Number System-Railway Maths Part V

Total Questions: 50

21. How many 3 - digit numbers leave remainder 1 when divided by 7? [RRB NTPC 28/01/2021 (Morning)]

Correct Answer: (c) 128
Solution:

How many 3-digit numbers leave remainder 1 when divided by 7
First such number is 105+1 = 106
Last such number is 994 + 1 = 995
AP with d = 7 , a(First term) = 106,
I (last term) = 995, Then n = ?
So, 106 + (n - 1) × 7 = 995
n = 889/7 + 1 = 128

22. The six digit number 87937A is divided by 6 where A is the least natural number. Find the value of A. [RRB NTPC 28/01/2021 (Morning)]

Correct Answer: (d) 2
Solution:

Any number divided by 2 and 3 then number is divided by 6
Divisibility of 6 = 3 × 2
Every option is an even number. So, We only have to check the divisibility by 3.
→ 87937A = 8 + 7 + 9 + 3 + 7 + A = 7 + A
Here, we need the least value of A.
So, 2 is the correct answer

23. Find the sum of the face values of 8 and 5 in the number 817354. [RRB NTPC 28/01/2021 (Evening)]

Correct Answer: (c) 13
Solution:

The face values of 8 and 5 in the number 817354 = 8 and 5
The sum of the face values - 13
[NOTE - Face value is the actual value of a digit in a number.]

24. A number when divided by 7 leaves a remainder 4. What will be the remainder when the square of the same number is divided by 7: [RRB NTPC 29/01/2021 (Morning)]

Correct Answer: (d) 2
Solution:

When we divide square of same number the remainder
= 4²/7 = 16/7 = 2

25. The 10th term of the Arithmetic Progression 2, 7, 12, .... is: [RRB NTPC 29/01/2021 (Morning)]

Correct Answer: (b) 47
Solution:

1st term = a = 2
Common difference = d = 7 - 2 = 5
10th term of AP = 2 + (10 - 1) × 5 = 47

26. What is the place value of 5 in the number 56789214? [RRB NTPC 29/01/2021 (Evening)]

Correct Answer: (b) 5 x 10⁷
Solution:

Place value of 5 = 50000000 = 5 × 10⁷

27. When 19³⁰⁰ is divided by 20, find the remainder. [RRB NTPC 29/01/2021 (Evening)]

Correct Answer: (b) 1
Solution:

28. How many numbers between 1 and 700 are completely divisible by 17? [RRB NTPC 29/01/2021 (Evening)]

Correct Answer: (d) 41
Solution:

Total numbers between 1 to 700 = 700
When we divide 700 by 17 we get 7 quotient=41
So 41 numbers are divisible by 17.

29. If the sum of two numbers is 30 and the product of 50, then the sum of their reciprocals is: [RRB NTPC 29/01/2021 (Evening)]

Correct Answer: (a) 3/5
Solution:

Let the numbers be x and y
A/Q, x + y = 30
And xy = 50
Now, 1/x + 1/y = (x + y)/(xy) = 30/50 = 3/5

30. The numerator of a fraction is 5 less than its denominator. If 2 is subtracted from the numerator and 2 is added to the denominator, the fraction becomes 2/5 , Find the original fraction. [RRB NTPC 30/01/2021 (Morning)]

Correct Answer: (a) 8/13
Solution: