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)
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)
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)
$10^2 + 11^2 + 12^2$ = 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)
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)
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)
$(x + 2)^2 – x^2 = 84$
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)
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)
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)
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)
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