model 2 average of consecutive numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

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

Answer: (a)

Fifth number = n

Tenth number = n + 5

Eleventh number = n + 6

New average = ${9n+n+5+n+6}/11$

= ${11n+11}/11$ = ${(n+1) ×11}/11$ = n+1

Answer: (c)

Numbers = x, x + 2, ...., x + 10 Required difference

= x + 10 – x = 10

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 = 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 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