multiples of 3

= ${3(1+3+5+7+9)}/5$

= ${3×25}/5$ = 15

Answer: (a)

x + x + 2 + x + 4 + x + 6 = 15 × 4

⇒ 4x + 12 = 60

⇒ 4x = 60 – 12 = 48

⇒ x = $48/4$ = 12

Hence, the numbers are 12, 14, 16, 18

∴ The second highest number is 16.

Answer: (b)

Using Rule 3,

Average of 1,2,3, .....n =${n +1}/2$

Formula,

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

Average of these numbers = ${n+1}/2$

∴ Required average

${100+1}/2$ = 50.5

Answer: (a)

x + x + 2 + x + 4 + x + 6 + x +

8 + x + 10 + x + 12 + x + 14 + x + 16 = 9 × 53

⇒ 9x + 72 = 477

⇒ 9x = 477 – 72 = 405

⇒ x = $405/9$ = 45

Answer: (d)

x + x + 2 + x + 4 + x + 6 = 9 × 4

⇒ 4x + 12 = 36

⇒ 4x = 36 – 12 = 24

∴ x = $24/4$ = 6

∴ Largest number = 6 + 6 = 12