Number Systems

In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football?

1. 4
2. 8
3. 10
4. 12

The number of times the digit 5 will appear while writing the integers from 1 to 1000 is

1. 269
2. 271
3. 300
4. 302

If X is between -3 and -1, and Y is between -1 and 1, then X² - Y² is in between which of the following?

1. -9 and 1
2. -9 and -1
3. 0 and 8
4. 0 and 9

While writing all the numbers from 700 to 1000, how many numbers occur in which the digit at hundred's place is greater than the digit at ten's place, and the digit at ten's place is greater than the digit at unit's place?

1. 61
2. 64
3. 85
4. 91

A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first and last digits is greater than the number itself by 198, then the difference between the first and last digits is

1. 1
2. 2
3. 3
4. 4

What is the remainder when the number (4444)⁴⁴⁴⁴ is divided by 9?

1. 4
2. 6
3. 7
4. 8

The number of prime numbers which are less than 100 is

1. 24
2. 25
3. 26
4. 27

The values of x which satisfy the equation 5^1+x + 5^1–x = 26 are

1. –1, 1
2. 0, 1
3. 1, 2
4. –1, 0

What is the number of all possible positive integer values of n for which n² + 96 is a perfect square?

1. 2
2. 4
3. 5
4. Infinite

The sum of two numbers is 143. If the greater number is divided by the difference of the numbers, the quotient is 7. What is the difference of the two numbers?

1. 9
2. 11
3. 14
4. 15

How many times will the digit 5 come in counting from 1 to 99 excluding those which are divisible by 3?

1. 16
2. 15
3. 14
4. 13

If N, N+2 and N+4 are prime numbers, then the number of possible solutions for N are

1. 1
2. 2
3. 3
4. 4

The digit in the units place of the product 81×82×83×84×....×99 is

1. 0
2. 4
3. 6
4. 8

If n is a natural number, then √n is

1. always a rational number
2. always a natural number
3. always an irrational number
4. either a natural number or an irrational number

What is the maximum value of m if the number 

N = 35 × 45 × 55 × 60 × 124 × 75 

is divisible by 5^m?

1. 4
2. 5
3. 6
4. 7

A student was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was

1. 15
2. 32
3. 12
4. 25

If x is a positive even integer and y is a negative odd integer, then x^y is

1. even integer
2. rational number
3. odd integer
4. none

The difference between the squares of two consecutive odd integers is always divisible by

1. 16
2. 8
3. 7
4. 3

What is the last digit in 7⁴⁰² + 3⁴⁰²?

1. 0
2. 2
3. 4
4. 8

The sum of two numbers is 10 and their product is 20. What is the sum of their reciprocals?

1. 1
2. 1/2
3. 2
4. 1/10

If n is a whole number greater than 1, then n²(n² - 1) is always divisible by

1. 12
2. 24
3. 48
4. 60

The sum of two positive integers is 52 and their LCM is 168. What is the ratio between the numbers?

1. 2 : 3
2. 5 : 4
3. 7 : 6
4. 7 : 8

Suppose you have sufficient amount of rupee currency in three denominations: Rs. 1, Rs. 10 and Rs. 50. In how many different ways can you pay a bill of Rs. 107?

1. 16
2. 17
3. 18
4. 19

The ratio of a two-digit natural number to a number formed by reversing its digits is 4:7. The number of such pairs is

1. 5
2. 4
3. 3
4. 2

A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have?

1. 1040
2. 1048
3. 1049
4. 1050

The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is

Given that x²⁰¹⁸y²⁰¹⁷ = 1/2 and x²⁰¹⁶y²⁰¹⁹ = 8, the value of x² + y³ is

1. 35/4
2. 37/4
3. 31/4
4. 33/4

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p² - 1) is

1. always divisible by 6, and may or may not be divisible by 12
2. always divisible by 24
3. never divisible by 6
4. always divisible by 12, and may or may not be divisible by 24

If n is a positive integer, then (√3+1)²ⁿ - (√3−1)²ⁿ is

1. An even positive integer
2. A rational number other than positive integers
3. An odd positive integer
4. An irrational number

The last digit of the number 3²⁰¹⁵ is

1. 1
2. 3
3. 5
4. 7

When we multiply a certain two-digit number by the sum of its digits, 405 is achieved. If you multiply the number written in reverse order of the same digits, we get 486. Find the number?

1. 81
2. 45
3. 36
4. 54

Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

1. 1
2. 2
3. 3
4. 4

The number of integers n satisfying -–n+2 ≥ 0 and 2n ≥ 4 is

1. 0
2. 1
3. 2
4. 3

What is the right most non-zero digit of the number 30²⁷²⁰?

1. 1
2. 3
3. 7
4. 9

The product of all integers from 1 to 100 will have the following numbers of zeros at the end?

1. 19
2. 20
3. 22
4. 24

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

1. 21
2. 25
3. 41
4. 67

The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

1. 55
2. 57
3. 58
4. 59

What are the last two digits of 7²⁰⁰⁸?

1. 01
2. 21
3. 41
4. 61

What is the digit in the unit’s place of 2⁵¹?

1. 1
2. 2
3. 4
4. 8

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

1. 5
2. 6
3. 7
4. 8

If N = (11^{p + 7})(7^{q – 2})(5^{r + 1})(3^s) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:

1. 5
2. 6
3. 7
4. 8
5. 9

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

1. 1777
2. 1785
3. 1875
4. 1877

Let f(x) = x² and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

1. 16
2. 18
3. 36
4. 40