Number System MCQ Questions for Competitive Exams

Number System MCQ Questions in English for Competitive Exams. Topic wise objective question and answer for practice of online test of Govt Jobs Exams.

Smallest and Largest Fraction

Q.1: Which is the largest of the following fractions?

$\frac 23, \frac 35, \frac {8}{11}, \frac {11}{17}$

a) $\frac 23$
b) $\frac 35$
c) $\frac {8}{11}$
d) $\frac {11}{17}$

Show Answer

Ans : c) $\frac {8}{11}$
Solution: Covert all into decimal 0.66, 0.6, 0.73, 0.65

Q.2: If a number is as much greater than 31 as it is less than 75, then the number is ?

a) 106
b) 44
c) 74
d) 53

Show Answer

Ans: d) 53
Sol: x-31 = 75-x, 2x=106, x= 53

Q.3: The greatest among the following numbers is ?

$(3)^ \frac13, (2)^ \frac12, 1, (6)^ \frac16$

a) $(3)^ \frac13$
b) $(2)^ \frac12$
c) $1$
d) $(6)^ \frac16$

Show Answer

Ans: a) $(3)^ \frac13$
Sol: LCM of 2,3,6 = 6
$(3)^ \frac13 = (3^2)^ \frac16 = (9)^ \frac16$
$(2)^ \frac12 = (2^3)^ \frac16 = (8)^ \frac16$
$1 = (1)^ \frac16$
$(6)^ \frac16$

Q.4: The largest among the following numbers is ?

$(0.1)^2, \sqrt {0.0121}, 0.12, \sqrt {0.0004}$

a) $(0.1)^2$
b) $\sqrt {0.0121}$
c) $0.12$
d) $\sqrt {0.0004}$

Show Answer

Ans: c) $0.12$
Sol: $(0.1)^2 = .01$
$\sqrt {0.0121} = .11$
$\sqrt {0.0004} = .02$

0.01< 0.02 < 0.11< 0.12

Q.5: Which of the following number is the greatest of all?

$0.9, 0.\bar 9, 0.0\bar9, 0.\overline{09}$

a) $0.9$
b) $0.\bar9$
c) $0.0\bar9$
d) $0.\overline{09}$

Show Answer

Ans: b) $0.\bar9$
Sol:
$0.\bar9 = 0.99999.......$
$0.0\bar9 = 0.09999.....$
$0.\overline{09} = 0.090909....$

Number System MCQ Questions for Competitive Exams

Division , Multiplication, Addition and Subtraction

Q.1: The difference between the greatest and the least prime numbers which are less than 100 is ?

a) 98
b) 97
c) 96
d) 95

Show Answer

Ans: d) 95
Greatest Prime number below 100 is 97
Least Prime number below 100 is 2
97 -2 = 95

Q.2: The sum of two numbers is 75 and their difference is 25. The product of the two number is ?

a) 1350
b) 1250
c) 125
d) 1000

Show Answer

Ans : b) 1250
a + b = 75
a – b = 25
2a = 100, a = 50 and b = 25

Q.3: The difference between the greatest and the least four-digit numbers that begin with 3 and ends with 5 is ?

a) 999
b) 900
c) 990
d) 909

Q.4: I have x marbles. My elder brother has 3 more than mine, while my younger brother has 3 less than mine. If the total number of marbles is 15, then the number of marbles that I have is ?

a) 3
b) 5
c) 7
d) 8

Show Answer

Ans : b) 5
x + (x+3) + (x-3) = 15
3 x = 15 , x= 5

Q.5: 5349 is added to 3957. Then 7062 is subtracted from the sum. The result is not divisible by ?

a) 4
b) 3
c) 7
d) 11

Show Answer

Ans : c) 7
(5349 + 3957) −7062 = 2244
It is devisable by 3, 4, 11, but not 7

Q.6: When n is divided by 6, the remainder is 4. When 2n is divided by 6, the remainder is

a) 0
b) 1
c) 2
d) 4

Show Answer

Ans : c) 2
Let quotient be q then
n = 6q + 4
2n = 12 q + 8
2n = 6(2q+1) + 2
Here remainder is 2.

Q.7: A number when divided by 136 leaves remainder 36. If the same number is divided by 17, then the remainder will be ?

a) 9
b) 7
c) 3
d) 2

Show Answer

Ans : d) 2
if the first divisor is exactly divisible by second divisor then Required remainder = Remainder obtained on dividing first remainder by second divisor.
136 is exactly devisable by 17. Therefore, Remainder on dividing 36 by 17 = 2

Q.8: A number, when divided by 119, leaves a remainder of 19. If it is divided by 17, it will leave a remainder of ?

a) 19
b) 10
c) 7
d) 2

Show Answer

Ans : d) 2
Number = 119q + 19
=17x7xq + 17×1 + 2
= 17(7q+1) + 2
Hence the same number divided by 17 will leave a remainder of 2.

Q.9: If 78*3945 is divisible by 11, where * is a digit, then * is equal to ?

a) 1
b) 0
c) 3
d) 5

Show Answer

Ans : d) 5
(7+*+9+5) – (8+3+4)
= 21 + * -15 = 6 + *
6 + * , must be 11 or multiple of 11.
6 + * = 11, * = 5

Q.10: $(3^{25} + 3^{26} + 3^{27} + 3^{28})$ is divisible by ?
a) 11
b) 16
c) 25
d) 30

Show Answer

Ans : d) 30
$(3^{25} + 3^{26} + 3^{27} + 3^{28}) = 3^{25}(1+3+3^2+3^3)$
$= 3^{25}(1+3+9+27) = 3^{25}(40) = 3^{25}(5 \times 2^3)$
The number is multiple of prime number 2, 3 and 5, hence divisible by 2x3x5 = 30.

Q.11: The sum of first 60 numbers from 1 to 60 is divisible by ?
a) 13
b) 59
c) 60
d) 61

Show Answer

Ans : ) 61
Sum of 1+2+3+4 …… +60
$\frac {n(n+1)}{2}$
= $\frac {60(60+1)}{2} = \frac {60 \times 61}{2} =1830$
1830 is divisible by 61.

Fractions of Numbers : Number System MCQ Questions for Competitive Exams

Q.1: The vulgar fraction of $0.39\overline{39}$ is
a) $\frac {15}{33}$
b) $\frac {11}{39}$
c) $\frac {17}{39}$
d) $\frac {13}{33}$

Show Answer

Ans: d) $\frac {13}{33}$
$0.39\overline{39} = 0.\overline{39} = \frac {39}{99} = \frac {13}{33}$

Q.2: In a school $\frac {1}{10}$ of the boys are same in number as $\frac {1}{4}$ of the girls and $\frac {5}{8}$ of the girls are same in number as $\frac {1}{4}$ of the boys. The ratio of the boys to girls in that school is ?
a) 2 : 1
b) 5 : 2
c) 4 : 3
d) 3 : 2

Show Answer

Ans : b) 5 : 2
$\frac {b}{10} = \frac {g}{4}$
$\frac {b}{g} = \frac {10}{4} = \frac {5}{2}$

Q.3: In an office, there are 108 tables and 132 chairs. If 1/6 of the tables and 1/4 of the chairs are broken. How many people can work in the office if each person requires one table and one chair?
a) 86
b) 90
c) 92
d) 99

Show Answer

Ans : b) 90
Broken Chair = $108 \times \frac 16 = 18$
un-broken chair = 108 – 18 = 90
Broken Table = $132 \times \frac 14= 33$
Un-broken Table = 132-33= 99
Un-broken pair of chair and table is 90.

Q.4: A person gives 1/4 of his property to his daughter, 1/2 to his sons and 1/5 for charity. How much has he given away?
a) $\frac {1}{20}$
b) $\frac {19}{20}$
c) $\frac {1}{10}$
d) $\frac {9}{10}$

Show Answer

Ans: b) $\frac {19}{20}$
$\frac14 + \frac12 + \frac15 = \frac{19}{20}$

Q.5: The decimal fraction $2.3\overline{49}$ is equal to
a) $\frac {2326}{999}$
b) $\frac {2326}{990}$
c) $\frac {2347}{999}$
d) $\frac {2347}{990}$

Show Answer

Ans : b) $\frac {2326}{990}$
$2.3\overline{49} = \frac{2349-23}{990} = \frac{2326}{990}$

Q.6: A tree increases annually by 1/8th of its height. By how much will it increase after 2 years, if it stands 64 cm high today?
a) 72 cm
b) 74 cm
d) 75 cm
d) 81 cm

Show Answer

Ans : d) 81 cm
Height after one year 64 + 1/8 of 64 = 72
Height after second year 72+1/8 of 72=81

Q.7: $\frac {1}{11}$ is equal to
a) $0.009$
b) $0.0\overline{9}$
c) $0.\overline{09}$
d) $0.\overline{009}$

Show Answer

Ans : c) $0.\overline{09}$
$\frac {1}{11}= \frac {9}{99} = 0.\overline{09}$

Q.8: A student was asked to multiply a given number by 8/17. Instead, he divided the number by 8/17. His answer was 225 more than the correct answer. The given number was ?
a) 64
b) 289
c) 136
d) 225

Show Answer

Ans : c) 136
$\frac {n} {8/17} = n \times \frac {8}{17} +225$
$n(\frac {17}{8} - \frac {8}{17}) = 225$
$n(\frac {289-64}{136}) =225$
$n(\frac {225}{136}) =225$
n= 136

Q.9: How many $\frac 16$ all together make $41\frac23$ ?
a) 125
b) 150
c) 250
d) 350

Show Answer

Ans : c) 250
Divide $41\frac23$ by $\frac 16$

Q.10: A tin of oil was 4/5 full. When 6 bottles of oil was taken out and 4 bottles of oil was poured into it, it was 3/4 full. How many bottles of oil can the tin contain?
a) 10
b) 20
c) 30
d) 40

Show Answer

Ans : d) 40
6 bottle taken out – 4 bottle poured = 2 bottle taken out
4/5 – 3/4 = 1/20
1/20 part of Tin= 2 bottle
Full tin = 2 x 20 = 40 bottle

Number System MCQ Questions for Competitive Exams

Finding the Ascending and Descending order of Numbers

Q.1: Six numbers are arranged in decreasing order. The average of the first five numbers is 30 and the average of the last five numbers is 25. The difference of the first and the last numbers is
a) 20
b) 25
c) 5
d) 30

Show Answer

Ans : b) 25
a>b>c>d>e>f
$\frac{(a+b+c+d+e)}{5} = 30$ – (i)
$\frac{(b+c+d+e+f)}{5} = 25$ – (ii)
(i) – (ii) = $\frac{(a-f)}{5} = 30-25 =5$
a – f = 5×5 = 25

Q.2: Arrange the following fractions in decreasing order.
$\frac 35, \frac 79, \frac {11}{13}$

a) $\frac 35, \frac 79, \frac {11}{13}$
b) $\frac 79, \frac 35, \frac {11}{13}$
c) $\frac {11}{13}, \frac 35, \frac 79$
d) $\frac {11}{13}, \frac 79, \frac 35$

Show Answer

Ans : d) $\frac {11}{13}, \frac 79, \frac 35$
Convert fraction to decimal
$\frac35 = 0.6, \frac 79 = 0.777..., \frac {11}{13}=0.846$

Finding the Unit place of Number

Q.1: The digit in unit’s place of the following number is ?
(1570)² + (1571)² + (1572)² + (1573)²
a) 4
b) 1
c) 2
d) 3

Show Answer

Ans : a) 4
Unit digit in (1570)²= 0
Unit digit in (1571)²= 1² =1
Unit digit in (1572)²= 2² =4
Unit digit in (1573)²= 3² =9
0+1+4+9 =14, Unit digit is 4

Q.2: One’s digit of the number (22)²³ is ?
a) 4
b) 6
c) 8
d) 2

Show Answer

Ans : c) 8
2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁵=32, 2⁶=64 ……
After index 4, the unit digit of 2 is repeated.
Divide index 23 by 4 and remainder is 3.
Therefore, unit digit in (22)²³ = unit digit in 2²³ = unit digit in 2³ = 8.

Q.3: The digit in the unit’s place of the product (2464)¹⁷⁹³ × (615)³¹⁷ × (131)⁴⁹¹ is ?
a) 0
b) 2
c) 3
d) 5

Show Answer

Ans : a) 0
We know Unit digit in 4²ⁿ is 6 and 42ⁿ⁺¹ is 4
Unit Digit in 5ⁿ = 5
Unit Digit 1ⁿ=1
Therefore, unit digit of product 4x5x1 = 0,

Number System MCQ Questions for Competitive Exams

Sum of Consecutive Numbers (Odd, Even, etc.)

Q.1: Find the three consecutive numbers such that twice the first, three times the second and four times the third together make 191.
a) 19, 20, 21
b) 20, 21, 22
c) 21, 22, 23
d) 23, 24, 25