NUMBER SYSTEM (CDS)

Total Questions: 101

31. All odd prime numbers upto 110 are multiplied together. What is the unit digit in this product? [2018 (I) Morning Shift ]

Correct Answer: (c) 5
Solution:All odd prime numbers upto 110 are 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107

Now, we know that if 5 is multiplied with any odd digit the digit at unit place will be 5.

∴ The unit digit of the product of all odd prime digits upto 110 is 5.

32. 1/25 of the students who registered did not appear for the exam, 11/20 those who appeared passed. If number of registered students is 2000, the number who passed is [2018 (I) Morning Shift ]

Correct Answer: (b) 1056
Solution:Number of registered students =2000

33. The arithmetic mean of two numbers is 10 and their geometric means is 8. What are the two numbers? [2018 (I) Morning Shift ]

Correct Answer: (c) 16, 4
Solution:Let the two numbers be x and y.

34. Three numbers which are co-prime to each other, are such that the product of the first two is 286 and that of the last two is 770. What is the sum of the three numbers ? [2018 (I) Morning Shift ]

Correct Answer: (d) 70
Solution:Let the three numbers which are co-prime to each other be x, y and z.
According to the question, xy = 286 = 13 × 22 and yz = 770 = 22 × 35
∴ Required numbers are 13, 22 and 35
Hence, required um = 13 + 22 + 35 = 70

35. How many numbers from 1 to 1000 are divisible by 2, 3, 4 and 5 ? [2017 (II) Evening Shift ]

Correct Answer: (a) 16
Solution:LCM of 2, 3, 4, 5 = 60
Therefor, the number from 1 to 1000 are divisible by 60 = [1000/60] = 16

36. a, b, c, d are non-zero integers such that (ab) divides (cd). If a and c are coprime, then which one of the following is correct ? [2017 (II) Evening Shift ]

Correct Answer: (c) a is a factor of d
Solution:Since, a and c are coprime, therefore HCF (a, c) = 1
⇒ a divides d ⇒ a is a factor of d

37. How many numbers between 500 and 1000 are divisible by 13 ? [2017 (II) Evening Shift ]

Correct Answer: (c) 38
Solution:

38. Consider the following numbers [2017 (II) Evening Shift ]

1. 2222
2. 11664
3. 343343
4. 220347

Which of the above are not perfect squares?

Correct Answer: (d) 1, 3 and 4
Solution:We know that, if last digit of number is either 2 or 3 or 7 or 8, then that number cannot be a perfect square number.
∴ The number in 1, 3 and 4 are not perfect squares.

39. What is the remainder when the number (4444)⁴⁴⁴⁴ is divided by 9 ? [2017 (I) Morning Shift ]

Correct Answer: (c) 7
Solution:According to Euler theorem

40. The number of prime numbers which are less then 100 is [2017 (I) Morning Shift ]

Correct Answer: (b) 25
Solution:Prime numbers less than 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

∴ There are 25 prime numbers less than 100.