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MOST IMPORTANT quantitative aptitude - 9 EXERCISES

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The following question based on average topic of quantitative aptitude

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

(a) $\text"2n+5"/2$

(b) $n+2$

(c) $n+3$

(d) $\text"2n+9"/2$

The correct answers to the above question in:

Answer: (a)

According to the question let m = 1

∴ 5 consecutive integers are = 1,2,3,4,5

$\text"1+2+3+4+5"/5=n$

$n = 15/5=3$

6 consecutive integers starting with (m + 2) are = 3,4,5,6,7,8

∴$\text"3+4+5+6+7+8"/6=33/6=11/2$

Now check from option to put n = 3

While in Option :(a) $\text"2n+5"/2 = 11/2 $

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Read more simple average Based Quantitative Aptitude Questions and Answers

Question : 1

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

a) $5(a+4)$

b) $\text"abcde"/5$

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

d) $a+4$

Answer: (d) 

Question : 2

The average monthly income (in ₨) of certain agricultural workers is S and that of other workers is T. The number of agricultural workers is 11 times that of other workers. Then, the average monthly income (in ₨) of all the workers is :

a) $\text"S+11T"/12$

b) $\text"S+T"/12$

c) $\text"11S+T"/12$

d) $1/\text"11S"+T$

Answer: (c)

Question : 3

If the average of x and $1/x (x ≠ 0)$ is M, then the average of $x^2$ and $1/x^2$is :

a) $1-M^2$

b) $1-2M$

c) $2M^2-1$

d) $2M^2+1$

Answer: (c)

Question : 4

The average of nine consecutive numbers is n. If the next two numbers are also included the new average w

a) increase by 2

b) remain the same

c) increase by 1.5

d) increase by 1

Answer: (d)

Given,

$\text"(a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 + a + 7 + a + 8)"/9 = n$

$=> \text"(9a + 36)"/9 = n$

=> a + 4 = n -------------------- ( 1 )

If the next 2 numbers are included , let new average = k

$\text"(a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 + a + 7 + a + 8 + a + 9 + a + 10)"/11 = k$

$\text"(11a + 55)"/11 = k$

a + 5 = k -------------------- ( 2 )

Subtracting ( 1 ) from ( 2 ) , we get :

a + 5 - a - 4 = k - n

=> k - n = 1

=> k = n + 1

Therefore the new average is n + 1

Question : 5

a, b, c, d, e, f, g are consecutive even numbers. j, k, l, m, n are consecutive odd numbers. The average of all the numbers is

a) $3(\text"a+n"/2)$

b) $(\text"l+d"/2)$

c) $\text"a+b+m+n"/4$

d) $\text"j+c+n+g"/4$

Answer: (b)

According to the question consecutive even numbers = a, b, c, d, e, f, g

Consecutive odd numbers = j, k, l, m, n

Consecutive even number = 2, 4, 6, 8, 10, 12, 14

$\text"2+4+6+8+10+12+14"/7=56/7=8$ middle term

Consecutive odd numbers 1, 3, 5, 7, 9

$\text"1+3+5+7+9"/5=25/5$ middle term

Same as in the above situation.

Average of a, b, c, d, e, f, g = d

Average of j, k, l, m, n, = l

∴ Required average = ${d+l}/2$ 

Question : 6

Average of n numbers is a. The first number is increased by 2, second one is increased by 4, the third one is increased by 8 and so on. The average of the new numbers is

a) $a+(2^(n-1)-1)/n$

b) $a+2(2^n-1)/n$

c) $a+2^(n-1)/n$

d) $a+(2^n-1)/n$

Answer: (b)

Sum of new numbers

= na + (2 + 4 + 8 + 16 ..... to n terms)

Now, S = 2 + 4 + 8 + 16 + ..... to n terms

Here, a = first term = 2

r = common ratio = $4/2$ = 2

It is a geometric series.

∴ S =${a({r^n} - 1)}/{r-1}$= ${2({2^n} - 1)}/{2-1}$

= 2 ($2^n$ –1)

∴ Required average

= ${na +2({2^n}-1)}/n$

a +${2({2^n}-1)}/n$

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