NUMBER SYSTEM (CDS)

Total Questions: 101

21. A five-digit number XY235 is divisible by 3 where X and Y are digits satisfying X + Y ≤ 5. What is the number of possible pairs of values of (X, Y) ? [2018 (II) Evening Shift ]

Correct Answer: (c) 7
Solution:Given, XY235 is divisible by 3 and X + Y ≤ 5

22. The number of divisors of the number 38808 exclusive of the divisors 1 and itself, is [2018 (II) Evening Shift ]

Correct Answer: (c) 70
Solution:

23. If the sum of the squares of three consecutive natural numbers is 110, then the sum of their cubes is [2018 (II) Evening Shift ]

Correct Answer: (c) 684
Solution:Let the three consecutive natural numbers be (x - 1), x, (x + 1)

24. Consider the following statements in respect of three 3-digit numbers XYZ, YZX and ZXY: [2018 (II) Evening Shift ]

1. The sum of the numbers is not divisible by (X + Y + Z) .
2. The sum of the numbers is divisible by 111.

Which of the above statements is / are correct?

Correct Answer: (b) 2 only
Solution:We have, 3-digits numbers are

25. The number of all pairs (m, n) where m and n are positive integers, such that [2018 (II) Evening Shift ]

Correct Answer: (c) 4
Solution:


26. Solve the following equation [2018 (II) Evening Shift ]

Correct Answer: (b)
Solution:We know that, harmonic mean of a and b is

27. 5¹⁷ + 5¹⁸ + 5¹⁹ + 5²⁰ is divisible by [2018 (I) Morning Shift ]

Correct Answer: (d) 13
Solution:5¹⁷ + 5¹⁸ + 5¹⁹ + 5²⁰

28. Which one of the following is correct? [2018 (I) Morning Shift ]

Correct Answer: (d) Decimal expansion of an irrational number is non-terminating and non repeating
Solution:Decimal expansion of an irrational number is non-terminating and non repeating.

29. The smallest integer with 4-digits which is a perfect square is ? [2018 (I) Morning Shift ]

Correct Answer: (b) 1024
Solution:

Square of any number last digit must be, 0, 1, 4, 5, 6 or 9.
Here, 1024 is only possible square.
Hence, smallest four digit number which is a perfect square is 1024.

30. The age of a woman is a two-digit integer. On reversing this integer, the new integer is the age of her husband who is elder to her. The difference between their ages is one-eleventh of their sum. What is the difference between their ages ? [2018 (I) Morning Shift ]

Correct Answer: (b) 9 year
Solution:Let the age of woman = (10x + y) year