EASY
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The smallest number which when increased by 17, is exactly divisible by both 520 and 468 is -

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Important Questions on Number Systems

HARD
For a real number r let r denote the largest integer less than or equal to r. Let a>1 a real number which is not an integer and k be the smallest positive integer such that ak>ak Then which of the following statement is always true?
MEDIUM
The largest non-negative integer k such that 24k divides 13! is
HARD
For a real number r we denote by r the largest integer less than or equal to r. If x, y are real numbers with x, y 1 then which of the following statements is always true?
EASY

The sum of three consecutive numbers is 126. Find the highest number-

1. 41
2. 42
3. 43
4. 44

MEDIUM
A thrice of the square of a natural number decreased by 4 times the number is equal to 50 more than the number. Find the number.
EASY

Twice the difference between two numbers is equal to their sum. If one number is 15, Find the other number.

1. 15
2. 10
3. 5
4. 20 

HARD
The function f :NI defined by fx=x-5x5 , where N is the set of natural numbers and x denotes the greatest integer less than or equal to x, is:
EASY
The sum of two digits of a number is 13. If 9 is subtracted from the number, the digits are interchanged. What is the number?
EASY
Three-digit numbers are formed from the digits 1,2 and 3 in such a way that the digits are not repeated. What is the sum of such three-digit numbers?
MEDIUM
How many natural numbers n are there such that n!+10 is a perfect square ?
EASY

1 USD = Rs. 67.89. A money changer adds a margin of Rs. 1.11. What will be the cost of 150 USD ? 

1. Rs. 10,183
2. Rs. 10,350
3. Rs. 10,330
4. Rs. 10,450

EASY
The sum of four consecutive even numbers is 107 more than the sum of three consecutive odd numbers. If the sum of the smallest odd number and the smallest even number is 55, then what is the smallest even number?
EASY
The difference of the cubes of two consecutive numbers is 127. What are the numbers?
EASY

How many times does the number 3 occur in unit's place for numbers ranging from 1 to 100?

1. 20
2. 11
3. 10
4. 19

MEDIUM
If 59 is added to a square of a number, the result is 900. What is the number?
MEDIUM
The least number, which is to be added to the greatest number of 4 digits so that the sum may be divisible by 345, is _____.
EASY
If 14 of third-part of number is 5, then the number is:
MEDIUM
The number of distinct primes dividing 12!+13!+14! Is
MEDIUM
If a quantity is divided in the ratio 3:5, the larger part is 75. Find the quantity.
MEDIUM
The annual salary of Arun is Rs. 7.68 lakh. In a month if he spends Rs. 12000 on his children, 113th of rest on food and Rs. 8000 in mutual funds from his monthly salary, then find the monthly saving he is left with.