Aptitude & Reasoning

# Number Theory and Number System Questions and Answers ## Number System - Quantitative Aptitude

 Question 1
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 14 B 16 C 21 D 24
 Question 2
P and Q are only two odd numbers with P > Q. The largest even integer which divides P2  -Q2 is :
 A 2 B 6 C 8 D 4
 Question 3
Find the total number of prime numbers lying between 120 and 140.
 A 3 B 4 C 5 D 6
 Question 4
For any natural number n(52n+2 – 24 n – 25) is divisible by :

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 A 576 B 510 C 50 D 25
 Question 5
The smallest whole number by which 79633125 must be multiplied for the product to be a perfect square is :
 A 3 B 5 C 11 D 13
 Question 6
M and N are only two even numbers with M > N. The largest even integer which divides M2  -N2 is :
 A 4 B 2 C 8 D 10
 Question 7
The smallest number which must be added to 803642 in order to obtain a multiple of 9 is
 A 5 B 6 C 3 D 4
 Question 8
If n is even number, then n(n2 + 10) is always divisible by:
 A 6 B 10 C 4 D 28
 Question 9
Which of the following is divisible by 9?
 A 1754 B 1770 C 1779 D 1278
 Question 10
If a number is divisible by 2 and 3 both, then it is necessarily divisible by :
 A 6 B 9 C 12 D 8
 Question 11
5/8 th of 120% of a number is 235 more than 245. Find that number.
 A 523 B 684 C 576 D 640
 Question 12
If the six digit number 4A52B6 is divisible by 2 as well as 3, then the number AB is :
 A 12 B 22 C 20 D 21
 Question 13
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 140 D 156
 Question 14
4/5th of a number exceeds its 2/3rd of 9/10th by 120. Find the number.
 A 800 B 600 C 140 D 660
 Question 15
A sum is divided between Rajiv and Raghav such that 5/6th of the amount of Rajiv is equal to 4/5th the amount of Raghav. If Rajiv gets Rs. 240, find the sum.
 A Rs. 400 B Rs. 500 C Rs. 250 D Rs. 490
 Question 16
The number of terms in the sequence 2, 9, 16,23 …………….338 is
 A 49 B 46 C 45 D 48
 Question 17
The largest number, which on dividing by 27, 77, and 202 leaves equal remainder in each case, is :
 A 7 B 25 C 23 D 8
 Question 18
If n is odd, n(n2-1) is always divisible by :
 A 20 B 24 C 32 D 18
 Question 19
If the number 42573* is completely divisible by 72, then which number should replace the asterick(*)?
 A 9 B 7 C 5 D 6
 Question 20
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 11 B 99 C 9 D 15
 Question 21
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 55326485 B 53282246 C 53582246 D 58565452
 Question 22
The value of x, when 2x+4. 3x+1 = 288
 A 0 B –1 C 1 D None of these
 Question 23
The largest natural number which exactly divides the product of any four consecutive natural numbers, is :
 A 6 B 12 C 24 D 120
 Question 24
A box contains 44 more than 1/5th of total number of oranges. How many oranges are there in the box?
 A 66 B 55 C 33 D 65
 Question 25
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 286 B 154 C 300 D 265
 Question 26
Find the least number which when divided by 6, 9, 12, 15, and 18 leaves the same remainder 2 in each case.
 A 182 B 185 C 184 D 135
 Question 27
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 18 sec B 7m 12 sec C 7 m 16 sec D 7 m 14 sec
 Question 28
A sum of Rs. 9.00 is made up of 90 coins which are either 20 Paise or 5 Paise coins. The number of 5 Paise coins are ?
 A 30 B 60 C 40 D 50
 Question 29
Three Burger and a sandwiches cost Rs. 70 and 2 sandwiches and a Burger cost Rs. 40. How much will a Burger and a sandwiches cost?
 A Rs. 20 B Rs. 10 C Rs. 30 D Rs. 40
 Question 30
Sum of two numbers is 1/3rd of 1/5th of 195 and their product is 1/6th  of 1/4th of 960. Find 1/3rd of the difference between them.
 A 9 B 27 C 1 D 3
 Question 31
If a number consists of units digit as 6 and the ten’s digit as 5, such a number is:
 A 506 B 65 C 605 D 56
 Question 32
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 6 B 8 C 4 D 2
 Question 33
9876543210 is divisible by :
 A 5, 9 but not by 11 B 11 and 5 but not by 9 C 5, 9 and 11 D 9 and 11 but not by 5
 Question 34
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 12 B 18 C 17 D 16
 Question 35
Two candies and a cookie cost Rs. 18 and two cookies and a candy cost Rs. 12. Find the cost of a candy.
 A 6 B 16 C 8 D 2
 Question 36
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 12 D 10
 Question 37
7/8 th of a number exceeds its 7/16 th by 84. Find 3/4th of the number.
 A 192 B 204 C 144 D 138
 Question 38
The tenth term of 8, 15, 22, 29,………..
 A 91 B 81 C 51 D 71
 Question 39
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 2, 4, 3 B 4, 3, 2 C 3, 4, 2 D 4, 2, 3
 Question 40
If a number consists of units digit as a and the ten’s digit as b, such a number is:
 A b + a B 10a + b C bx D 10b + x
 Question 41
In a country, 5/9th of the population are adults.1/2 of the adults are male, 3/5th of the adult females are illiterate. If 800 adult females are illiterate, then the population of the village is

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 A 9,000 B 5,600 C 4,800 D 4,000
 Question 42
The next number in the sequence 4/41, 5/51, 6/61, 7/71, is
 A 8/81 B 8/75 C 8/78 D 9/81
 Question 43
If n is even, n(n2-1) is always divisible by :
 A 15 B 17 C 6 D 8
 Question 44
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.

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 A 20 B 23 C 13 D 24
 Question 45
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 10256 B 10396 C 11396 D 12546
 Question 46
If a four digit number 2AB5 ( A and B  digits ) is divisible by 9, then the number AB is :
 A 44 B 24 C 13 D 38
 Question 47
If (2158) 258 is multiplied out, the units’ digit in the product is:
 A 4 B 5 C 6 D 3
 Question 48
The largest natural number by which the product of three consecutive odd numbers is always divisible is :
 A 10 B 35 C 15 D 25
 Question 49
At an election, a candidate who gets 3/4th 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 5000, 3000 B 4000, 3000 C 4500, 2500 D 8000, 6000
 Question 50
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 535 B 660 C 600 D 550
 Question 51
A sum is divided between Vijay and Aman such that3/5th of the amount of Vijay is equal to5/7th of the amount of Aman. If Vijay gets Rs. 750, how much does Aman get?
 A Rs. 600 B Rs. 450 C Rs. 630 D Rs. 730
 Question 52
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 9 B 4 C 8 D 1
 Question 53
The amount that Satheesh had was Rs. 675 more than 3/5th of 1/9th of Rs. 450. Find the amount.
 A Rs. 705 B Rs. 625 C Rs. 605 D Rs. 700
 Question 54
The smallest number which must be subtracted from 1300 to make it a perfect square is
 A 6 B 4 C 2 D 3
 Question 55
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

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 A 28 B 26 C 23 D 25
 Question 56
Each student in a class contributed as many paise as the number of students in the class. The teacher contributed Rs. 13 to make the total collection of Rs.49. How many students are there in the class?
 A 65 B 70 C 50 D 60
 Question 57
If (21567)125 is multiplied out, the units’ digit in the product is :
 A 1 B 7 C 5 D 3
 Question 58
If (874516)145689 is multiplied out, the units’ digit in the product :
 A 6 B 1 C 3 D 4
 Question 59
If 5x–3 = 1, then the value of x is
 A 1 B 3 C 0 D 2
 Question 60
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
 Question 61
If a and b are whole numbers such that ab = 169. The value of (a-3)b-1 is :
 A 13 B 169 C 1 D 10
 Question 62
In a school library,1/2 of the books are story books, 2/3rd 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 750 C 2,000 D 1,500
 Question 63
In an exam, a student was asked to find 4/5th  of a number. By mistake, he found 5/4th of it and his answer was180 more than the correct answer. Find the given number.
 A 810 B 400 C 500 D 890
 Question 64
The number of students in a school are 1125 more than 1/4th of it. Find the total strength.
 A 1750 B 2000 C 1500 D 1225
 Question 65
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 144 C 89 D 103
 Question 66
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 48 C 35 D 45
 Question 67
The least multiple of 9 which leaves a remainder 7 when divided by 9 or 13 or 15 is :
 A 4212 B 4102 C 4402 D 4302
 Question 68
The seventh term of 112, 140, 168, …………..
 A 280 B 270 C 300 D 250
 Question 69
If 3th power of 9 is subtracted from 6th power of 2, then the digit in 10s place is
 A 9 B 7 C 8 D 6
 Question 70
The next number in the sequence 1/22,4/25, 9/28, 16/31, 25/34, is

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 A 36/37 B 30/37 C 28/35 D 36/35
 Question 71
The least multiple of 5 which leaves a remainder 5 when divided by 6 or 10 or 15 is :
 A 155 B 162 C 153 D 152
 Question 72
The least number which leaves remainders 2, 3, 4, 5 and 6 on dividing by 3, 4, 5, 6 and 7 respectively, is:
 A 426 B 421 C 419 D 412
 Question 73
The least perfect square, which is divisible by each of 21, 36 and 66 is
 A 214344 B 231444 C 214434 D 213444
 Question 74
The sum of four consecutive numbers is 90. Find the difference between five times the third number and 4 times the fourth number.
 A 19 B 21 C 24 D 29
 Question 75
The number of terms in the sequence 5, 9, 13, …………….189 is
 A 48 B 47 C 46 D 45
There are 75 questions to complete. #### Vishal Arora

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