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Number System Practice Quiz

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Number System Practice Quiz

shape Introduction

Number system is one of the important topic in the Quantitative Aptitude section . Number system is a system to represent numbers using digits and symbols. Number system provides a unique representation of every number and represents arithmetic and algebraic structure of the figures. Number System is all about finding the face value & place value of a digit, basic rules and different types of numbers, rules for divisibility, factors and multiples


The article of Number system Practice Quiz consists of different models of Number system questions with solutions. The Number System Practice Quiz is extremely important for aspirants of different competitive exams across the globe. In India, the Quantitative Aptitude quiz helps the candidates preparing different competitive exams like RRB ALP/Technical Exams/Junior Engineer Recruitment Exams, SSC, IBPS PO Exams and etc.


shape Quiz

1. 1. If the following groups of fractions is arranged in
ascending order?


    A. \(\frac{5}{16}\), \(\frac{7}{18}\), \(\frac{6}{17}\)
    B. \(\frac{7}{18}\), \(\frac{6}{17}\), \(\frac{5}{16}\)
    C. \(\frac{5}{16}\), \(\frac{6}{17}\), \(\frac{7}{18}\)
    D. \(\frac{6}{17}\), \(\frac{7}{18}\), \(\frac{5}{16}\)


Answer – Option C

Explanation –

\(\frac{5}{16}\) = 0.312

\(\frac{6}{17}\) = 0.352

\(\frac{7}{18}\) = 0.388

2. If fractions\(\frac{9}{13}\), \(\frac{2}{3}\), \(\frac{8}{11}\), \(\frac{5}{7}\), are arranged in ascending order, then the correct sequenceis

    A. \(\frac{9}{13}\), \(\frac{2}{3}\), \(\frac{8}{11}\), \(\frac{5}{7}\)
    B. \(\frac{2}{3}\), \(\frac{9}{13}\), \(\frac{5}{7}\), \(\frac{8}{11}\)
    C. \(\frac{2}{3}\), \(\frac{8}{11}\), \(\frac{5}{7}\), \(\frac{9}{13}\)
    D. \(\frac{5}{7}\), \(\frac{8}{11}\), \(\frac{2}{3}\), \(\frac{9}{13}\)


Answer – Option B

Explanation –

\(\frac{9}{13}\) = 0.692, \(\frac{2}{3}\) = 0.666,

\(\frac{8}{11}\) = 0.727, \(\frac{5}{7}\) = 0.714

Hence ascending order is \(\frac{2}{3}\) = \(\frac{9}{13}\), \(\frac{5}{7}\), \(\frac{8}{11}\)

3. Which one of the following is the largest?
2\(\sqrt{5}\), 6\(\sqrt{3}\), 3\(\sqrt{7}\) and 8\(\sqrt{2}\)


    A. 8\(\sqrt{2}\)
    B. 2\(\sqrt{5}\)
    C. 6\(\sqrt{3}\)
    D. 3\(\sqrt{7}\)


Answer – Option A

Explanation –

2\(\sqrt{5}\) = 2 * 2.236 = 4.472

6\(\sqrt{3}\) = 6 * 1.732 = 10.392

3\(\sqrt{7}\) = 3 * 2.646 = 7.938

8\(\sqrt{2}\) = 8 * 1.414 = 11.312

Clearly8\(\sqrt{2}\) is largest

4. I f numer at or and denomi nat or of a pr oper fractions are increased by the same quantity, then the resulting fraction is

    A. always greater than the original fraction
    B. always less than the original fraction
    C. always equal to the original fraction
    D. none of these


Answer – Option A

Explanation –

Let proper fraction = \(\frac{2}{3}\) =

therefore Resulting fraction = \(\frac{2 + 1}{3 + 1}\) = \(\frac{3}{4}\)

Hence \(\frac{2}{3}\) < \(\frac{3}{4}\)

\(\frac{1}{2}\) < \(\frac{2}{3}\)

\(\frac{3}{5}\) < \(\frac{3 + 1}{5 + 1}\)

\(\frac{3}{5}\) < \(\frac{4}{6}\) etc.

5. If x + y > 5 and x – y > 3, then which of the following gives all possible values of x ?

    A. x > 3
    B. x > 4
    C. x > 5
    D. x < 5


Answer – Option B

Explanation –

Solving x + y > 5 and x – y > 3 we get,

x > 4.

6. I f x and y ar e negat ive, then which of the following statements is/are always true ?

    I. x + y is positive
    II. xy is positive
    III. x – y is positive


    A. I only
    B. II only
    C. III only
    D. I and III only


Answer – Option B

Explanation –

Product of – ve numbers is also +ve.

7. The value of \(\sqrt{ \sqrt{0.000064}}^{3}\)

    A. 0.02
    B. 0.2
    C. 2.0
    D. None


Answer – Option B

Explanation –
Given expression =\(\sqrt{0.008}^{3}\) = 0.2

8. If 11, 109, 999 is divided by 1111, then what is the remainder ?

    A. 1098
    B. 11888
    C. 1010
    D. 1110


Answer – Option D

Explanation –

9. The value of \(\frac {\frac{1}{2}\frac{1}{2}of \frac{1}{2}}{\frac{1}{2}\frac{1}{2}of \frac{1}{2}}\)

    A. 2\(\frac{2}{3}\)
    B. 1
    C. 1\(\frac{1}{3}\)
    D. 3


Answer – Option A

Explanation –

\(\frac {\frac{1}{2}\frac{1}{2} * \frac{1}{2}}{\frac{1}{2}\frac{1}{2} * \frac{1}{2}}\)

= \(\frac {\frac {1}{2} \frac{4}{1}}{\frac{3}{4}}\) = 2 * \(\frac{4}{3}\)

= \(\frac{8}{3}\)

= 2\(\frac{2}{3}\)

10. Taking \(\sqrt{2}\) = 1.414, \(\sqrt{3}\) = 1.732, \(\sqrt{5}\) = 2.236 and \(\sqrt{6} \) = 2.449,then the value of \(\frac{9 +\sqrt{2}}{\sqrt{5} +\sqrt{3}}\) + \(\frac{9 -\sqrt{2}}{\sqrt{5} -\sqrt{3}}\) to three places of decimals is

    A. 9.2321
    B. 13.716
    C. 10.723
    D. 15.892


Answer – Option C

Explanation –

\(\frac{9 +\sqrt{2}}{\sqrt{5} +\sqrt{3}}\) + \(\frac{9 -\sqrt{2}}{\sqrt{5} -\sqrt{3}}\)

= \(\frac{1}{2}\)[15\(\sqrt{5}\)– 3\(\sqrt{5}\) + 2\(\sqrt{6}\)]

= \(\frac{1}{2}\) [33.540 – 5.196 – 7.898]

= 10.732

11. The cube root to 1.061208

    A. 1.022
    B. 10.22
    C. 0.102
    D. 1.02


Answer – Option D

Explanation –

Here 1.061208 = \({1.02}^{3}\)

Required cube root = 1.02

12. The least number having four digits which is a perfect square is

    A. 1004
    B. 1016
    C. 1036
    D. None of these


Answer – Option D

Explanation –

Required number =1024 = \({32}^{2}\)

13. The missing number in the series 8, 24, 12, 36, 18, 54, ______ is

    A. 27
    B. 108
    C. 68
    D. 72


Answer – Option A

Explanation –

Second term is 3 times of the first term and third term is half of the second term, repeat this process the missing term is half of 54, i.e. 27

14. What is the eighth term of the sequence 1, 4, 9, 16, 25,_______ ?

    A. 8
    B. 64
    C. 128
    D. 200


Answer – Option B

Explanation –

Given sequence can be written as \({1}^{2}, {2}^{2}, {3}^{2}, {4}^{2}, {5}^{2}\), …

Hence it’s eighth term

=\({8}^{2}\)

= 64

15. Which of the following is the best approximation for the following expression \(\sqrt{{7.9986 / 0.115} + 19.97}\)?

    A. 15
    B. 10
    C. 1.0
    D. 1.3


Answer – Option B

Explanation –

Rounding off, we get \(\sqrt{{\frac{8}{0.1}} + 20}\) = \(\sqrt{100}\)

1. The value of (1 +0.1 +0.11 +0.111) is

    A. 1.321
    B. 1.211
    C. 1.111
    D. 1.331


Answer – Option A

Explanation –

1 + 0.1000 + 0.110 + 0.111 = 1.321

2. When a number is divided by 5, it gives remainder 3. What is the remainder when square of that number is divided by 5?

    A. 9
    B. 3
    C. 4
    D. 1


Answer – Option C

Explanation –

Let the number be 8.

Thus, when \( {8}^{2}\) = 64 will be divided by 5, then remainder will be 4.

3. \(\sqrt{10}\) = 3.1623(approx). What is the approx, value of \(\frac{1}{\sqrt{10}}?\)

    A. 0.333
    B. 0.3162
    C. 0.3221
    D. 0.3437


Answer – Option A

Explanation –

\(\frac{1}{3.1623}\) will be less than 0.3333

4. . Find the value of \({(2744)}^{\frac{1}{3}}\)?

    A. 24
    B. 14
    C. 34
    D. 16


Answer – Option B

2744 is a multiple of 7.

Hence, the answer has to be 14.

Explanation –

5. Find the L.C.M. of 148 and 185.

    A. 680
    B. 740
    C. 2960
    D. 3700


Answer – Option B

Explanation –

148 = 37 × 4 and 185 = 37 × 5

LCM = 37 × 4 × 5 = 740

6. If \({2}^{2n – 1}\) = \(\frac{1}{{8}^{2n – 1}}\) then the value of ‘n’ is:

    1. A. 3
    B. 2
    C. 0
    D. -2


Answer – Option B

Explanation –

\({2}^{2n – 1}\) = \(\frac{1}{3n – 9}\)

\({2}^{2n – 1}\) = \({2}^{3n – 9}\) = \({2}^{0}\)

5n – 10 = 0

n = \(\frac{10}{5}\) = 2

7. What is the largest possible length of a scale that can be used to measure exactly the lengths 3 m, 5 m 10 cm and 12 m 90 cm ?

    A. 10 cm
    B. 20 cm
    C. 25 cm
    D. 30 cm


Answer – Option A

Explanation –

Required scale has to be of length 10 cm because 10 cm is the shortest length in in given question.

8. After measuring 120 metres of a rope, it was discovered that the metre rod was 3 cm longer. The true length of the rope measured is :

    A. 116 m 40 cm
    B. 121m 20 cm
    C. 123m
    D. 123m 60 cm


Answer – Option D

Explanation –

Actual length has to be

120m + (120 × 3) cm = 120 m + 360 cm

= 123 m 60 cm.

9. Solve \(\sqrt{0.000064}^{3}\)

    A. 0.4
    B. 0.04
    C. 0.004
    D. 0.0004


Answer – Option B

Explanation –

\( \sqrt{0.000064}^{3}\) = \( \sqrt{\frac{4}{100} * \frac{4}{100} * \frac{4}{100}}^{3}\) = 0.4

10. The HCF of two numbers is 6 and their LCM is 72. If one number is 24, the other number is

    1. A. 12
    B. 18
    C. 36
    D. 72


Answer – Option B

Explanation –

We know that, x × y = LCM × HCF (x, y are the two distinct numbers)

x × 24 = 72 × 6

x = 18.

11. The largest number which divides by 72 and 125, leaving remainders 7 and 8 respectively is

    A. 13
    B. 56
    C. 65
    D. 900


Answer – Option A

Explanation –

In such a questions it is better to check the options. In this case 13 satisfies the given condition. Rest of the numbers are large enough to be eliminated easily.

12. The HCF of two numbers is 12 and their LCM is 72. If one number is 36, the other number is

    A. 12
    B. 24
    C. 36
    D. 48


Answer – Option B

Explanation –

set the number be x

x × 36 = 12 × 72

x = 24

13. The largest number which divides 81 and 108, leaving remainders 6 and 3 respectively is

    A. 9
    B. 15
    C. 18
    D. 515


Answer – Option B

Explanation –

Checking the options we get the correct answer as 15.

14. The HCF of two numbers is 15 and their LCM is 270. If one number is 45, the other number is

    A. 9
    B. 15
    C. 18
    D. 515


Answer – Option B

Explanation –

HCF × LCM = Product of numbers

Other number =\(\frac{15 * 270}{45}\) = 90

15. The largest number which divides 247 and 319, leaving remainders 7 and 4 respectively is

    A. 15
    B. 30
    C. 45
    D. 56


Answer – Option A

Numbers = 247, 319

i.e, Remainders = 7 & 4,

i.e, 247 – 7 = 240, 319 – 4 = 315 are divisible

HCF (240, 315) = 15

1. \(2^{2^{4}}\)divided by \(2^{2^{3}}\) is equal to:.

    A. \(2^{2}\)
    B. \(2^{1}\)
    C. \(2^{-2}\)
    D. \(2^{-1}\)


Answer – Option A

Explanation –

\(2^{2^{4}}\)divided by \(2^{2^{3}}\)

=\(2^{8}\)divided by \(2^{6}\)

= \(2^{2}\)

2. Arrange the following fractions in ascending order. \(\frac{7}{10}\), \(\frac{3}{8}\), \(\frac{4}{5}\)

    A. \(\frac{3}{8}\), \(\frac{7}{10}\), \(\frac{7}{10}\)
    C. \(\frac{4}{5}\), \(\frac{3}{8}\), \(\frac{7}{10}\)
    D. \(\frac{7}{10}\), \(\frac{3}{8}\), \(\frac{4}{5}\)


Answer – Option A

Explanation –

\(\frac{7}{10}\) = 0.7

\(\frac{3}{8}\) = 0.375

i.e, \(\frac{3}{8}\) < \(\frac{7}{10}\) < \(\frac{4}{5}\)

\(\frac{4}{5}\) = 0.8

3. By what least number should 192,000 be divided so as to become a perfect cube?

    A. 2
    B. 5
    C. 3
    D. 7


Answer – Option C

Explanation –

\(\frac{192000}{2}\) = 96,000 Not a perfect cube.

\(\frac{192000}{3}\) = 64,000 A perfect cube

4. Find the value of: 3 + 0.03 + 0.003 + 0.0003

    A. 12
    B. 3.0333
    C. 3.3333
    D. 6.0333


Answer – Option B

Explanation –

3 + 0.03 + 0.003 + 0.0003

= 3.0333

5. Value of \(\pi\) (approx. value 3.14) is :

    A. Terminating decimal
    B. Recurring decimal
    C. Non-terminating non-repeating decimal
    D. Indeterminate


Answer – Option B

6. Which one of the following is not a prime number?

    A. 71
    B. 91
    C. 61
    D. 31


Answer – Option B

Explanation –

91 is not a prime number

91 = 7 × 13

7. Find the value of : \(\frac{{489 + 375}^{2}-{489 – 375}^{2}}{489*375}\)

    A. 144
    B. 864
    C. 2
    D. 4


Answer – Option D

Explanation –

\(\frac{{(489 + 375)}^{2}-{(489 – 375)}^{2}}{489*375}\)

\(\frac{{(a + b)}^{2}-{(a – b)}^{2}}{a * b}\)

\(\frac{4ab}{ab}\) = 4

8. Find the L.C.M. of \(\frac{1}{3}\), \(\frac{5}{6}\), \(\frac{2}{9}\), \(\frac{4}{27}\)

    A. \(\frac{1}{54}\)
    B. \(\frac{10}{27}\)
    C. \(\frac{20}{3}\)
    D. None of these


Answer – Option C

Explanation –

= \(\frac{(LCM 1, 5, 2, 4)}{(HCF 3, 6, 9, 27)}\)

\(\frac{20}{3}\)

9. . Arrange the fractions \(\frac{5}{7}\), \(\frac{13}{16}\), \(\frac{8}{12}\), \(\frac{16}{29}\) and \(\frac{3}{4}\) in ascending order of magnitude :

    A. \(\frac{16}{29}\) < \(\frac{7}{12}\)< \(\frac{5}{8}\) < \(\frac{3}{4}\)< \(\frac{13}{16}\)
    B. \(\frac{16}{29}\) < \(\frac{5}{8}\) < \(\frac{7}{12}\) < \(\frac{13}{16}\) < \(\frac{3}{4}\)
    C. \(\frac{3}{4}\) < \(\frac{13}{16}\) < \(\frac{7}{12}\) < \(\frac{5}{8}\) < \(\frac{16}{29}\)
    D. \(\frac{3}{4}\) < \(\frac{5}{8}\) < \(\frac{7}{12}\) < \(\frac{13}{16}\) < \(\frac{16}{29}\)


Answer – Option A

Explanation –

\(\frac{5}{8}\) = 0.625

\(\frac{7}{12}\) = 0.0.583

\(\frac{13}{16}\) = 0.8125

\(\frac{16}{29}\) = 0.551

10. If \(\frac{a}{b}^{x-1}\) = \(\frac{b}{a}^{x-3}\), then the value of ‘x’ is :

    A. \(\frac{1}{2}\)
    B. 1
    C. 2
    D. -1


Answer – Option C

Explanation –

\(\frac{a}{b^{x – 1}}\) = \(\frac{b}{a^{x – 3}}\)

\(\frac{a}{b^{x – 1}}\) = \(\frac{b}{a^{3 – x}}\)

x – 1 + 3 – x

2x = 4

x = 2

11. . Find the value of (0.000216)3

    A. 0.6
    B. 0.06
    C. 0.006
    D. 0.0006


Answer – Option B

Explanation –

\({0.000326}{\frac{1}{3}}\) = \({216}^{\frac{1}{3}}\) * \({216}^{{(-6)}^\frac{1}{3}}\)

= 6 × \({10}^{-2}\)= 0.06

12. If a =\({2}^{129}\) * \({3}^{81}\) * \({5}^{128}, \), b = \({2}^{125}\) \({3}^{81}\) * \({5}^{128} \), c = \({2}^{126}\) * \({3}^{82}\) * \({5}^{128} \), d = \({2}^{125}\) * \({3}^{82}\) * \({5}^{129}\)then HCF OF a, b, c and d is

    A. \({2}^{125}\) * \({3}^{81}\) * \({5}^{129} \)
    B. \({2}^{125}\) * \({3}^{81}\) * \({5}^{128} \)
    C. \({2}^{125}\) * \({3}^{82}\) * \({5}^{128}\)
    D. \({2}^{129}\) * \({3}^{82}\) * \({5}^{129}\)


Answer – Option B

Explanation –

Highest power of 2 common in a1, b1, c1, d1= 125

Highest power of 3 common in a1, b1, c1, d1 = 81

Highest power of 5 common in a1, b1, c1, d1 = 128

i.e, HCF = \({2}^{125}\) * \({3}^{81}\) * \({5}^{128} \),

13. Let x be a least number which when divided by 21,33,35 and 55 leaves in each case a remainder 3, but is exactly divisible by 67. The sum of digits of x is

    A. 8
    B. 10
    C. 12
    D. 15


Answer – Option D

Explanation –

= LCM (211, 331, 351, 55)k + 3

= 1155k + 3

\(\frac{A}{Q}\) x = 67 k5

= 67k = 1155k + 3

at k = 4

Number = 4623 which satisfies all conditions.

i.e, sum of digits = 4 + 6 + 2 + 3 = 15

14. HCF of two numbers, each consisting of four digits, is 103 and their LCM is 19261. The difference of the numbers is

    A. \(\frac{6}{8}\)
    B. \(\frac{5}{9}\)
    C. \(\frac{5}{8}\)
    D. \(\frac{4}{8}\)


Answer – Option A

Explanation –

Product of two Numbers = LCM × HCF

x × y = 103 × 19261

= 103 × 103 × 11 × 17 = 1133 × 1751

Difference = \(\frac{6}{8}\)

15. Let a =\({3}^{129}\) * \({5}^{128}\) * \({7}^{22}, \), b = \({3}^{128}\) \({5}^{129}\) * \({7}^{22} \), c = \({3}^{128}\) * \({5}^{128}\) * \({7}^{128} \), d = \({2}^{129}\) * \({5}^{128}\) * \({7}^{33}\)then HCF OF a, b, c and d is

    A. \({3}^{129}\) * \({5}^{128}\) * \({7}^{22} \)
    B. \({15}^{128}\) * \({7}^{22} \)
    C. \({3}^{128}\) * \({5}^{128}\) * \({7}^{23}\)
    D. \({15}^{129}\) * \({7}^{23} \)


Answer – Option D

Explanation –

Highest power of 3 common in a1, b1, c1, d1= 129

Highest power of 5 common in a1, b1, c1, d1 = 129

Highest power of 7 common in a1, b1, c1, d1 = 23