# Number Systems

### The number of integers x such that 0.25 2^x 200, and 2^x + 2

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

### While multiplying three real numbers, Ashok took one of the numbers

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 x^2018 y^2017 = 1/2 and x^2016 y^2019 = 8

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

### 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

### Let p be a prime number greater than 5. Then (p^2 - 1) is

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

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 3^2015 is

The last digit of the number 32015 is

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

### When we multiply a certain two-digit number

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

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

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 30^2720

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

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

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

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 7^2008

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 2^51

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

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

### 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

### If N = (11^(p+7)) (7^(q-2)) (5^(r+1)) (3^s) is a perfect cube

If N = (11p + 7)(7q – 2)(5r + 1)(3s) 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

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) = x^2 and g(x) = 2x, for all real x

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