Number systems questions and answers

1.What least number must be added to 859622, to get a number exactly divisible by 456?
321 394 450 497

2.The ratio between two numbers is 4:5 and their sum is 540. The greater of the two numbers is?
270 220 300 410

3. 1/4 of a number subtracted from 1/3 of the number gives 12. The Number is
144 157 180 201

4.Three fifth of one fourth of a number is 90. The number is?
301 500 600 700

5.The sum of two numbers is 60 and their difference is 43 .The difference of there squeare is?
2060 2580 2700 3110

6.The sum of three consecutive even numbers is 36.s The middle one is?
12 14 16 18

7.Find the divisior if dividend = 27541, quotient = 233 and remainder = 47?
328 150 497 118

8.A number when divided by 627 leaves a remainder 43. By dividing the same number by 19, the remainder will be?
19 11 8 5

9.The greatest 5 digit number that is exactly divisible by 100 is?
99899 99800 99900 99889

10.What is the total number of numbers up to 9999?
98900 10000 9999 98100

Part 2 of a Aptitude – Number systems

1.The number of prime numbers in (25)13 * (10)7 * (27)5 is?
25 32 55 42

2.what will be the remainder when (29)36 is divided by 28?
0 1 29 5

3.what is the difference in intrinsic value and local value of 6 in 8631
496 594 725 122

4.Replace the * in the number 6* 106 by a suitable digit so that the number formed is exactly divisible by 11?
2 8 5 12

5.A number is greater than 3 but less than 8. Also the number is greater than 6 but less than 10 What is the number?
7 10 5 3

6.The number that is nearest to 2160 and exactly divisible by 52 is?
2132 2148 2184 2177

7.what will be the digit in the unit place in the product (3807)194 * (932)84?
1 9 4 2

8.How many numbers between 101 and 300 are divisible by both 3 and 5?
14 20 107 34

9.There is a number 8*20 which if multiplied by 6, the product is divisible by 8. The digit replacing * mark is?
4 Any digit in between 0 and 9 0 2

10.(1/3 – 1/4) is added to a number. From the sum so obtained, 1/3 of 1/4 is subtracted and the remainder is (1/3+1/4). The number is:
7/12 1/12 1/4 2/4

Numbers Aptitude Questions with Answers

1.In a 2 digit numbers, the digit in the unit’s place is 2 times the digit in 10’s place and sum of the digits is equal to 9. What is the number?

30 16 36 56

2.The difference between a 2 digit numbers & the number getting by place changing the 2 digits is 54. What is the difference between the 2 digits of that particular number?

5 6 7 8

3.The sum of the digits of a 2 number is 2/5 of the difference between the number and the number obtained by place changing the positions of the particular digits. What is the exact difference between the particular digits of the number?

5 6 Cannot be determined None of these

4.The difference between 2 numbers is 1356. When the largest number is divided by the smallest one, the quotient is 6 and the remainder is 15. The smaller number is ?

570 270 370 470

5.If the number getting on position changing the digits of a 2 digit number is 18 more than the original number and the sum of the digits is 6. What is the particular original number?

42 52 62 72

6.The product of 4 consecutive even numbers is always divisible by?

384 284 584 684

7.The sum of two positive integers multiplied by the bigger number is 204, and their difference multiplied by the smaller number is 35. What are the numbers?

12,5 13,5 14,5 16,5

8.The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. What is the sum of the numbers?

500 400 600 700

LCM and HCF

1.About the number of pairs which have 16 as their HCF and 136 as their LCM, the conclusion can be
only one such pair exists only two such pair exists many such pairs exist no such pair exists

2. The HCF of two numbers is 12 and their difference is also 12. The numbers are
66,78 94,106 70,82 84,96

3.The HCF of two numbers is 16 and their LCM is 160. If one of the numbers is 32, then the other number is
48 80 96 112

4.HCF of three numbers is 12. If they are in the ratio 1:2:3, then the numbers are
12,24,36 10,20,30 5,10,15 4,8,12

5.Six bells commence tolling together and toll at intervals of 2,4,6,8,10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
4 10 15 16

Number System: Factors and Coprimes

Formula 6: The number of ways of writing a number N as a product of two co-prime numbers = 2n−1 where n=the number of prime factors of a number.

Example: Find the number of ways of writing 60 as a product of two co - primes
Ans: The prime factorization of 60 = 22×3×5
The number of ways of writing 60 as a product of two co - primes = 23−1 = 4

Formula 7: Product of all the factors of N = N⎛⎝Number of factors2⎞⎠ = N⎛⎝⎜(p+1).(q+1).(r+1)....2⎞⎠⎟

Example: Find the product of all the factors of 50
Ans: Prime factorization of 50 = 2×52 
Product of all the factors of 50 = 50(1+1).(2+1)2=503

                                                

1. P is the product of all the factors of 15552.  If P = 12N×M, where M is not a multiple of 12, then find the value of M.  [M and N are positive Integers]
Ans: 15552 = 26×35 
Product of all the factors of 15552 = (26×35)(6+1).(5+1)2=2126×3105 
⇒(22)63×363×342 = 1263×342 
So M = 342

2. Let M be the set of all the distinct factors of the number N=65×52×10,Which are perfect squares.  Find the product of the elements contained in the set M. 
N = 65×52×10 = 26×35×53
Even powers of 2 available: 20,22,24,26
Even powers of 3 available: 30,32,34
Even powers of 5 available: 50,52
Therefore number of factors of the number N that are perfect squares = 4 x 3 x 2 = 24
Product of the elements contained in M 
= 2(2+4+6)×6×3(2+4)×8×52×12=272×348×524