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

Question : 21 [SSC CHSL 2012]

Eight consecutive numbers are given. If the average of the two numbers that appear in the middle is 6, then the sum of the eight given numbers is

a) 48

b) 36

c) 64

d) 54

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

Question : 22 [SSC CGL Tier-II 2015]

If the average of eight consecutive even numbers be 93, then the greatest number among them is

a) 98

b) 102

c) 86

d) 100

Answer: (d)

Average of 8 consecutive even numbers = 93

∴ Fifth number = 93 + 1 = 94

∴ Largest number = 94 + 6 = 100

Question : 23 [SSC CGL Tier-II 2015]

The average of five consecutive positive integers is n. If the next two integers are also included, the average of all these integers will

a) increase by 2

b) remain the same

c) increase by 1

d) increase by 1.5

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

Question : 24 [SSC SAS 2010]

The average of the squares of first ten natural numbers is

a) 38.5

b) 37.5

c) 36

d) 35.5

Answer: (a)

Using Rule 4,

Average of $1^2,2^2,3^2,4^2…x^2$ = ${(n+1)(2n+1)}/6$

${1^2+2^2+3^2+…+n^2}/n$ = ${(n+1)(2n+1)}/6$

∴ ${1^2+2^2+3^2+…+10^2}/10$ = ${(10+1)(2×10+1)}/6$

= ${11×21}/6$ = 38.5

Question : 25 [ SSC CGL Tier-I 2010]

The average of odd numbers upto 100 is

a) 49

b) 49.5

c) 50

d) 50.5

Answer: (c)

Formula,

Average of the first n natural odd numbers = $n/2$

Number of odd numbers upto $100/2$ = 50 = required average

Aliter : Using Rule 7,

Odd numbers are 1, 3, 5, ............., 99

Total odd numbers are= 50

∴ Average = 50

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