**Multiple choice questions (MCQ) on Numbers**

**1. When a natural number n is divided by 4, the remainder is 3. What is the remainder when 2n is divided by 4?**

a. 1 b. 2 c. 3 d. 6

** 2. What is the last digit in the expansion of (2457) ^{754}?**

a. 3 b. 7 c. 8 d. 9

** 3. The product of two alternate odd integers exceeds three times the smaller by 12. What is the larger number?**

a. 3 b. 5 c. 7 d. 9

** 4. Nine numbers are written in ascending order. The middle number is the average of the nine numbers. The average of the first five larger numbers is 68 and that of five smaller numbers is 44. What is the sum of all nine numbers?**

a. 450 b. 501 c. 504 d. 540

** 5. If a:b = 3/2:9/2 and b:c = 2:7/2 then what is a:b:c?**

a. 12:8:21 b. 8:21:12 c. 8:12:21 d. 21:8:12

** 6. A bag contains Rs. 114 in the form of 1 rupee, 50 paise and 10 paisa coins in the ratio 3:4:10. What is the number of 50 paisa coins?**

a. 76 b. 72 c. 56 d. 48

** 7. What is the total number of three digit numbers with unit digit 7 and divisible by 11?**

a. 6 b. 7 c. 8 d. 9

** 8. What is the sum of positive integers less than 100 which leave a remainder 1 when divided by 3 and leave a remainder 2 when divided by 4?**

a. 416 b. 620 c. 1250 d. 1314

** 9. What is the greatest number which divides 392, 486 and 627 so as to leave the same remainder in each case?**

a. 47 b. 43 c. 37 d. 34

** 10. Consider those numbers between 300 and 400 such that when each number is divided by 6, 9 and 12, it leaves 4 as remainder in each case. What is the sum of the numbers? **

a. 692 b. 764 c. 1080 d. 1092

** 11. A three digit number is divisible by 11 and has its digit in the unit’s place equal to 1. The number is 297 more than the number obtained by reversing the digits. What is the number?**

a. 121 b. 231 c. 561 d. 451

** 12. If the highest common factor of two positive integers is 24 then their least common multiple cannot be**

a. 72 b. 216 c. 372 d. 600

** 13. Which of the following numbers is not a square of any natural numbers?**

a. 5041 b. 9852 c. 1936 d. 6241

** 14. The least number which when divided by 5, 6, 7 and 8 leaves a remainder is**

a. 423 b. 843 c. 1683 d. 2523

** 15. Two numbers are in the ratio 3:5. If 9 is subtracted from each number, then they are in the ratio of 12:23. What is the second number?**

a. 44 b. 55 c. 66 d. 77

** 16. The sum of digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. What is the difference between the digits of the number?**

a. 1 b. 2 c. 3 d. 4

** 17. What is the smallest number that must be added to 1780 to make it a perfect square?**

a. 39 b. 49 c. 59 d. 69

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

a. 1/10 b. ½ c. 1 d. 2

** 19. Which among the following is the largest four digit number that is divisible by 88?**

a. 9988 b. 9966 c. 9944 d. 8888

** 20. A number when divided by 2, 3 or 5 gives remainder 1. This number is**

a. 31 b. 47 c. 49 d. 53

** 21. Which one of the following is a prime number?**

a. 161 b. 171 c. 173 d. 221

** 22. What is the value of √0.0032/√0.32?**

a. 0.0001 b. 0.001 c. 0.01 d. 0.1

** 23. If 2 ^{m} + 2^{1+m} = 24, then what is value of m?**

a. 0 b. 1/3 c. 3 d. 6

** 24. If n is a natural number, then √n is**

a. always a natural number b. always a rational number

c. always a irrational number d. either a natural or an irrational number

** 25. The largest integer that divides product of any four consecutive integers is**

a. 4 b. 6 c. 12 d. 24

** 26. What is [(√5+√3)/(√5-√3)]+[(√5-√3)/(√5+√3)] equal to**

a. 16 b. 8 c. 4 d. √15

** 27. How many numbers lie between 300 and 500 in which 4 comes only one time?**

a. 99 b. 100 c. 110 d. 120

** 28. How many integers from 1 to 1000 have none of their digits repeated?**

a. 735 b. 736 c. 737 d. 738

** 29. How many numbers will be left out of the numbers from 1 to 30, if all numbers which are exactly divisible by 3 and also those which have 3 as one of the digits are removed?**

a. 12 b. 17 c. 18 d. 20

** 30. When a certain number is divided by 5, the remainder is 1. When the same number is divided by 3, the remainder is 2. What is that number?**

a. 8 b. 11 c. 16 d. 21

** 31. A number consists of two digits. If the digits interchanges places and the new number is added to the original number, then the resulting number will always be divisible by:**

a. 10 b. 11 c. 12 d. 13

** 32. If the ratio of the sum and difference of two numbers be 17:13, which one of the following is the ratio of the numbers?**

a. 12:5 b. 15:2 c. 9:8 d. 2:15

** 33. How many integers from 1 to 1000 have none of their digits repeated?**

a. 735 b. 736 c. 737 d. 738

** 34. x/y=20 and if y/z=1, then what is the value of (x/y) + (x/z)?**

a. 20 b. 25 c. 30 d. 40

** 35. The value of 6+(1/10)+(6/1000)+(61/10000) is**

a. 6.1021 b. 6.221 c. 6.1121 d. 6.167

** 36. The value of 2(a ^{2}+ab+3)-ab when a=5 and b=-3, is**

a. 35 b. 41 c. 53 d. 23

** 37. The value of [2-3(2-3) ^{-1}]^{-1} is**

a. -5 b. 1/5 c. -1/5 d. 5