Number System-Railway Maths Part IX

Total Questions: 50

31. A number when divided by 15 leaves the remainder 12. Another number When divided by 5 leaves the remainder 2. What is the remainder when their sum is divided by 5? [RRB JE 31/05/2019 (Afternoon)]

Correct Answer: (d) 4
Solution:

1st no. (N₁) = (15a + 12)
and 2nd no. (N₂) = (5a + 2)

32. Find the value of 1² + 2² + 3² + ... ... ... + 10² [RRB JE 31/05/2019 (Evening)]

Correct Answer: (d) 385
Solution:

33. If a and b are coprime, then a² and b² are— [RRB JE 31/05/2019 (Evening)]

Correct Answer: (d) Coprime
Solution:

If a and b are coprime, then a² and b² are also coprime numbers.

34. Find the largest 4-digit number that is exactly divisible by 88. [RRB JE 02/06/2019 (Morning)]

Correct Answer: (a) 9944
Solution:

Largest 4-digit number = 9999
9999/88 = 88 × 113 + 55 ⇒ remainder = 55
Required number = 9999 − 55 = 9944

35. (2²⁵+ 2²⁶+ 2²⁷+ 2²⁸) is a multiple of which of the following numbers? [RRB JE 02/06/2019 (Afternoon)]

Correct Answer: (d) 15
Solution:

36. If the numerator of a fraction is increased by 100% and the denominator is increased by 150%, then the fraction becomes 16/25. What is the original fraction? [RRB JE 02/06/2019 (Afternoon)]

Correct Answer: (d) 4/5​
Solution:

37. From the set of prime numbers between 50 and 100, how many pairs of primes are there that add up to a prime number? [RRB JE 02/06/2019 (Afternoon)]

Correct Answer: (a) 0
Solution:

Prime numbers between 50 and 100 = 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
No pairs of these prime numbers add up to another prime number.

38. Find the largest number that will divide exactly the product of four consecutive integers. [RRB JE 02/06/2019 (Afternoon)]

Correct Answer: (d) 24
Solution:

Let the four consecutive numbers be x, x + 1, x + 2, and x + 3.
Their product = x(x + 1)(x + 2)(x + 3).

Let x = 1 ⇒ (1)(2)(3)(4) = 24.

39. Choose the number that is divisible by 11. [RRB JE 02/06/2019 (Evening)]

Correct Answer: (c) 325182
Solution:

Divisibility rule of 11:
If the difference between the sums of the alternate digits of a number is either 0 or divisible by 11, then the number is divisible by 11.

Let’s choose option (c):
(3 + 5 + 8) − (2 + 1 + 2) = 11
Clearly, option (c) 325182 is divisible by 11.

40. When a positive number is decreased by 4, it is equal to 21 times the reciprocal of the number. Find the number. [RRB JE 02/06/2019 (Evening)]

Correct Answer: (d) 7
Solution: