This document contains 14 multiple choice questions related to number theory and arithmetic concepts. The questions cover topics such as sums and differences of consecutive numbers, products of numbers, properties of two and three digit numbers, and arithmetic operations involving fractions and reciprocals. The last two questions involve calculating keystrokes to type numbers and determining the minimum number of square tiles needed to cover a floor of given dimensions.

1. Number Theory

2. What is the sum of two consecutive even numbers, the difference of whose squares is 84? A. 34B. 38C. 42D. 46

3. The sum of two number is 25 and their difference is 13. Find their product. A. 104B. 114C. 315D. 325

4. A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is: A. 145B. 253C. 370D. 352

5. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is: A. 20B. 23 C. 169D. None of these

6. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is: A. 380B. 395C. 400 D. 425

7. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number. A. 3 B. 10C. 17D. 20

8. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is: A. 20 B. 30C. 40D. None of these

9. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? A. 69B. 78C. 96D. Cannot be determined E. None of these

10. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: A. 18B. 24 C. 42D. 81

11. If one-third of one-fourth of a number is 15, then three-tenth of that number is: A. 35B. 36C. 45D. 54

12. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is: A. 9B. 11C. 13D. 15

13. The largest number amongst the following that will perfectly divide 101100 - 1 is10010,000100100100,000

14. How many keystrokes are needed to type numbers from 1 to 1000? 3001289327042890

15. What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?17618754043748