Number System-Railway Maths Part IX

Total Questions: 50

21. Find the smallest integer whose cube is equal to itself. [RRB JE 22/05/2019 (Afternoon)]

Correct Answer: (c) -1
Solution:

Check each option one by one.
We get that −1 = (−1)³
⇒ −1 = −1

22. A number of two digits has 3 for its unit's digit, and the sum of the digits is 1/7 of the number itself. Find the number. [RRB JE 22/05/2019 (Evening)]

Correct Answer: (d) 63
Solution:

23. Which of these numbers has the most number of divisors? [RRB JE 23/05/2019 (Morning)]

Correct Answer: (a) 240
Solution:

Option (a) 240 = 1 × 2 × 2 × 2 × 2 × 3 × 5

Divisor of 240 = 1, 2, 4, 8, 16, 48, 240, 3, 6, 12, 24, 5, 10, 20, 40 and 80
No. of divisors of 240 is 16.

Option (b) 156 = 1 × 2 × 2 × 3 × 13
Divisors of 156 = 1, 2, 4, 12, 156, 3, 6, 13, 26 and 52
No. of divisors of 156 is 11.

Option (c) 200 = 1 × 2 × 2 × 2 × 5 × 5
Divisors of 200 = 1, 2, 4, 8, 40, 200, 5, 10, 20, 25, 50 and 100
No. of divisors of 200 is 13.

Option (d) 172 = 1 × 2 × 2 × 43
Divisors of 172 = 1, 2, 4, 172, 43 and 86
No. of divisors of 172 is 6.

Clearly, 240 has the maximum number of divisors.

24. The arithmetic mean and geometric mean of two numbers are 7 and 2√10 respectively. Then find the numbers. [RRB JE 24/05/2019 (Morning)]

Correct Answer: (c) 4, 10
Solution:

25. A number when divided by 234 gives the remainder 36. What will be the remainder when it is divided by 13? [RRB JE 24/05/2019 (Evening)]

Correct Answer: (c) 10
Solution:

Let number be x.
According to the question,
x = 234q + 36 (where q is quotient)
x = 13(18q + 2) + 10.

26. When 8 times of a number is increased by 4, the result is the smallest 3-digit number. What is the number? [RRB JE 25/05/2019 (Morning)]

Correct Answer: (b) 12
Solution:

Let the number be x.
Then, 8x + 4 = 100 → x = 12

27. Find the sum of first 12 even natural numbers. [RRB JE 28/05/2019 (Afternoon)]

Correct Answer: (a) 156
Solution:

The sum of ‘n’ even natural numbers = n(n + 1)
The sum of ‘12’ even natural numbers = 12×13 = 156

28. Three times the square of a number decreased by 4 times the number is equal to 50 more than the number. Find the number. [RRB JE 28/05/2019 (Afternoon)]

Correct Answer: (d) 5
Solution:

29. The product of two numbers is 9375. The quotient, when the largest number is divided by the smallest number, is 15. Find the sum of these numbers. [RRB JE 30/05/2019 (Afternoon)]

Correct Answer: (a) 400
Solution:

Let, the largest number is a and the smallest number is b
According to question,
a = 15b, and product of these number
→ (a × b) = 9375 ⇒ (15b × b) = 9375
b² = 9375/15 ⇒ b² = 625 ⇒ b = 25
Now, a = 15b ⇒ a = 15 × 25 = 375
Required sum = 375 + 25 = 400

30. In a two-digit number, the digit in the unit's place is four times the digit in ten's place and sum of the digits is equal to 10. Find the number. [RRB JE 31/05/2019 (Morning)]

Correct Answer: (a) 28
Solution:

Let, unit digit of a two digit number is 4x and the digit in ten’s place is x

According to question,
(x + 4x) = 10 ⇒ 5x = 10 ⇒ x = 2
So, unit digit is 4x = (4 × 2) = 8 and digit in ten’s place is 2,
Therefore number = 28