# Number System Questions and Answers updated daily – Aptitude

Number System Questions: Solved 444 Number System Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

## Number System Questions

21. A number 18567332145x is divisible by 8. What can be the minimum value of x?

SHOW ANSWER

Correct Ans:6

Explanation:

A number 18567332145x is divisible by 8. What can be the minimum value of x

Reference :

For a number to be divisible by 8; its last 3 digits should be divisible by 8

-----> So (45x) is divisible by 8

------> Thus x = 6 is the correct answer

Reference :

For a number to be divisible by 8; its last 3 digits should be divisible by 8

-----> So (45x) is divisible by 8

------> Thus x = 6 is the correct answer

**Hence the correct answer is x = 6**
Workspace

22. A fraction becomes (1/3) when 1 is subtracted from both the numerator and the denominator. The same fraction becomes (Â½) when 1 is added to both numerator and the denominator the sum of numerator and denominator of the fraction is"“

SHOW ANSWER

Correct Ans:10

Explanation:

Let fraction be (x/y)

-----> Then,((x-1)/(y-1)) = (1/3)

-----> Or, 3x â€“ 3 = y â€“ 1

-----> 3x â€“ y = 2 â€¦â€¦â€¦â€¦..(i)

-----> Again, ((x+1)/(y+1)) = (1/2)

-----> 2x + 2 = y + 1

-----> 2x â€“ y = â€“1 â€¦â€¦â€¦..(ii)

-----> On solving eqn (i) and (ii)

-----> x = 3, y = 7

-----> Sum of numerator and denominator of the fraction

-----> = 3 + 7 = 10.

-----> Then,((x-1)/(y-1)) = (1/3)

-----> Or, 3x â€“ 3 = y â€“ 1

-----> 3x â€“ y = 2 â€¦â€¦â€¦â€¦..(i)

-----> Again, ((x+1)/(y+1)) = (1/2)

-----> 2x + 2 = y + 1

-----> 2x â€“ y = â€“1 â€¦â€¦â€¦..(ii)

-----> On solving eqn (i) and (ii)

-----> x = 3, y = 7

-----> Sum of numerator and denominator of the fraction

-----> = 3 + 7 = 10.

**Hence the answer is : 10**
Workspace

23. If the sum of three odd natural numbers is 357, each of the number is divisible by 7. which one of the following is the largest number?

SHOW ANSWER

Correct Ans:133

Explanation:

If the sum of three odd natural numbers is 357, each of the number is divisible by 7. which one of the following is the largest number

Reference :

Let the number be (x, x+14,x+28)

-----> x+x+14+x+28 = 357

-----> 3x + 42 = 357

-----> 3x = 315

-----> x =105

-----> Required,

-----> x +28 = 105 +28 = 133

Reference :

Let the number be (x, x+14,x+28)

-----> x+x+14+x+28 = 357

-----> 3x + 42 = 357

-----> 3x = 315

-----> x =105

-----> Required,

-----> x +28 = 105 +28 = 133

**Hence the answer is : 133**
Workspace

24. The arithmetic mean of two numbers is 30 and their geometric mean is 24. What is the value of larger number?

SHOW ANSWER

Correct Ans:48

Explanation:

The arithmetic mean of two numbers is 30 and their geometric mean is 24. What is the value of larger number

Reference :

Let the numbers to be â€˜aâ€™ & â€˜bâ€™.

Arithmetic mean of the numbers = ((a+b)/2)

Geometric mean of the numbers = √ab

According to the question:

----> [(a+b)/2] = 30

----> (a+b) = 60

----> And

----> √(ab) = 24

----> ab = 576

Solving both equations:

----> a(60-a) = 576

----> 60a â€“ a

----> a

----> a

----> a(a-48)-12(a-48) = 0

----> (a-12)(a-48) = 0

----> a = 12, 48

Reference :

Let the numbers to be â€˜aâ€™ & â€˜bâ€™.

Arithmetic mean of the numbers = ((a+b)/2)

Geometric mean of the numbers = √ab

According to the question:

----> [(a+b)/2] = 30

----> (a+b) = 60

----> And

----> √(ab) = 24

----> ab = 576

Solving both equations:

----> a(60-a) = 576

----> 60a â€“ a

^{2 }= 576----> a

^{2 }â€“ 60a + 576 = 0----> a

^{2 }â€“ 48a - 12a + 576 = 0----> a(a-48)-12(a-48) = 0

----> (a-12)(a-48) = 0

----> a = 12, 48

**Hence larger number is = 48**
Workspace

25. The greatest among the numbers 3√2, 3√7, 6√5, 2√20 is

SHOW ANSWER

Correct Ans:6√5

Explanation:

WKT, √2 = 1.4

√7 = 2.6

√5 = 2.2

3√2 = 3 x 1.4 = 4.2

3√7 = 3x 2.6 = 7.8

6√5 = 6 x 2.2 = 13.2

2√20 = 2 x 2√5

= 4√5 = 4 x 2.2 = 8.8

Hence, 6√5 is greatest.

√7 = 2.6

√5 = 2.2

3√2 = 3 x 1.4 = 4.2

3√7 = 3x 2.6 = 7.8

6√5 = 6 x 2.2 = 13.2

2√20 = 2 x 2√5

= 4√5 = 4 x 2.2 = 8.8

Hence, 6√5 is greatest.

Workspace

26. What is the least value of K so that the number 6735K1 is divisible by 9?

SHOW ANSWER

Correct Ans:5

Explanation:

Given: 6735K1

6 + 7 + 3 + 5 + K + 1 = 22 + K

Here, the least number K should be greater than 22 and divisible by 9.

Therefore, the least number is27.

27 = 22 + K

K = 5

6 + 7 + 3 + 5 + K + 1 = 22 + K

Here, the least number K should be greater than 22 and divisible by 9.

Therefore, the least number is27.

27 = 22 + K

K = 5

Workspace

27. A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232, etc., Any number of this form is always exactly divisible by

SHOW ANSWER

Correct Ans:Smallest 3-digit prime number

Explanation:

Let the unit digit be x and ten's digit be y.

Number = 1000y + 100x + 10y + x

= 1010y + 101x

= 101(10y + x)

Hence, this number is divisible by 101, which is the smallest three-digit prime number.

Number = 1000y + 100x + 10y + x

= 1010y + 101x

= 101(10y + x)

Hence, this number is divisible by 101, which is the smallest three-digit prime number.

Workspace

28. In a zoo there are rabbits and pigeons. If their heads are counted, they are 90 while their legs are 224. Find the number of pigeons in the zoo?

SHOW ANSWER

Correct Ans:68

Explanation:

Let number of pigeons be 'X'.

Number of rabbits and pigeons = 90

Therefore, number of rabbits = 90 - X

According to the question,

2X + 4(90 - X) = 224

2X + 360 - 4X = 224

360 - 224 = 2X

136 = 2X

X = 68

Hence, there are 68 pigeons in the zoo.

Number of rabbits and pigeons = 90

Therefore, number of rabbits = 90 - X

According to the question,

2X + 4(90 - X) = 224

2X + 360 - 4X = 224

360 - 224 = 2X

136 = 2X

X = 68

Hence, there are 68 pigeons in the zoo.

Workspace

29. Five-eight of three-tenth of four-ninth of a number is 60. What is the number?

SHOW ANSWER

Correct Ans:720

Explanation:

Let the number be Y.

(5/8)x(3/10)x(4/9)x Y = 60

Y = 60 x (8/5) x (10/3) x (9/4)

Y = 720

(5/8)x(3/10)x(4/9)x Y = 60

Y = 60 x (8/5) x (10/3) x (9/4)

Y = 720

Workspace

30. What is the sum of first 12 terms of an arithmetic progression, if the first term is -19 and the last term is 36?

SHOW ANSWER

Correct Ans:102

Explanation:

Given: First term, a = -19; Last term, a

WKT, Required sum = (n/2)[a + a

= (12/2)[(-19 + 36)]

= 102

_{n}= 36; n =12WKT, Required sum = (n/2)[a + a

_{n}]= (12/2)[(-19 + 36)]

= 102

Workspace

31. The sum of three consecutive odd numbers is 20 more than the smallest number. What is the middle number?

SHOW ANSWER

Correct Ans:9

Explanation:

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

As per the question,

x + x + 2 + x + 4 = x + 20

3x + 6 = x + 20

3x - x = 20 - 6

2x = 14

x = 7

Therefore, three odd numbers are 7, 9, 13 and the middle number is 9.

As per the question,

x + x + 2 + x + 4 = x + 20

3x + 6 = x + 20

3x - x = 20 - 6

2x = 14

x = 7

Therefore, three odd numbers are 7, 9, 13 and the middle number is 9.

Workspace

32. The 4th and 7th term of an arithmetic progression are 11 and -4, respectively. What is the 15th term?

SHOW ANSWER

Correct Ans:-44

Explanation:

WKT, aâ‚™ = a + (n - 1)d

where a - first term; d - difference

Given 4th term of AP is 11,

a + (4 - 1)d = 11

a + 3d = 11 .....(1)

Also given that 7th term of AP is -4,

a + (7 - 1)d = -4

a + 6d = -4 .....(2)

On solving (1) and (2),

a = 26; d = -5

Therefore, 15th term = a + (15 - 1)d

= 26 + 14(-5)

= 26 - 70

= -44

where a - first term; d - difference

Given 4th term of AP is 11,

a + (4 - 1)d = 11

a + 3d = 11 .....(1)

Also given that 7th term of AP is -4,

a + (7 - 1)d = -4

a + 6d = -4 .....(2)

On solving (1) and (2),

a = 26; d = -5

Therefore, 15th term = a + (15 - 1)d

= 26 + 14(-5)

= 26 - 70

= -44

Workspace

33. What is the 507th term of the sequence 1, -1, 2, -2, 1, -1, 2, -2, 1,...........?

SHOW ANSWER

Correct Ans:2

Explanation:

Given sequence: 1, -1, 2, -2, 1, -1, 2, -2, 1,.......

From the sequence it is clear that repetition take place for each set of four terms.

Hence, remainder of 507/4 = 3.

In the given sequence, we know that four terms are repeated again and again. In that 3rd term is 2.

Therefore, 507th term is 2.

From the sequence it is clear that repetition take place for each set of four terms.

Hence, remainder of 507/4 = 3.

In the given sequence, we know that four terms are repeated again and again. In that 3rd term is 2.

Therefore, 507th term is 2.

Workspace

34. What number must be subtracted from both the numerator and the denominator of the fraction 27/35 so that it becomes 2/3?

SHOW ANSWER

Correct Ans:11

Explanation:

Let the number be 'X'.

(27 - X)/(35 - X) = 2/3

3(27 - X) = 2(35 - X)

81 - 3X = 70 - 2X

81 - 70 = 3X - 2X

X = 11

(27 - X)/(35 - X) = 2/3

3(27 - X) = 2(35 - X)

81 - 3X = 70 - 2X

81 - 70 = 3X - 2X

X = 11

Workspace

35. Sum of a fraction and thrice its reciprocal is 31/6. What is the fraction?

SHOW ANSWER

Correct Ans:9/2

Explanation:

Let the fraction be x/1.

Accoroding to the question,

(x/1) + 3(1/x) = 31/6

(x

6x

6x

6x

2x(3x - 2) - 9(3x -2) = 0

(2x - 9) (3x - 2) = 0

x = 9/2, 2/3

From the options, 9/2 is the correct answer.

Accoroding to the question,

(x/1) + 3(1/x) = 31/6

(x

^{2}) + 3)/x = 31/66x

^{2}+ 18 = 31x6x

^{2}-31x + 81 = 06x

^{2}-4x - 27x + 18 = 02x(3x - 2) - 9(3x -2) = 0

(2x - 9) (3x - 2) = 0

x = 9/2, 2/3

From the options, 9/2 is the correct answer.

Workspace

36. Which one of the following is the minimum value of the sum of two integers whose product is 24?

SHOW ANSWER

Correct Ans:10

Explanation:

Let the two integers be 'x' and 'y'.

Given: Product of two integers, xy = 24

The possible integers are (1, 24) or (2, 12) or (3, 8) or (4, 6)

Therefore, mininmum value of (x + y) = 4 + 6 = 10.

Given: Product of two integers, xy = 24

The possible integers are (1, 24) or (2, 12) or (3, 8) or (4, 6)

Therefore, mininmum value of (x + y) = 4 + 6 = 10.

Workspace

37. A man plants 5184 orange trees in his garden and arrange them,so that there are as many rows as there are orange trees in a row. How many rows are there in the garden?

SHOW ANSWER

Correct Ans:72

Explanation:

Given, number of rows and columns of trees are same.

So, let the number of rows and columns be 'Y'.

As per the question,

Y x Y = 5184

Y

Y = 72 rows.

So, let the number of rows and columns be 'Y'.

As per the question,

Y x Y = 5184

Y

^{2}= 5184Y = 72 rows.

Workspace

38. In a division problem, the divisor is 4 times the quotient and 3 times the remainder. If remainder is 4, then the dividend is

SHOW ANSWER

Correct Ans:40

Explanation:

Given: Remainder = 4

As per the question,

Divisor = 3 x Remainder = 3 x 4 = 12

Also, Divisor = 4 x Quotient

12 = 4 x Quotient

Quotient = 12/4

Quotient = 3

WKT, Dividend = Quotient x Divisor + Remainder

Dividend = 3 x 12 + 4

Dividend = 40.

As per the question,

Divisor = 3 x Remainder = 3 x 4 = 12

Also, Divisor = 4 x Quotient

12 = 4 x Quotient

Quotient = 12/4

Quotient = 3

WKT, Dividend = Quotient x Divisor + Remainder

Dividend = 3 x 12 + 4

Dividend = 40.

Workspace

39. The first term of an Arithmetic Progression is 22 and the last term is 11. If the sum is 66, the number of terms in the sequences are

SHOW ANSWER

Correct Ans:12

Explanation:

Given: s - 66, a - 22, l - 11

The sum of Arithmetic Progression is given by

s = (n/2)(a + l)

66 = (n/2)(22 - 11)

66 = (n/2)(11)

n = (66 x 2)/11

n = 12

The sum of Arithmetic Progression is given by

s = (n/2)(a + l)

66 = (n/2)(22 - 11)

66 = (n/2)(11)

n = (66 x 2)/11

n = 12

Workspace

40. Find the number lying between 900 and 1000 which when divided by 38 and 57 leaves in each case a remainder 23.

SHOW ANSWER

Correct Ans:935

Explanation:

Here, LCM of 38 and 57 is 114.

Where 114 is divisible by both 38 and 57.

Therefore, the required number is multiple of 114.

Number divisible by 114 between 900 and 1000 is 912.

Required number = 912 + 23 = 935.

Where 114 is divisible by both 38 and 57.

Therefore, the required number is multiple of 114.

Number divisible by 114 between 900 and 1000 is 912.

Required number = 912 + 23 = 935.

Workspace

Are you seeking for good platform for practicing Number System questions in online. This is the right place. The time you spent in Fresherslive will be the most beneficial one for you.

## Online Test on Number System @ Fresherslive

This page provides important questions on Number System along with correct answers and clear explanation, which will be very useful for various Interviews, Competitive examinations and Entrance tests. Here, Most of the Number System questions are framed with Latest concepts, so that you may get updated through these Number System Online tests. Number System Online Test questions are granted from basic level to complex level.

## Why To Practice Number System Test questions Online @ Fresherslive?

Number System questions are delivered with accurate answer. For solving each and every question, very lucid explanations are provided with diagrams wherever necessary.

Practice in advance of similar questions on Number System may improve your performance in the real Exams and Interview.

Time Management for answering the Number System questions quickly is foremost important for success in Competitive Exams and Placement Interviews.

Through Fresherslive Number System questions and answers, you can acquire all the essential idea to solve any difficult questions on Number System in short time and also in short cut method.

Winners are those who can use the simplest method for solving a question. So that they have enough time for solving all the questions in examination, correctly without any tense. Fresherslive provides most simplest methods to answer any tough questions. Practise through Fresherslive test series to ensure success in all competitive exams, entrance exams and placement tests.

## Why Fresherslive For Number System Online Test Preparation?

Most of the job seekers finding it hard to clear Number System test or get stuck on any particular question, our Number System test sections will help you to success in Exams as well as Interviews. To acquire clear understanding of Number System, exercise these advanced Number System questions with answers.

You're Welcome to use the Fresherslive Online Test at any time you want. Start your beginning, of anything you want by using our sample Number System Online Test and create yourself a successful one. Fresherslive provides you a new opportunity to improve yourself. Take it and make use of it to the fullest. GOODLUCK for Your Bright Future.