# 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) $\frac {11}{17}$

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

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) $(6)^ \frac16$

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) $\sqrt {0.0004}$

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) $0.\overline{09}$

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

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

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

Ans : c) 990
3995 – 3005 = 990

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

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

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

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

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

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

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

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

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) $\frac {13}{33}$

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

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

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) $\frac {9}{10}$

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) $\frac {2347}{990}$

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

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) $0.\overline{009}$

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

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

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

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

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) $\frac {11}{13}, \frac 79, \frac 35$

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

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

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

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

Ans : b) 20, 21, 22
Let number is n, n+1, n+2
2(n) + 3(n+1) + 4(n+2) = 191
9n + 11 = 191
n = 20

Q.2: If the sum of five consecutive integers is S, then the largest of those integers in terms of S is ?
a) $\frac {S-10}{5}$
b) $\frac {S+4}{4}$
c) $\frac {S+5}{4}$
d) $\frac {S+10}{5}$

Ans : d) $\frac {S+10}{5}$
Third integer is $\frac S5$ (Average of 5 consecutive integers )
Largest is 5th number = $\frac S5 + 2 = \frac {S+10}{5}$

Q.3: Which one of the following is a factor of the sum of first 25 natural numbers?
a) 26
b) 24
c) 13
d) 12

Ans : c) 13
Sum of first 25 natural numbers is = $\frac {25}{2}(1+25) = 25\times 13$

Q.4: In an exam the sum of the scores of A and B is 120, that of B and C is 130 and that of C and A is 140. Then the score of C is
a) 65
b) 75
c) 70
d) 60

Ans : b) 75
A+B=120, B+C=130, C+D=140
(A+B) + (B+C) + (C+A) = 120+130+140
2(A+B+C) = 390
A+B+C= 195
C = (A+B+C) – (A+B) = 195-120 = 75

Q.5: The length of a road is one Kilometer. The number of plants required for plantation at a gap of 20 Meters in both sides of the road is ?
a) 102
b) 100
c) 51
d) 50

Ans : a) 102
One side at the distance of 20 Meters = $(\frac {1000}{20} + 1) = 51$