Number System MCQ Quiz - Objective Question with Answer for Number System - Download Free PDF

Given:

Time taken by the first person to complete one cycle = 120 seconds

Time taken by the second person to complete one cycle = 150 seconds

Time taken by the third person to complete one cycle = 80 seconds

Formula used:

To find when the three people will meet at the starting point, we need to calculate the LCM (Least Common Multiple) of the times they take to complete one cycle.

Calculation:

Prime factorizations:

120 = 2³ × 3 × 5

150 = 2 × 3 × 5²

80 = 2⁴ × 5

LCM = Highest power of each prime factor:

LCM = 2⁴ × 3 × 5² = 16 × 3 × 25 = 1200 seconds

∴ The three people will meet at the starting point after 1200 seconds (or 20 minutes).

Given:

The numbers are: 26, 20, 40, 13

Formula used:

To find the smallest number divisible by these numbers, we need to calculate the LCM (Least Common Multiple).

Calculation:

Prime factorizations:

26 = 2 × 13

20 = 2² × 5

40 = 2³ × 5

13 = 13

LCM = Highest power of each prime factor:

LCM = 2³ × 5 × 13 = 8 × 5 × 13 = 520

∴ The smallest natural number divisible by 26, 20, 40, and 13 is 520.

Given :

The number of three consecutive numbers = 87

Calculation :

Let the three consecutive natural numbers be x , (x + 1) , (x + 2)

According to the question,

x + (x + 1) + (x + 2) = 87

⇒ 3x + 3 = 87

⇒ 3x = 87 - 3

⇒ 3x = 84

⇒ x = 28

Middle term = x+1 

⇒ 28 + 1 = 29

∴ The middle number is 29.

Given:

$\sqrt[6]{64}+\sqrt[4]{50625}+\sqrt[3]{21952}+\sqrt{4489}$

Calculation:

$\sqrt[6]{64}+\sqrt[4]{50625}+\sqrt[3]{21952}+\sqrt{4489}$

​⇒ $\sqrt[6]{2^6}+\sqrt[4]{{15}^4}+\sqrt[3]{{28}^3}+\sqrt{{67}^2}$

⇒ 2 + 15 + 28 + 67 = 112

∴ Option 2 is the correct answer.

Given:

Number 1: 446, leaving remainder 9.

Number 2: 487, leaving remainder 12.

Formula Used:

To find the greatest number that divides two given numbers leaving specific remainders, subtract the remainders from each number and then find the GCD (Greatest Common Divisor) of the results.

Calculation:

Number 1 - Remainder 1 = 446 - 9

Number 2 - Remainder 2 = 487 - 12

⇒ 446 - 9 = 437

⇒ 487 - 12 = 475

Now find the GCD of 437 and 475.

437 = 19 × 23

475 = 19 × 25

GCD (437, 475) = 19

The greatest number that will divide 446 and 487 leaving remainders 9 and 12 respectively is 19.

Given:

3240

Concept:

If k = ax × by, then

a, and b must be prime number 

Sum of all factors = (a0 + a1 + a2 + ….. + ax) (b0 + b1 + b2 + ….. + by)

Solution:

3240 = 2³ × 3⁴ × 5¹

Sum of factors = (20 + 21 + 22 + 23) (3⁰ + 3¹ + 3² + 3³ + 3⁴) (5⁰ + 5¹)

⇒ (1 + 2 + 4 + 8) (1 + 3 + 9 + 27 + 81) (1 + 5)

⇒ 15 × 121 × 6

⇒ 10890

∴ required sum is 10890

Given:-

A+B+C+D+E = Rs. 720 

E - A = 40

Concept used:-

Arithmatic progression -

a, a + d, a + 2d, a + 3d, a + 4d

n^th term(T_n) = a + (n -1)d

Calculation:- 

Let, A receive Rs. a and the difference between each consecutive person be Rs. d.

Amount_E = a + 4d

AmountA = a

According to the question,

⇒ a + 4d - a = 40

⇒ 4d = 40

⇒ d = 10

Also,

a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 720

⇒ 5a + 10d = 720

⇒ 5a + 10 × 10 = 720

⇒ 5a = 720 - 100

⇒ a = 620/5 = 124

So, Amount_B = a + d = 124 + 10 = Rs. 134

Alternate Method

Calculation:

A, B, C, D and E 

As the amount received is in AP,

Difference in an amount of two consecutive members is the same.

⇒ B – A = C – B = D – C = E – D

We have E – A = 40, 

⇒ B – A = 10, C – B = 10, D – C  = 10, E – D = 10,

Let say A received Rs. x,

Then B, C, D and E will receive,

⇒ x + 10, x + 20, x + 30, x + 40

According to the question,

⇒ x + (x + 10) + (x + 20) + (x + 30) + (x + 40) = 720

⇒ 5x + 100 = 720

⇒ 5x = 620

⇒ x = 124

B will receive = x + 10 = 124 + 10 = 134

∴ B will receive amount of Rs. 134

Given:

The sum of seven consecutive natural numbers = 1617

Calculation:

Let the numbers be n, n + 1, n + 2, n + 3, n + 4, n + 5, n + 6 respectively

⇒ 7n + 21 = 1617

⇒ 7n = 1596

⇒ n = 228

The numbers is 228, 229, 230, 231, 232, 233, 234

Out of these 229, 233 are prime numbers

∴ Required prime numbers is 2

Given:

Length of timber₁ = 143 m

Length of timber2 = 78 m

Length of timber3 = 117 m

Calculation:

Greatest possible length of each plank = HCF of 143, 78 and 117

143 = 13 × 11

78 = 13 × 2 × 3

117 = 13 × 3 × 3 

HCF is 13

∴ Greatest possible length of each plank is 13 m.

Concept used:

Twin prime numbers are pairs of prime numbers that have a difference of exactly two.

In other words, if (p, p+2) are both prime numbers, then they are considered twin primes.

Formally, if p and p+2 are both primes, then they are known as twin primes.

For example, (3, 5), (11, 13), and (17, 19) are pairs of twin primes.

Calculation:

Twin primes are pairs of successive primes that differ by two. 

The primes from 1 to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Options:

(37, 41) - Difference between them is 4.

(3, 7) - The difference between them is 4.

(43, 47) - Difference between them is 4.

(71, 73) - Difference between them is 2.

Here, in the given option (71 and 73) are prime numbers and their difference is '2'.

GIVEN:

Four bells ring simultaneously at starting and an interval of 6 sec, 12 sec, 15 sec and 20 sec respectively.

CONCEPT:

LCM: It is a number which is a multiple of two or more numbers.

CALCULATION:

LCM of (6, 12, 15, 20) = 60

All 4 bells ring together again after every 60 seconds

Now,

In 2 Hours, they ring together = [(2 × 60 × 60)/60] times + 1 (at the starting) = 121 times

∴ In 2 hours they ring together for 121 times

Mistake Points

In these type of question we assume that we have started counting the time after first ringing. Due to this when we calculate the LCM it gives us the ringing at 2nd time not the first time. So, we needed to add 1.

Given:

Four bells ringing timing is 12 sec, 15 sec, 20 sec,30 sec 

Calculation:

Four bells ringing timing is 12 sec, 15 sec, 20 sec,30 sec 

Now we have to take LCM of time interval

⇒ LCM of (12, 15, 20, 30) = 60

Total seconds in 8 hours = 8 × 3600 = 28800

Number of times bell rings = 28800/60

⇒ Number of times bell rings = 480

If four bells ring together in starting

⇒ 480 + 1 

∴ The bell ringing 481 times in 8 hours.

Mistake PointsThe bells start tolling together, the first toll also needs to be counted, that is the number of times of tolling since the first time.

Given:

The number is 8¹⁰ × 9⁷ × 7⁸ 

Concept used:

If a number of the form x^a × y^b × z^c ...... and so on, then total prime factors = a + b + c ..... and so on

Where x, y, z, ... are prime numbers

Calculation:

The number 8¹⁰ × 9⁷ × 7⁸ can be written as (2³)¹⁰ × (3²)⁷ × 7⁸ 

The number can ve written as 2³⁰ × 3¹⁴ × 7⁸ 

Total number of prime factors = 30 + 14 + 8

∴ The total number of prime factors are 52

Given:

676xy is divisible by 3, 7 & 11

Concept:

When 676xy is divisible by 3, 7 &11, it will also be divisible by the LCM of 3, 7 &11. 

Dividend = Divisor × Quotient + Remainder

Calculation:

LCM (3, 7, 11) = 231

By taking the largest 5-digit number 67699 and divide it by 231.

∵ 67699 = 231 × 293 + 16

⇒ 67699 = 67683 + 16 

⇒ 67699 - 16 = 67683 (completely divisible by 231)

∴ 67683 = 676xy (where x = 8, y = 3)

(3x - 5y) = 3 × 8 - 5 × 3

⇒ 24 - 15 = 9 

∴ The required result = 9

We know that,

product of two numbers = L.C.M × H.C.F of those numbers

Let the second number be x.

24 × x = 168 × 6

x = 6 × 7