Number System-Railway Maths

Total Questions: 50

41. The sum of the double of the largest two-digit prime number and triple of the largest three-digit prime number is equal to_______. [Group D 22/08/2022 (Afternoon)]

Correct Answer: (a) 3185
Solution:

Largest 2-digit prime number = 97
and Largest 3-digit prime number = 997
Required sum = 2 × 97 + 3 × 997 = 194 + 2991 = 3185

42. From the numbers 51, 52, 53,....... 100. find the sum of the smallest and the greatest prime numbers as given. [Group D 22/08/2022 (Afternoon)]

Correct Answer: (b) 150
Solution:

Prime numbers between 51 and 100 are 53, 59, 61, 67, 71,.......... 97
Sum of the smallest and the greatest prime numbers = 53 + 97 = 150

43. 3 pencils and 5 pens together cost ₹81, whereas 5 pencils and 3 pens together cost ₹71. The cost of 1 pencil and 2 pens together is: [Group D 22/08/2022 (Afternoon)]

Correct Answer: (d) ₹31
Solution:

Let the price of each pencil be ₹ x and price of each pen be y
3x + 5y = 81........(1)
5x + 3y = 71........(2)
By solving eq, (1) and (2), we get x = 7 and y = 12
C.P of 1 pencil and 2 pens = (1 × 7) + (2 × 12) = 7 + 24 = ₹31

44. The sum of the digits in a two-digit number is 9. If the value of the number is 6 more than 5 times the digit in the ones' place, then the number is: [Group D 22/08/2022 (Evening)]

Correct Answer: (d) 36
Solution:

Let the digit at one's place be x and the digit at ten place be y.
⇒ x + y = 9.......(1) ⇒ 10y + x = 5x + 6
4x - 10y = -6........(2)
By solving eq, (1) and (2), we get x = 6 , y = 3 Required number = 10y + x = 10 × 3 + 6 = 30 + 6 = 36

45. The sum of the first 8 prime numbers divided by 7 equal to_______. [Group D 22/08/2022 (Evening)]

Correct Answer: (b) 11
Solution:

Sum of first 8 prime numbers = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 Required number = 77 ÷ 7 = 11

46. The sum of three consecutive multiples of 9 is 2457, find the largest one. [Group D 23/08/2022 (Morning)]

Correct Answer: (a) 828
Solution:

Let the first multiple of 9 be x.
9x + 9(x + 1) + 9(x + 2) = 2457
⇒ 9x + 9x + 9 + 9x + 18 = 2457
⇒ 27x = 2457 - 27
⇒ 27x = 2430 ⇒ x = 90
Largest number = 9 × (90 + 2) = 9 × 92 = 828

47. The total number of three-digit numbers divisible by 2 or 5 is? [Group D 23/08/2022 (Afternoon)]

Correct Answer: (a) 540
Solution:

Three digit numbers are 100, 101...........998, 999
total numbers divisible by 2 = 450 = n(2)
total numbers divisible by 5 = 180 = n(5)
total numbers divisible by both 2 and 5 = 90 = n(2 and 5)
The total numbers of three-digit numbers divisible by 2 or 5 = n(2 or 5) = n(2) + n(5) -n(2 and 5)
The total number of three-digit numbers divisible by 2 or 5 = 450 +180 - 90  = 540

48. There are two consecutive natural numbers such that the sum of their squares is 313. Find the smaller of these two numbers. [Group D 24/08/2022 (Morning)]

Correct Answer: (a) 12
Solution:

Let the first consecutive natural number be x
Now, x² + (x + 1)² = 313
⇒ x² + x² + 1 + 2x = 313
⇒ 2x² + 2x - 312 = 0
⇒ x²  + x - 156 = 0
⇒ x² + 13x - 12x - 156 = 0
⇒ (x + 13) (x - 12) = 0
Smaller number = 12

49. The value of 1 + 3 + 5 + 7 +... +21= [Group D 25/08/2022 (Morning)]

Correct Answer: (a) 121
Solution:

1 + 3 + 5 + 7+…………+ 21
Sum of odd numbers = n²,  where n is number of terms.
Here n = 11 , sum = 11² = 121

50. How many numbers between 1 to 150 are divisible by 3 and 4 both? [Group D 26/08/2022 (Morning)]

Correct Answer: (c) 12
Solution:

Divisible by both 3 and 4 → divisible by 12
The numbers between 1 to 150 divisible 150 by 12 = 150/12 = 12