Directions for Questions 1 to 4: Read the following passage and answer the questions that follow.
In a family of five persons A, B, C, D and E, each and everyone loves one another very much. Their birthdays are in different months and on different dates. A remembers that his birthday is between 25th and 30th, of B it is between 20th and 25th, of C it is between 10th and 20th, of D it is between 5th and 10th and of E it is between 1st to 5th of the month. The sum of the date of birth is defined as the addition of the date and the month, for example 12th January will be written as 12/1 and will add to a sum of the date of 13. (Between 25th and 30th includes both 25 and 30).
1. What may be the maximum average of their sum of the dates of birth?
(a) 24.6
(b) 15.2
(c) 28
(d) 32
2. What may be the minimum average of their sum of the dates of births?
(a) 24.6
(b) 15.2
(c) 28
(d) 32
3. If it is known that the dates of birth of three of them are even numbers then find maximum average of their sum of the dates of birth.
(a) 24.6
(b) 15.2
(c) 27.6
(d) 28
4. If the date of birth of four of them are prime numbers, then find the maximum average of the sum of their dates of birth.
(a) 27.2
(b) 26.4
(c) 28
(d) None of these
5. The average age of a group of persons going for a picnic is 16.75 years. 20 new persons with an average age of 13.25 years join the group on the spot due to which the average of the group becomes 15 years. Find the number of persons initially going for the picnic.
(a) 24
(b) 20
(c) 15
(d) 18
6. A school has only four classes that contain 10, 20, 30 and 40 students respectively. The pass percentage of these classes are 20%, 30%, 60% and 100% respectively. Find the pass % of the entire school.
(a) 56%
(b) 76%
(c) 34%
(d) 66%
Answers:-
1. (c)
2. (b)
3. (d)
4. (a)
5. (b)
6. (d)
Solutions:-
1. The maximum average will occur when the maximum possible values are used. Thus: A should have been born on 30th, B on 25th, C on 20th, D on 10th and E on 5th. Further, the months of births in random order will have to be between August to December to maximize the average. Hence the total will be 30 + 25 + 20 + 10 + 5 + 12 + 11 + 10 + 9 + 8 = 140. Hence average is 28.
2. The minimum average will be when we have 1 + 5 + 10 + 20 + 25 + 1 + 2 + 3 + 4 + 5 = 76. Hence, average is 15.2.
3. This does not change anything. Hence the answer is the same as Q. 27.
4. The prime dates must be 29th, 23rd, 19th and 5th. Hence, the maximum possible average will reduce by 4/5 = 0.8. Hence, answer will be 27.2.
5. Solve using alligation. Since 15 is the mid-point of 13.25 and 16.75, the ratio is 1:1 and hence there are 20 people who were going for the picnic initially.
6. The number of pass candidates are 2 + 6 + 18 + 40 = 66 out of a total of 100. Hence, 66%.
