Number System-Railway Maths Part IX

Total Questions: 50

41. The square of a number ends in 4. Then its cube ends in — [RRB JE 26/06/2019 (Evening)]

Correct Answer: (d) 2 or 8
Solution:

If the number ends with 2 and 8, their square always ends with 4 and the cube of that number always ends with 2 or 8.

42. Three times the first of three consecutive odd integers is 3 more than two times the third. Find the third integer. [RRB JE 26/06/2019 (Evening)]

Correct Answer: (a) 15
Solution:

Let three consecutive odd integers be (x − 2), (x), (x + 2)
According to the question
⇒ 3 × (x − 2) = 2 × (x + 2) + 3 ⇒ x = 13,
So the third integer (x + 2) ⇒ (13 + 2) = 15.

43. The end digit of the square of a number is 1. Then the end digit of its cube is: [RRB JE 27/06/2019 (Morning)]

Correct Answer: (b) 1 or 9
Solution:

Numbers having unit digit 1 and 9, their square will always end with unit digit 1, but the unit digit of their cube is either 1 or 9.

44. In a school picnic group, 2/9 of the group were adults and there were 95 more children than adults. How many children were there? [RRB JE 27/06/2019 (Morning)]

Correct Answer: (b) 133
Solution:

Total persons in picnic group = 9 units,
Total adults in that group = 2 units.
Then, total children = 7 units.

Difference between children and adults (7 − 2) units ⇒ 5 units = 95.
Total children (7 units) = 19 × 7 = 133.

45. A two-digit number gets reversed on adding 18 to it. The product of the digits is ‘8’. What is the number? [RRB JE 27/06/2019 (Morning)]

Correct Answer: (d) 24
Solution:

According to question,
Let the number be (10x + y). Then
(10x + y) + 18 = (10y + x)

9x − 9y = −18 ⇒ x − y = −2 …… eq.(1)
(x × y) = 8 …… (given)

(x + y)² − (x − y)² = 4xy
⇒ (x + y)² − (−2)² = 4 × 8
⇒ (x + y)² = 36 ⇒ (x + y) = √36
⇒ (x + y) = 6 …… eq.(2)

From eq.(1) and eq.(2) we get,
x = 2, y = 4 ⇒ so number is 24.

46. Find the range of the first 7 prime numbers. [RRB JE 27/06/2019 (Evening)]

Correct Answer: (a) 15
Solution:

First seven prime numbers are 2, 3, 5, 7, 11, 13, 17.
Range ⇒ Larger number − smaller number
Range ⇒ 17 − 2 = 15.

47. How many perfect squares are there between 100 and 200? [RRB JE 27/06/2019 (Evening)]

Correct Answer: (b) 4
Solution:

Number of perfect squares between 100 and 200 are 4.
These are 121, 144, 169, 196.

48. If the sum of two numbers is 13 and the sum of their squares is 97, what is their product? [RRB JE 28/06/2019 (Evening)]

Correct Answer: (d) 36
Solution:

Let two numbers be x and y.
x + y = 13 and x² + y² = 97.

Using formula,
(x + y)² = x² + y² + 2xy ⇒ (13)² = 97 + 2xy
⇒ 169 = 97 + 2xy
⇒ 2xy = 169 − 97 ⇒ xy = 36.

49. The sum of three consecutive odd numbers is 20 more than the first of these numbers. Find the largest of these numbers. [RRB JE 28/06/2019 (Evening)]

Correct Answer: (b) 11
Solution:

Let three consecutive odd numbers be (x − 2), x, (x + 2)
According to given question,
(x + 2) + x + (x − 2) = 20 + (x − 2)
⇒ 2x = 18 ⇒ x = 9

So, the largest number be (x + 2)
⇒ 9 + 2 = 11

50. Find the number which is as much greater than 55 as it is smaller than 95. [RRB JE 28/06/2019 (Evening)]

Correct Answer: (b) 75
Solution:

According to question,
95 − x = 55 + x ⇒ 2x = 40 ⇒ x = 20
Required no. → 55 + x = 75