# Number Systems

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

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

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

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

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

### The sum of two positive integers is 52 and their LCM is 168

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

### If n is a whole number greater than 1, then n^2(n^2 - 1)

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 numbers is 10 and their product is 20

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

### What is the last digit in 7^402 + 3^402

What is the last digit in 7402 + 3402?

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

### The difference between the squares of two consecutive odd

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

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

### If x is a positive even integer and y is a negative odd integer

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

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

### A student was asked to multiply a number by 25

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

### What is the maximum value of m if the number

What is the maximum value of m if the number

N = 35 × 45 × 55 × 60 × 124 × 75

is divisible by 5m?

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

### If n is a natural number, then √n is

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

### The digit in the units place of the product

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, N+2 and N+4 are prime numbers

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 sum of two numbers is 143. If the greater number is divided

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

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

The values of x which satisfy the equation 51+x + 51–x = 26 are

1. –1, 1
2. 0, 1
3. 1, 2
4. –1, 0

### The number of prime numbers which are less than 100 is

The number of prime numbers which are less than 100 is

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

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

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

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

### How many times will the digit 5 come in counting from 1 to 99

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

### What is the number of all possible positive integer values of n for which n^2 + 96 is a perfect square

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
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