Integers MCQ Quiz - Objective Question with Answer for Integers - Download Free PDF

Last updated on May 13, 2025

In this article, the Testbook stages an Integers MCQs Quiz question bank, which comprises intermediate-level questions and their solution and detailed explanation. Accompanying this, some tips and tricks are also given with the questions. Integers come under basic mathematics and contain complex numericals on real, whole its negative counterparts, natural numbers, etc. Integers objective questions are a part of various recruitments including GMAT, Bank and Railway Exams. To sharpen your mathematical skills, solve these Integers Questions.

Latest Integers MCQ Objective Questions

Integers Question 1:

What is the number of prime numbers less than 20?

  1. 8
  2. 9
  3. 5
  4. 7
  5. None of the above

Answer (Detailed Solution Below)

Option 1 : 8

Integers Question 1 Detailed Solution

Concept used:

A prime number is a number that is divisible only by itself and 1 (e.g. 2, 3, 5, 7, 11).

Calculation:

Prime numbers that are lesser than 20

⇒ 2, 3, 5, 7, 11, 13, 17, 19

Now, there are 8 such numbers.

∴ 8 prime numbers are there less than 20.

Integers Question 2:

When the digits of a two-digit number are reversed, the value of the number is increased by 45. The sum of the digits is 11. What is the original number?

  1. 83
  2. 65
  3. 38
  4. 24
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : 38

Integers Question 2 Detailed Solution

Given:

When the digits of a two-digit number are reversed, the value of the number is increased by 45.

The sum of the digits is 11.

Formula Used:

Let the original number be 10x + y, where x and y are the digits of the number.

Reversed number = 10y + x

Given that the reversed number is 45 more than the original number:

10y + x = 10x + y + 45

Given that the sum of the digits is 11:

x + y = 11

Calculation:

From the equation 10y + x = 10x + y + 45:

⇒ 10y + x - 10x - y = 45

⇒ 9y - 9x = 45

⇒ y - x = 5

We have two equations:

1) x + y = 11

2) y - x = 5

Adding the two equations:

⇒ (x + y) + (y - x) = 11 + 5

⇒ 2y = 16

⇒ y = 8

Substituting y = 8 in x + y = 11:

⇒ x + 8 = 11

⇒ x = 3

Original number = 10x + y

⇒ 10(3) + 8

⇒ 30 + 8

⇒ 38

The original number is 38.

Integers Question 3:

How many two digit prime numbers are there between 10 to 100 which remains prime numbers when the order of their digits is reversed?

  1. 8
  2. 9
  3. 10
  4. 12
  5. None of the above

Answer (Detailed Solution Below)

Option 2 : 9

Integers Question 3 Detailed Solution

A prime number is a number that has only two factors 1 and itself.

As every number is a factor of itself.

So the two-digit prime numbers which remain prime even when interchanging the digits are-

11,13,17,31,37,71,73,79,97

11

13

31

17

71

37

73

79

97

 

 

∴ There are "9" two-digit prime numbers are there between 10 to 100 which remain prime numbers when the order of their digits is reversed.

Integers Question 4:

X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number?

  1. XY
  2. X/Y
  3. Y/X
  4. (X + Y)/XY
  5. None of the above

Answer (Detailed Solution Below)

Option 1 : XY

Integers Question 4 Detailed Solution

Given :

X and Y are natural numbers other than 1, and Y is greater than X

Calculations :

1 < X < Y 

Let X be 2 and Y be 3         (X and Y are natural numbers)

Now put value in each option to get the values 

Option(1) ⇒ XY = 2 × 3 = 6 

Option(2) ⇒ X/Y = 2/3 

Option(3) ⇒ Y/X = 3/2 

Option(4) ⇒ (X + Y)XY = 5/6 

We can see that option 1 represents the largest value among all 

∴ Option1 will be the correct choice. 

 

Integers Question 5:

If the sum of two quantities is equal to six times their difference, then find the ratio of the two quantities.

  1. 7 ∶ 5
  2. 3 ∶ 7
  3. 4 ∶ 9
  4. 5 ∶ 2
  5. None of the above

Answer (Detailed Solution Below)

Option 1 : 7 ∶ 5

Integers Question 5 Detailed Solution

Given:

The sum of two quantities = 6 times their difference.

Formula Used:

Let the two quantities be a and b where a > b.

According to the given condition:

a + b = 6(a - b)

Calculation:

Given:

a + b = 6(a - b)

First, simplify the equation:

⇒ a + b = 6a - 6b

Combine like terms:

⇒ a + b - 6a + 6b = 0

⇒ -5a + 7b = 0

⇒ 7b = 5a

Divide both sides by a and b:

⇒ (a)/(b) = (7)/(5)

Therefore, the ratio of the two quantities is:

7 ∶ 5

The correct answer is option 1.

Top Integers MCQ Objective Questions

Rs. 720 was divided among A, B, C, D, E. The sum received by them was in ascending order and in arithmetic progression. E received Rs. 40 more than A. How much did B receive?

  1. Rs. 134
  2. Rs. 154
  3. Rs. 144
  4. Rs. 124

Answer (Detailed Solution Below)

Option 1 : Rs. 134

Integers Question 6 Detailed Solution

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Given:-

A+B+C+D+E = Rs. 720 

E - A = 40

Concept used:-

Arithmatic progression -

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

nth term(Tn) = a + (n -1)d

Calculation:- 

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

AmountE = a + 4d

Amount= 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, AmountB = 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

The sum of 7 consecutive natural numbers is 1617. Find how many of these are prime numbers?

  1. 2
  2. 3
  3. 1
  4. 4

Answer (Detailed Solution Below)

Option 1 : 2

Integers Question 7 Detailed Solution

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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

Find which of the following are twin Primes.

  1. (37, 41)
  2. (3 , 7)
  3. (43 , 47)
  4. (71, 73)

Answer (Detailed Solution Below)

Option 4 : (71, 73)

Integers Question 8 Detailed Solution

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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'.

If \(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}},\) where a, b and c are positive integers, then what is the value of (4a - b + 3c)

  1. 6
  2. 4
  3. 7
  4. 5

Answer (Detailed Solution Below)

Option 4 : 5

Integers Question 9 Detailed Solution

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Calculations:

\(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}}\)

\(⇒ \frac{1}{{1 \; + \;\frac{8}{{45}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)

\(⇒ \frac{1}{{1\; + \;\frac{1}{{5\; + \;\frac{5}{8}}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)

\(⇒ \frac{1}{{1\; + \;\frac{1}{{5\; + \;\frac{1}{{2 \;- \;\frac{2}{5}}}}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)

Compare both the sides

⇒ a = 1, b = 5 and c = 2

Value of (4a – b + 3c) = 4 × 1 – 5 + 3 × 2

⇒ 10 – 5 = 5

∴ The value of 4a – b + 3c is 5

Find the number of trailing zeros in 142!

  1. 36
  2. 30
  3. 34
  4. 32

Answer (Detailed Solution Below)

Option 3 : 34

Integers Question 10 Detailed Solution

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Given:

The number of trailing zeros in 142!

Concept used:

Number of trailing zeroes in n! = Number of times n! is divisible by 10 = Highest power of 10 which divides n! = Highest power of 5 in n!

Calculation:

According to the question,

142/5 = 28

28/5 = 5

5/5 = 1

∴ Total number of zeros = 28 + 5 + 1 is 34.

Find the number of trailing zeros in 375!.

  1. 93
  2. 94
  3. 92
  4. 91

Answer (Detailed Solution Below)

Option 1 : 93

Integers Question 11 Detailed Solution

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Given:

375!

Concept Used:

Number of zeros = Number of pairs of 2 × 5

Calculation:

Quotient of  375/5 = 75

Quotient of  75/5 = 15

Quotient of  15/5 = 3

∴ Total number of zeros = 75 + 15 + 3 = 93

Find the number of factors of 40.

  1. 2
  2. 6
  3. 8
  4. 12

Answer (Detailed Solution Below)

Option 3 : 8

Integers Question 12 Detailed Solution

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Concept used:

For finding number of factors of any number we do prime factorisation of that number.

If X = p1a × p2b, then

Number of factors of X = (a + 1) × (b + 1)

where, p1, p2 → Prime factors of X

Calculation:

Now, 40 = 23 × 51

⇒ Number of factors of 40 = (3 + 1) × (1 + 1) = 4 × 2 = 8

∴ The number of factors of 40 is 8.

What is the mean of the first five triangular numbers?

  1. 7
  2. 5
  3. 8
  4. 6

Answer (Detailed Solution Below)

Option 1 : 7

Integers Question 13 Detailed Solution

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Triangular number will satisfy following conditions,

Xn = n(n + 1) /2

⇒ X1 = 1

⇒ X2 = 3

⇒ X3 = 6

⇒ X4 = 10

⇒ X5 = 15

N∴ Mean of first five triangular number = (1 + 3 + 6 + 10 + 15) /5 = 7

Which of the numbers is NOT composite?

  1. 943
  2. 323
  3. 713
  4. 409

Answer (Detailed Solution Below)

Option 4 : 409

Integers Question 14 Detailed Solution

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⇒ A composite number is a positive integer which is not prime (i.e., which has factors other than 1 and itself).

⇒ Prime Factors of 943 = 23 × 41

⇒ Prime Factors of 323 = 17 × 19

⇒ Prime factors of 713 = 23 × 31

⇒ Prime factors of 409 = 1 × 409

∴ 409 is not composite as it does not have factors other than 1 and itself.

What is the number of factors of the expression: 60 × 18 × 15?

  1. 36
  2. 72
  3. 60
  4. 48

Answer (Detailed Solution Below)

Option 3 : 60

Integers Question 15 Detailed Solution

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⇒ 60 × 18 × 15

⇒ (4 × 3 × 5) × (2 × 9) × (3 × 5)

⇒ 23 × 34 × 52

∴ Number of factors of the expression,

⇒ (3 + 1) × (4 + 1) × (2 + 1) = 60
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