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

Answer: (a)

Let the first number be x.

∴ x + 3 + x + 4 = 2 × 6

⇒ 2x + 7 = 12

⇒ 2x = 5 ⇒ x =$5/2$

∴ x + (x + 1) + ....... + (x + 7) = 8x + 28

= 8×$5/2$+ 28 = 20 + 28 = 48

Answer: (d)

Average of 8 consecutive even numbers = 93

∴ Fifth number = 93 + 1 = 94

∴ Largest number = 94 + 6 = 100

Answer: (c)

Five consecutive integers are :

x, x + 1, x + 2, x + 3 and x + 4

∴ Their average

= ${x+x+1+x+2+x+3+x+4}/5$

= ${5x+10}/5$ = x+2

New average

= ${(5x+10)+x+5+x+6}/7$

= ${7x+21}/7$= x + 3

Difference = x + 3 – x – 2 = 1

Answer: (d)

Average of 25 consecutive odd numbers = 55

∴ Mid number i.e. 13th number = 55

∴ 25th number = 55 + 2 × 12

= 55 + 24 = 79

Answer: (a)

Using Rule 1,

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

The required average

=${2+3+5+7+11+13+17+19+23}/9$

=$100/9$ = 11 $1/9$

Answer: (c)

Let three consecutive even numbers be x, x + 2 and x + 4. According to the question,

(x + x + 2 + x + 4) – ${x+x+2+x+4}/3$= 28

⇒ (3x + 6) – ${3x+6}/3$ = 28

⇒ (3x + 6) – (x + 2) = 28

⇒ 3x + 6 – x – 2 = 28

⇒ 2x + 4 = 28

⇒ 2x = 28 – 4 = 24

⇒ x = $24/2$ = 12