### Problems on Number System:

**Ques.** A number when successively divided by 2, 5, 9 leaves 2, 3 and 4 as remainders respectively. If the number be divided by 9, 5 and 2 respectively, the respective remainders will be :

(a) 4, 3, 2

(b) 3, 4, 2

(c) 2, 4, 3

(d) 4, 2, 3

**Ques.** The largest natural number which exactly divides the product of any four consecutive natural numbers, is :

(a) 6

(b) 24

(c) 120

(d) 12

**Ques.** If 3^{th} power of 9 is subtracted from 6^{th} power of 2, then the digit in 10s place is

(a) 6

(b) 8

(c) 9

(d) 7

**Ques.** Consider the decimal 0.111010100010 …, when the digit in the “n^{th}” decimal place is 1 if either n = 1 or n is a prime then the decimal

(a) terminates

(b) has only finite number of zeros

(c) recurs and denote a rational number

(d)

**Ques.** A number when divided by 136 leaves 36 as remainder. If the same number is divided by 17, what will be the remainder:

(a) 2

(b) 3

(c) 5

(d) 15

Related: Area of parallelogram worksheet

**Ques.** The traffic lights at 3 different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m. then the next change will appear after

(a) 7 m 14 sec

(b) 7 m 16 sec

(c) 7m 12 sec

(d) 7 m 18 sec

**Ques.** The largest number, which on dividing by 27, 77, and 202 leaves equal remainder in each case, is :

(a) 7

(b) 8

(c) 25

(d) 23

**Ques.** If the number 42573* is completely divisible by 72, then which number should replace the asterick(*)?

(a) 9

(b) 5

(c) 7

(d) 6

**Ques.** The representation of 2.317317317………….in the form of p/q is x and the representation of 18.484848…….. in form of a/b is y . Then x/y is

(a) 40626/5093

(b) 50926/6233

(c) 72341/52317

(d) None

**Ques.** If a number, of two digits, is 2 times the sum of its digits, the number formed by interchange the digits is equal to sum of the digits multiplied by :

(a) 1

(b) 8

(c) 9

(d) 4

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**Ques.** The value of x, when 2^{x+4}. 3^{x+1} = 288

(a) 1

(b) –1

(c) 0

(d) None of these

**Ques.** The product or the sum of two irrational numbers is always

(a) irrational

(b) rational

(c) neither rational nor irrational

(d) Either rational or irrational

**Ques.** If (874516)^{145689} is multiplied out, the units’ digit in the product :

(a) 4

(b) 3

(c) 6

(d) 1

**Ques.** The number of digits to the right of the decimal point in the product of 95.75 and 0.0255 is

(a) 5

(b) 6

(c) 7

(d) None of these

**Ques.** If (21567)^{125} is multiplied out, the units’ digit in the product is :

(a) 1

(b) 7

(c) 5

(d) 3

Related:

**Ques.** There are four composite numbers written in ascending order of magnitude. If the product of the first three is 192 and the last three is 432, then the first number is:

(a) 4

(b) 6

(c) 2

(d) 8

**Ques.** M and N are only two even numbers with M > N. The largest even integer which divides M^{2 } -N^{2} is :

(a) 2

(b) 4

(c) 8

(d) 10

**Ques.** The least multiple of 5 which leaves a remainder 5 when divided by 6 or 10 or 15 is :

(a) 152

(b) 153

(c) 162

(d) 155

**Ques.** What is the least number which when divided by 16, 20, 32, 42, and 50 leaves the remainder 12, 16, 28,38, and 46 respectively?

(a) 11396

(b) 10396

(c) 10256

(d) 12546

Related:

**Ques.** For any natural number n(5^{2n+2} – 24 n – 25) is divisible by :

(a) 25

(b) 50

(c) 510

(d) 576

**Ques.** 9876543210 is divisible by :

(a) 5, 9 and 11

(b) 5, 9 but not by 11

(c) 9 and 11 but not by 5

(d) 11 and 5 but not by 9

**Ques.** If n is odd, n(n^{2}-1) is always divisible by :

(a) 18

(b) 20

(c) 24

(d) 32

**Ques.** If n is even number, then n(n^{2 }+ 10) is always divisible by:

(a) 10

(b) 4

(c) 6

(d) 28

**Ques.** If a number consists of units digit as *a* and the ten’s digit as *b*, such a number is:

(a) b + a

(b) bx

(c) 10b + x

(d) 10a + b

Related: Complex numbers questions

**Ques.** If a number consists of units digit as *6* and the ten’s digit as *5*, such a number is:

(a) 65

(b) 56

(c) 605

(d) 506

**Ques.** If n is even, n(n^{2}-1) is always divisible by :

(a) 6

(b) 8

(c) 15

(d) 17

**Ques.** If a four digit number 2AB5 ( A and B digits ) is divisible by 9, then the number AB is :

(a) 38

(b) 24

(c) 44

(d) 13

**Ques.** If the six digit number 4A52B6 is divisible by 2 as well as 3, then the number AB is :

(a) 22

(b) 21

(c) 20

(d) 12

**Ques.** If a number is divisible by 2 and 3 both, then it is necessarily divisible by :

(a) 6

(b) 8

(c) 9

(d) 12

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**Ques.** The smallest whole number by which 79633125 must be multiplied for the product to be a perfect square is :

(a) 11

(b) 5

(c) 13

(d) 3

**Ques.** The next number in the sequence 1/22,4/25, 9/28, 16/31, 25/34, is

(a) 28/35

(b) 30/37

(c) 36/37

(d) 36/35

**Ques.** The next number in the sequence 4/41, 5/51, 6/61, 7/71, is

(a) 8/81

(b) 9/81

(c) 8/75

(d) 8/78

**Ques.** The number of terms in the sequence 5, 9, 13, …………….189 is

(a) 45

(b) 46

(c) 48

(d) 47

**Ques.** The number of terms in the sequence 2, 9, 16,23 ……………. 338 is

(a) 48

(b) 46

(c) 49

(d) 45

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**Ques.** What is the least number which when divided by 26, 34, 47, 58, and 112 leaves the remainder 16, 24, 37,48, and 102 respectively?

(a) 53282246

(b) 53582246

(c) 55326485

(d) 58565452

**Ques.** The least multiple of 9 which leaves a remainder 7 when divided by 9 or 13 or 15 is :

(a) 4102

(b) 4212

(c) 4302

(d) 4402

**Ques.** The tenth term of 8, 15, 22, 29,………..

(a) 81

(b) 71

(c) 51

(d) 91

**Ques.** The number 2.5252525………. as a fraction, when reduced to lowest terms, the sum of the numerator and denominator is

(a) 7

(b) 29

(c) 141

(d) 349

**Ques.** The seventh term of 112, 140, 168, …………..

(a) 270

(b) 250

(c) 280

(d) 300

**Related:** Simple and Compound Interest Quiz

**Ques.** P and Q are only two odd numbers with P > Q. The largest even integer which divides P^{2 } -Q^{2} is :

(a) 2

(b) 8

(c) 4

(d) 6

**Ques.** If the square of a number of two digits is subtracted from the square of the number formed by interchanging the digits, the largest number by which the result is always divisible is :

(a) 9

(b) 99

(c) 11

(d) 15

**Ques.** The largest natural number by which the product of three consecutive odd numbers is always divisible is :

(a) 10

(b) 15

(c) 25

(d) 35

**Ques.** The smallest number which must be added to 803642 in order to obtain a multiple of 9 is

(a) 3

(b) 4

(c) 5

(d) 6

**Ques.** If (2158) ^{258} is multiplied out, the units’ digit in the product is:

(a) 3

(b) 5

(c) 6

(d) 4

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**Ques.** If 5^{x–3} = 1, then the value of *x* is

(a) 2

(b) 3

(c) 1

(d) 1

**Ques.** Find the total number of prime numbers lying between 120 and 140.

(a) 3

(b) 4

(c) 5

(d) 6

**Ques.** If a and b are whole numbers such that a^{b} = 169. The value of (a-3)^{b-1} is :

(a) 1

(b) 169

(c) 13

(d) 10

**Ques.** The least number which leaves remainders 2, 3, 4, 5 and 6 on dividing by 3, 4, 5, 6 and 7 respectively, is:

(a) 412

(b) 419

(c) 421

(d) 426

**Ques.** The total marks secured by Amit, Bhuvnesh and Chander are 540. Amit’s marks were three times that of Bhuvnesh’s and Bhuvnesh ‘s marks were twice that of Chander Amit’s marks are how much more than those of Chander ?

(a) 154

(b) 300

(c) 265

(d) 286

Related: questions of set theory

**Ques.** In an exam, a student was asked to find 5/7 of a number. By mistake, she found 7/5 of it. Her answer was 96 more than the correct answer. The given number is

(a) 196

(b) 128

(c) 156

(d) 140

**Ques.** If x^{2} = 31423 , then x is

(a) an irrational number

(b) a complex number

(c) a rational number

(d) None

**Ques.** Two candies and a cookie cost Rs. 18 and two cookies and a candy cost Rs. 12. Find the cost of a candy.

(a) 8

(b) 2

(c) 16

(d) 6

**Ques.** The number of students in a school are 1125 more than 1/4^{th} of it. Find the total strength.

(a) 1750

(b) 1500

(c) 2000

(d) 1225

**Ques.** Three Burger and a sandwiches cost 70 and 2 sandwiches and a Burger cost 40. How much will a Burger and a sandwiches cost?

(a) 10

(b) 20

(c) 30

(d) 40

Related: area of parallelograms and triangles worksheet

**Ques.** The sum of 11 results is 55. The sum of the first 6 results is 30 and that of the last 6 is 48. Find the sixth result.

(a) 20

(b) 24

(c) 13

(d) 23

**Ques.** One-third of the total marks are required to pass an exam. A candidate who gets 178 marks, fails by 22 marks. The total marks in the exam are

(a) 550

(b) 600

(c) 535

(d) 660

**Ques.** At an election, a candidate who gets 3/4^{th} of the total votes, is elected by a majority of 2000 votes. The total number of votes polled and the number of votes secured by the candidate who was elected, are respectively

(a) 4000, 3000

(b) 8000, 6000

(c) 4500, 2500

(d) 5000, 3000

**Ques.** Each student in a class contributed as many paise as the number of students in the class. The teacher contributed $13 to make the total collection of $49. How many students are there in the class?

(a) 70

(b) 50

(c) 60

(d) 65

**Ques.** A box contains 44 more than 1/5^{th} of total number of oranges. How many oranges are there in the box?

(a) 66

(b) 55

(c) 65

(d) 33

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**Ques.** A water tank having 1300 litres of capacity was filled by adding 75 litres of water and as many buckets of water as each bucket had a capacity. What was the capacity of each bucket in litres ?

(a) 32

(b) 35

(c) 48

(d) 45

**Ques.** The sum of four consecutive numbers is 90. Find the difference between five times the third number and 4 times the fourth number.

(a) 21

(b) 29

(c) 24

(d) 19

**Ques.** The smallest number which must be subtracted from 1300 to make it a perfect square is

(a) 2

(b) 3

(c) 4

(d) 6

**Ques.** In an exam, a student was asked to find 4/5^{th} of a number. By mistake, he found 5/4^{th} of it and his answer was180 more than the correct answer. Find the given number.

(a) 810

(b) 890

(c) 400

(d) 500

**Ques.** In a school library,1/2 of the books are story books, 2/3^{rd} of the remaining books are reference books and the remaining 250 books are encyclopaedias. Find the total number of books in the library.

(a) 1,200

(b) 1,500

(c) 2,000

(d) 750

Related: Average math question

**Ques.** 4/5^{th} of a number exceeds its 2/3^{rd} of 9/10^{th} by 120. Find the number.

(a) 600

(b) 140

(c) 800

(d) 660

**Ques.** 5/8 th of 120% of a number is 235 more than 245. Find that number.

(a) 523

(b) 684

(c) 576

(d) 640

**Ques.** 24 is divided into two parts such that 6 times the first part exceeds 4 times the second part by 4. Find the first part.

(a) 14

(b) 16

(c) 10

(d) 12

**Ques.** The amount that Satheesh had was $675 more than 3/5^{th} of 1/9^{th} of $450. Find the amount.

(a) 700

(b) 705

(c) 625

(d) 605

**Ques.** 340 students are arranged in a parade such that the number of students in each column is the same as the number of columns. Find how many students are excluded from the group to make such an arrangement possible.

(a) 16

(b) 21

(c) 14

(d) 24

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**Ques.** A sum is divided between Rajiv and Raghav such that 5/6^{th} of the amount of Rajiv is equal to 4/5^{th} the amount of Raghav. If Rajiv gets $240, find the sum.

(a) 500

(b) 250

(c) 490

(d) 400

**Ques.** The total age of 9 girls is 128. The total age of the first 4 girls is 62 and that of the next 4 girls is 48. Find the age of the 9th girls.

(a) 16

(b) 18

(c) 12

(d) 17

**Ques.** A sum is divided between Vijay and Aman such that3/5^{th} of the amount of Vijay is equal to5/7^{th} of the amount of Aman. If Vijay gets $750, how much does Aman get?

(a) 450

(b) 600

(c) 630

(d) 730

**Ques.** Sum of two numbers is 1/3^{rd} of 1/5^{th} of 195 and their product is 1/6^{th} of 1/4^{th} of 960. Find 1/3^{rd} of the difference between them.

(a) 1

(b) 9

(c) 3

(d) 27

**Ques.** In a country, 5/9^{th} of the population are adults.1/2 of the adults are male, 3/5^{th} of the adult females are illiterate. If 800 adult females are illiterate, then the population of the village is

(a) 4,000

(b) 4,800

(c) 9,000

(d) 5,600

Related: binomial expansion practice

**Ques.** When 6 is added to a number and the sum is multiplied by 8, the result is same as when 26 is multiplied by 10 and 12 is added to the product. The number is

(a) 28

(b) 23

(c) 26

(d) 25

**Ques.** If x^{2} = 84681, then x is

(a) an irrational number

(b) a rational number

(c) a complex number

(d) None of these

**Ques.** The sum of three consecutive even integers is 132. Find the difference between 3 times the least and 1/2 of the greatest.

(a) 44

(b) 89

(c) 144

(d) 103

**Ques.** 7/8 th of a number exceeds its 7/16 th by 84. Find 3/4^{th} of the number.

(a) 144

(b) 192

(c) 138

(d) 204

**Ques.** The conjugate of √7 + 4 is

(a) √7 – 4

(b) -√7 – 4

(c) -√7 + 4

(d) All the above

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**Ques.** Which of the following is divisible by 9?

(a) 1278

(b) 1754

(c) 1779

(d) 1770

**Ques.** The least perfect square, which is divisible by each of 21, 36 and 66 is

(a) 214344

(b) 214434

(c) 213444

(d) 231444

**Ques.** The number of rationalizing factors of an irrational number is

(a) One

(b) Two

(c) Three

(d) Infinite

Number series is reasoning and number system is quantitative part

Sir number system aur number series ek he hota ha ya alag