Number System-Railway Maths Part IX

Total Questions: 50

1. Find the largest four - digit number which when divided by 7, 9 and 11 leaves a remainder of 5 in each case. [RRB NTPC 24/07/2021 (Evening)]

Correct Answer: (b) 9707
Solution:

As we know the largest 4-digit number = 9999.
LCM of 7, 9, 11 = 693.
Multiple of the LCM nearest to 9999 is:
693 × 14 = 9702

Then, the largest 4-digit number which when divided by 7, 9, and 11 leaves a remainder of 5 in each case =  .

2. Find the divisor, given that dividend is 2200, remainder is 13 and the divisor is one-third of the quotient. [RRB NTPC 24/07/2021 (Evening)]

Correct Answer: (b) 27
Solution:

Let the divisor = d and the divisor is one-third of the quotient q.
i.e., q = 3d;
Given: Dividend = 2200, remainder = 13

3. What is the least positive integer that should be subtracted from 2750, so that the difference is a perfect cube? [RRB NTPC 24/07/2021 (Evening)]

Correct Answer: (c) 6
Solution:

4. How many four-digit numbers are completely divisible by 5, 12, and 18? [RRB NTPC 24/07/2021 (Evening)]

Correct Answer: (c) 50 
Solution:

LCM of 5, 12, 18 is 180.
The smallest 4-digit number divisible by 180 = 1080.
The largest 4-digit number divisible by 180 = 9900.

These multiples of 180 form an Arithmetic Progression having:
first term a = 1080, last term l = 9900, and common difference d = 180.

Then,

So, there are 50 four-digit numbers which are completely divisible by 5, 12, 18.

5. The ascending order of the fractions 2/3, 1/2 and 1/6 is: [RRB NTPC 26/07/2021 (Morning)]

Correct Answer: (c) 1/6, 1/2, 2/3
Solution:

6. The difference between two numbers is 45. When 20% of the larger number is added to 35% of the smaller number, we get a sum of 31. What is the sum of the original numbers? [RRB NTPC 26/07/2021 (Morning)]

Correct Answer: (a) 125
Solution:

Let the two numbers are a and b; i.e. a - b = 45 …..(1)
When 20% of the larger number is added to 35% of the smaller number, we get a sum of 31.

Solving these two equations we get:
a = 85 and b = 40 ;
Then the sum of the original numbers = 125

7. The number that has factors other than 1 and itself is called a _____ number. [RRB NTPC 26/07/2021 (Morning)]

Correct Answer: (b) Composite
Solution:

The number that has factors other than 1 and itself is called a composite number.

8. If the numerator of a fraction is strictly less than the denominator, then the fraction is a/an: [RRB NTPC 26/07/2021 (Morning)]

Correct Answer: (b) Proper fraction
Solution:

If the numerator of a fraction is strictly less than the denominator, then the fraction is a Proper fraction, e.g. 3/7

9. The remainder, when 11⁴¹ + 3 is divided by 10 is: [RRB NTPC 26/07/2021 (Morning)]

Correct Answer: (d) 4
Solution:

10. The number of pairs of twin primes between 1 and 100 are:

Correct Answer: (b) 8
Solution:

As we know:
Two prime numbers are called twin primes if there is present only one composite number between them, we can also say two prime numbers whose difference is two are called twin primes.

Then the number of pairs of twin primes between 1 and 100 are = 8 ;
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73) ;