Number System-Railway Maths Part IV

Total Questions: 50

1. 3⁷¹ + 3⁷² +3⁷³ +3⁷⁴ + 3⁷⁵ is divisible by. [RRB NTPC 08/01/2021 (Evening)]

Correct Answer: (c) 11
Solution:

3⁷¹ + 3⁷² +3⁷³ +3⁷⁴ + 3⁷⁵
= 3⁷¹ (1 + 3 + 3² + 3³+ 3⁴)
= 3⁷¹ (1 + 3 + 9 + 27+ 81) = 3⁷¹ × 121
This Will be divisible by 11.

2. If the sum of squares of two positive numbers is 2437 and square root of one number is 7. Find the other number. [RRB NTPC 08/01/2021 (Evening)]

Correct Answer: (a) 6
Solution:

Let both the numbers be, a and b.
ATQ, a² + b² = 2437 ---- (1))
And √(a) = 7 ---- (2)
Squaring both sides we get,
a = 49 ⇒ a² = 2401
From equation (1),
2401 + b² = 2437
⇒ b² = 2437 - 2401 = 36 ⇒ b=6

3. Express 0.03 overline 7 in the form of p/q, where p is a whole number and q is a natural number. [RRB NTPC 09/01/2021 (Morning)]

Correct Answer: (c) 17/45
Solution:

0.037̅ = (37 - 3)/900 = 17/450

4. How many numbers from 3 to 60 are odd numbers that are exactly divisible by 5? [RRB NTPC 09/01/2021 (Morning)]

Correct Answer: (d) 6
Solution:
Odd numbers from 3 to 60, that are exactly divisible by 5 are: 5, 15, 25, 35, 45, 55 i.e. 6 numbers.

5. Sum of the digits of a two-digit number is 6. If the digits are reversed, the new number equals double of the original number decreased by 6. Find the number. [RRB NTPC 09/01/2021 (Morning)]

Correct Answer: (c) 24
Solution:

Let the two digit number be 10x + y
So x + y = 6,
According to the question,
2 (10x + y) - (10y + x) = 6
⇒ 19x - 8y = 6 ⇒ 19(6 - y) - 8y = 6
⇒ y = 48x = 2
So, the number is 24.

6. How many numbers between 300 and 1000 are divisible by 7? [RRB NTPC 09/01/2021 (Morning)]

Correct Answer: (c) 100
Solution:

7. The sum of the digits of a two-digit number is 9. If the digits are reversed the new number when increased by 9 equals three times the original number. Find the number. [RRB NTPC 09/01/2021 (Evening)]

Correct Answer: (a) 27
Solution:

Let the number = xy
A/Q,
x + y = 9 ⇒ y = 9 - x - (1)
When the digits are reversed new number
= yx ⇒ 10y + x + 9 = 3(10x + y)
⇒ 10y + x + 9 = 30x + 3y
⇒ 7y - 29x + 9 =0......(2)
Put y = 9 - x in equation (2)
⇒ 7(9 - x) - 29x + 9 = 0
⇒ 63 - 36x + 9 = 0 ⇒ 72 = 36x ⇒ x = 2
From eq. (1)
y = 7 Number = 27

8. How many numbers greater than 2 and less than 30 are divisible by 1 ad themselves? [RRB NTPC 10/01/2021 (Morning)]

Correct Answer: (c) 9
Solution:

A number is divisible by 1 and itself are numbers from 3 to 29 are 3, 5, 7, 11, 13, 17, 19, 23 and 29.
Total = 9 no. are there.

9. The sum of all even integers from 2 to 281 is: [RRB NTPC 10/01/2021 (Morning)]

Correct Answer: (d) 19740
Solution:

10. Select the option that gives the fractions 2/5 ,1/3 , 3/5 ,1/4 , 7/10 , 5/8 , in ascending order. [RRB NTPC 10/01/2021 (Morning)]

Correct Answer: (b) 1/4, 1/3, 2/5, 3/5, 5/8, 7/10
Solution:

The fractions are given as : 2/5, 1/3, 3/5, 1/4, 7/10, 5/8
To arrange it in ascending order the denominators should be made equal to compare among them.
⇒ 48/120, 40/120, 72/120, 30/120, 84/120, 75/120
So, the ascending order will be:
1/4, 1/3, 2/5, 3/5, 5/8, 7/10