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

Question : 11 [SSC Multi-Tasking Staff 2013]

What is the average of the first six (positive) odd numbers each of which is divisible by 7?

a) 49

b) 47

c) 43

d) 42

Answer: (d)

Required average

= ${7+21+35+49+63+77}/6$

= ${7(1+3+5+7+9+11)}/6$

= ${7×36}/6$ = 42

Question : 12 [SSC CGL Tier-I 2014]

If a, b, c, d, e are five consecutive odd numbers, their average is

a) a+4

b) 5(a+b+c +d+e)

c) ${abcde}/5$

d) 5(a+4)

Answer: (a)

b = a + 2

c = b + 2 = a + 4

d = c + 2 = a + 6

e = d + 2 = a + 8

∴ Required average

= ${a+a+2+a+4+a+6+a+8}/5$

= ${5a+20}/5$ = a+4

Question : 13 [SSC CGL Tier-II 2012]

The average of 5 consecutive integers starting with ‘m’ is n. What is the average of 6 consecutive integers starting with (m + 2) ?

a) ${2n+9}/2$

b) (n+3)

c) (n+2)

d) ${2n+5}/2$

Answer: (d)

m + m + 1 + m + 2 + m + 3 + m + 4 = 5n

⇒ 5m + 10 = 5n

⇒ m + 2 = n ....(i)

Required average = ${m+2+m+3+m+4+m+5+m+6+m+7}/6$

= ${6m+27}/6$

= ${2m+9}/2$ = ${2(n-2)+9}/2$= ${2n+5}/2$ By (i) [m = n – 2]

Question : 14 [SSC Constable 2012]

The average of 7 consecutive numbers is 20. The largest of these numbers is :

a) 20

b) 22

c) 23

d) 24

Answer: (c)

Average of 7 consecutive numbers is 20.

Since the numbers are consecutive, they form an arithmetic series with common difference 1.

Since, 7 is odd, 20 must be the middle number.

We can write the series as below,

17, 18, 19, 20, 21, 22, 23

∴ The largest of these numbers is 23.

Question : 15 [SSC CGL Tier-1 2011]

The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers ?

a) Data inadequate

b) 19

c) 17

d) 15

Answer: (b)

If the smallest number be x, then

$x/3$+12 = x+2

⇒ x + 36 = 3x + 6

⇒ 3x – x = 36 – 6

⇒ 2x = 30 ⇒ x = 15

∴ Third number = 15 + 4 = 19

IMPORTANT quantitative aptitude EXERCISES

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