Arithmetic (UPSC) Part- III

Total Questions: 50

41. 19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform? [2018-II]

Correct Answer: (c) 6
Solution:

Using Venn diagram the given information can be represented as follows:
Let the number of players wearing both hockey shirt and pant be x

42. If X is between –3 and –1, and Y is between –1 and 1, then X² – Y² is in between which of the following? [2018-II]

Correct Answer: (d) 0 & 9
Solution:

43. X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number? [2018-II]

Correct Answer: (a) XY
Solution:

Let , then
(a) 4/8
(b) 3/4
(c) 4/3
(d) 7/24

Hence X.Y is largest number

44. Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is [2019-II]

Correct Answer: (d) 30 units
Solution:Let first Piece, second Piece and third Piece are x, y and z respectively.

45. An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible? [2019-II]

Correct Answer: (c) 4
Solution:

A number is divisible by '3' if sum of its digits be divisible by 3.
Here, Given number is 4252746 B
Sum of its digits = 4 + 2 + 5 + 2 + 7 + 4 + 6 + B
= 30 + B

For, B = 0,3,6,9
Sum of digits will be divisible by '3'.
Hence, number of values of B = 4.

46. A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time? [2019-II]

Correct Answer: (a) 5:36 p.m.
Solution:

In each hour clock moves fast by = 10/24 minutes

Number of hours between 8:00 am on Monday and 6:00 pm on Wednesday = 58 hours.
So, clock will move fast in 58 hours

=58×10/24=24.16 minutes

So, current time

=6 hr−24.16 minutes ≈ 5:36 pm

47. In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is [2019-II]

Correct Answer: (b) 9
Solution:

Number of people who read either or both languages:

= 15 − 3 = 12.

∴a + b + c = 12

Number of people who read French:

a + b = 7

Number of people who read English:

b + c = 8

∴ a = 4 and c = 5

Hence, number of people who can read exactly one language

=a + c = 9

48. A family has two children along with their parents. The average of the weights of the children and their mother is 50 kg. The average of the weights of the children and their father is 52 kg. If the weight of the father is 60 kg, then what is the weight of the mother? [2019-II]

Correct Answer: (d) 54 kg
Solution:Let the sum of the weight of two children is x kg, and weight of mother and father are y and z kg respectively.

ATQ,

49. Number 136 is added to 5B7 and the sum obtained is 7A3, where A and B are integers. It is given that 7A3 is exactly divisible by 3. The only possible value of B is [2019-II]

Correct Answer: (d) 8
Solution:

‘7A3’ is divisible by 3 only when sum of its digits is divisible by 3.

7 + A + 3 = 10 + A

For A = 2, 5, and 8 → (10 + A) would be divisible by 3.
ATQ,

50. The number of times the digit 5 will appear while writing the integers from 1 to 1000 is [2019-II]

Correct Answer: (c) 300
Solution:

Number of times ‘5’ appears from 1 to 100 = 20
Number of times ‘5’ appears from 101 to 200 = 20
Similarly, number of times ‘5’ appears from 201 to 499 = 60
Number of times ‘5’ appears from 600 to 1000 = 80
Number of times ‘5’ appears from 500 to 599 = 120

Total number of times ‘5’ appears from 1 to 1000
= 20 + 20 + 60 + 80 + 120 = 300