Number System-Railway Maths Part III

Total Questions: 50

1. When a number is divided by 15, it leaves a remainder of 3. If the same number is divided by 17, the remainder is 11. Which of the options below gives such a number? [Group D 28/09/2022 (Morning)]

Correct Answer: (a) 198
Solution:

By hit and trial method, From option (a)
198 when divided by 15 remainder = 3
198 when divided by 17 remainder = 11 (satisfies)
Hence option (a) is the right answer

2. Mr. Rao walks 45 minutes in a day. What fraction of a day does he walk per day, expressed as a fraction? [Group D 28/09/2022 (Afternoon)]

Correct Answer: (d) 1/32
Solution:

Required fraction = 45/(24 × 60) = 1/32

3. Which of the following is divisible by 17? [Group D 28/09/2022 (Evening)]

Correct Answer: (a) 1887
Solution:

By hit and trial From option (a), 1887÷17 = 111

4. The difference between two numbers is 18. If the difference between their squares is 360, find the larger number. [Group D 29/09/2022 (Morning)]

Correct Answer: (a) 19
Solution:

Let the number be a and b According to the question,
a - b = 18......(i), a² - b² = 360
(a + b)(a - b) = 360, (a + b) = 20......(ii)
Possible value of a = 19 and b = 1
So, larger number = 19

5. The average of the first 7 multiples of 3 is: [Group D 29/09/2022 (Morning)]

Correct Answer: (b) 12
Solution:

1st multiple of 3 = 3
7th multiple of 3 = 21
Therefore average = (21 + 3)/2 = 12

6. This question is based on the seven, three - digit numbers given below. 365, 125, 486, 548, 654, 552, 354 If 3 is added to the first digit of every number, in how many numbers will the first digit be exactly divisible by the second digit? (example - 697 - First digit = 6, second digit = 9 and third digit = 7) [Group D 29/09/2022 (Evening)]

Correct Answer: (b) Three
Solution:

Numbers: 365, 125, 486, 548, 654, 552, 354
If 3 is added to first digit of every number, then, Numbers = 665, 425, 786, 848, 954, 852, 654, Numbers in which the first digit is exactly divisible by the second digit = 665, 425, 848
Hence, there are 3 such numbers.

7. What is the difference between the biggest and the smallest fractions among 1/2 , 3/4 , 4/5 and 5/6 ? [Group D 29/09/2022 (Evening)]

Correct Answer: (b) 1/3
Solution:

8. Arrange the numbers given below in ascending order. [Group D 30/09/2022 (Morning)]

705.0, 7.005, 7.500, 70.50, 7050, 7.050, 75

Correct Answer: (d) 7.005, 7.050, 7.500, 70.50, 75, 705.0, 7050
Solution:

705.0, 7.005, 7.500, 70.50, 7050, 7.050, 75
On arranging in ascending order, 7.005, 7.050, 7.500, 70.50, 75, 705.0, 7050

9. In the set (61, 62...100}, find the sum of the second largest and the second smallest primes. [Group D 30/09/2022 (Afternoon)]

Correct Answer: (a) 156
Solution:

Prime numbers between 61 and 100 = 61, 67, 71, 73, 79, 83, 89, 97. Second smallest prime between 61 and 100 = 67
Second largest prime between 61 and 100 = 89
Hence, required sum = 67 + 89 = 156

10. Find the least number which, when divided by 12, 16 and 18, leaves a remainder of 5 in each case. [Group D 30/09/2022 (Evening)]

Correct Answer: (d) 149
Solution:

LCM of 12, 16 and 18 = 144 Remainder = 5
So, required number = 144 + 5 = 149