model 2 average of consecutive numbers Practice Questions Answers Test with Solutions & More Shortcuts

average PRACTICE TEST [9 - EXERCISES]

model 1 basic average questions

model 2 average of consecutive numbers

model 3 twice, thrice, one third etc. of numbers

model 4 find nth average from 1st & last number

model 5 find new average from error

model 6 find average of excluded number

model 7 average on ages/weight

model 8 find monthly income

model 9 average on cricket/exam

average Important Formulas, Rules, Concepts & Shortcuts

Question : 1 [SSC CHSL 2012]

Average of first five odd multiples of 3 is

a) 21

b) 15

c) 16

d) 12

Shortcut »

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

Question : 2 [SSC CHSL 2012]

The average of four consecutive even numbers is 15. The 2nd highest number is

a) 16

b) 14

c) 18

d) 12

Shortcut »

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.

Question : 3 [SSC CGL Tier-I 2010]

The average of the first 100 positive integers is

a) 49.5

b) 50.5

c) 51

d) 100

Shortcut »

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

Question : 4 [SSC Data Entry Operator 2008]

The average of nine consecutive odd numbers is 53. The least odd number is

a) 45

b) 35

c) 27

d) 22

Shortcut »

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

Question : 5 [SSC CHSL 2012]

The average of four consecutive even numbers is 9. Find the largest number.

a) 10

b) 8

c) 6

d) 12

Shortcut »

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

IMPORTANT quantitative aptitude EXERCISES

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