Practice Operations on consecutive numbers - quantitative aptitude Online Quiz (set-1) For All Competitive Exams

Q-1)   Out of six consecutive natural numbers, if the sum of first three is 27, what is the sum of the other three ?

(a)

(b)

(c)

(d)

Explanation:

x + x + 1 + x + 2 = 27

3x + 3 = 27

3x = 24

x = 8

Three consecutive no's whose sum is 27 are 8, 9,10.

Hence, next 3 consecutive no's having 36 as sum are 11, 12 and 13


Q-2)   The sum of three consecutive odd natural numbers each divisible by 3 is 72. What is the largest among them?

(a)

(b)

(c)

(d)

Explanation:

Let the numbers be 3x, 3x + 3 and 3x + 6

3x + 3x + 3 + 3x + 6 = 72

9x + 9 = 72

9x = 72 – 9 = 63

x =$63/9$ = 7

∴ Largest number = 3x + 6 = 3 × 7 + 6 = 27


Q-3)   The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is

(a)

(b)

(c)

(d)

Explanation:

$10^2 + 11^2 + 12^2$ = 100 + 121 + 144 = 365

Required sum =10 + 11 + 12 = 33


Q-4)   The sum of the squares of three consecutive natural numbers is 2030. Then, what is the middle number?

(a)

(b)

(c)

(d)

Explanation:

Let the three consecutive natural numbers be x, x + 1 and x + 2.

According to question,

$x^2 + (x + 1)^2 + (x + 2)^2$ = 2030

or $x^2 + x^2 + 2x + 1 + x^2 + 4x + 4$ = 2030

or $3x^2 + 6x + 5 = 2030 $

or $3x^2 + 6x – 2025$ = 0

or $x^2 + 2x – 675$ = 0

or $x^2 + 27x – 25x – 675$ = 0

$x (x + 27) – 25 (x + 27)$ = 0

or $(x – 25) (x + 27)$ = 0

$x = 25 and – 27$

∴ Required number = $x$ + 1 = 25 + 1 = 26


Q-5)   The sum of all those prime numbers which are not greater than17 is

(a)

(b)

(c)

(d)

Explanation:

Prime numbers upto 17⇒ 2, 3, 5, 7, 11, 13, 17

Required sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58


Q-6)   What is the sum of two consecutive even numbers, the difference of whose square is 84?

(a)

(b)

(c)

(d)

Explanation:

$(x + 2)^2 – x^2 = 84$

or $x^2 + 4x + 4 – x^2$ = 84

4x = 84 – 4 = 80

x = $80/4$ = 20

x + 2 = 20 + 2 = 22

∴ The required sum = 20 + 22 = 42


Q-7)   Which one of the following is a factor of the sum of first twentyfive natural numbers ?

(a)

(b)

(c)

(d)

Explanation:

1 + 2 + 3 + ... + n = ${n(n+1)}/2$

1 + 2 + 3 + .. + 25 = ${25(25 + 1)}/2$ = 25 × 13

Hence, 13 is a factor of required sum.


Q-8)   What is the arithmetic mean of first 20 odd natural numbers ?

(a)

(b)

(c)

(d)

Explanation:

Sum of first n odd natural numbers = $n^2 = (20)^2$ = 400

Required average = $400/20$ = 20


Q-9)   The sum of three consecutive natural numbers each divisible by 5, is 225. The largest among them is

(a)

(b)

(c)

(d)

Explanation:

Let the required largest number be x.

According to the question,

x + x – 5 + x – 10 = 225

3x – 15 = 225

3x = 225 + 15 = 240

x = $240/3$ = 80


Q-10)   The sum of three consecutive odd natural numbers is 87. The smallest of these numbers is :

(a)

(b)

(c)

(d)

Explanation:

Let the three odd consecutive natural numbers be x, x + 2 and x + 4.

According to the question

x + x + 2 + x + 4 = 87

or 3x + 6 = 87

or 3x = 81; x = 27

Smallest number = 27