Number System-Railway Maths Part VIII

Total Questions: 50

11. Find the units digit in the product of (127)¹⁵³ × (341)⁸⁹. [RRB NTPC 19/03/2021 (Evening)]

Correct Answer: (d) 7
Solution:

(127)¹⁵³ × (341)⁸⁹
153 ÷ 4 = Remainder = 1
unit digit = 7¹ × 1 = 7

12. Find the least multiple of 13, which on dividing by 4, 5, 6, 7, and 8 leaves a remainder 2 in each case. [RRB NTPC 19/03/2021 (Evening)]

Correct Answer: (b) 2522
Solution:

LCM of (4, 5, 6, 7, 8) = 840
The number should be multiple of 13 and remainder = 2, it will in the form of
840k + 2, Put k = 3
840 × 3 + 2 = 2522

13. How many 3-digit numbers are divisible by 7? [RRB NTPC 21/03/2021 (Morning)]

Correct Answer: (b) 128
Solution:

3 digits number which is divisible by 7 = 105, 112, 119..., 994
aₙ ​= a + (n−1 )d
Where, First term = a = 105, Common difference = d = 112 - 105 = 7
⇒ 994 = 105 + (n - 1)(7)
⇒ 994 = 105 + 7n - 7
⇒ 896 = 7n
⇒ n = 128

14. 6⁶¹ + 6⁶² + 6⁶³ + 6⁶⁴ + 6⁶⁵ is completely divisible by: [RRB NTPC 21/03/2021 (Morning)]

Correct Answer: (d) 15
Solution:

6⁶¹ + 6⁶² + 6⁶³ + 6⁶⁴ + 6⁶⁵
= 6⁶¹ (1 + 6 + 6² + 6³ + 6⁴)
= 6⁶¹ (1 + 6 + 36 + 216 + 1296)
= 6⁶¹ (1555) = 6⁶⁰ (9330)
= 6⁶⁰ (622 × 15) so, it is divisible by 15

15. Find the least number that, when divided by 72, 80 and 88, leaves the remainder 52, 60, 68 respectively. [RRB NTPC 21/03/2021 (Morning)]

Correct Answer: (b) 7900
Solution:

Here (72 - 52) = 20, (80 - 60) = 20 and (88 - 68) = 20
Required number (LCM of 72, 80 and 88) - 20 = 7920 - 20 = 7900

16. How many numbers between 100 and 300 are divisible by 7? [RRB NTPC 21/03/2021 (Evening)]

Correct Answer: (b) 28
Solution:

Total numbers between 100 and 300 = 200
Now  28 numbers are divisible by 7.

17. Kunal was asked to find 5/6 times of a number. He multiplied it by 6/5. As a result, he got an answer which was more than the correct answer by 572. The number was: [RRB NTPC 21/03/2021 (Evening)]

Correct Answer: (c) 1560
Solution:

18. The greatest number of four digits which is divisible by 5, 35, 39 and 65 is: [RRB NTPC 21/03/2021 (Evening)]

Correct Answer: (d) 9555
Solution:

Largest number of four digit = 9999
LCM of (5, 35, 39, 65) = 1365
When we divide 9999 by 1365, we get remainder = 444
Now, 9999 - 444 = 9555

19. Which of the following is a rational number? [RRB NTPC 27/03/2021 (Morning)]

Correct Answer: (d) (√2 + 1/√8)²
Solution:It is a rational number.

20. Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively. [RRB NTPC 27/03/2021 (Morning)]

Correct Answer: (b) 138 
Solution:

285 - 9 = 276
1249 - 7 = 1242
HCF of 276 and 1242 = 138