# PE 6 - Selection & Distribution | LR - Selection & Distribution

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**Answer the next 4 questions based on the information given below.**

Roomesh, the quant faculty at Quantile, has twelse students – A through L – enrolled in his class. He wanted to form study groups of these students, in the following manner, based on the marks that they scored in an examination:

For each study group that he wants to form, he first identifies the monitor of the study group. Any student whose marks fall within a 10% range of the marks of the monitor can be in the study group of that monitor. The monitors of the study groups can be any of the twelve students. The size of a study group includes the monitor and all the members of the study group. Further, the size of each study group must be at least two and the size of all the study groups need not be the same. Each student must be a part of exactly one study group. The following table provides the marks scored by the twelve students in the examination:

**PE 6 - Selection & Distribution | LR - Selection & Distribution**

The students given in which of the following options can be the only students in a study group?

- (a)
A, B, D, F

- (b)
C, F, G, L

- (c)
C, I, J, L

- (d)
F, G, I, J

Answer: Option C

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**Explanation** :

Let us start with H (least marks). If H is the monitor any student whose marks are within 10% range i.e., from 55.8 to 68.2 can be in his group.

∴ If H is the monitor only B can be in his group.

Similarly, we can make the following table.

In each of the options only 4 students should be part of a study group, hence monitor must be from one of the four students in each of the options.

Option (a):

If A is monitor, B cannot be part of that study group.

If B is monitor, A cannot be part of that study group.

If D is monitor, B cannot be part of that study group.

If F is monitor, B cannot be part of that study group.

∴ only A, B, D and F cannot be part of a group.

Similarly, we can eliminate options (b) and (d) as well.

Option (c):

If I is monitor, all four i.e., C, I, J and L can be part of the group.

Hence, option (c).

Workspace:

**PE 6 - Selection & Distribution | LR - Selection & Distribution**

Who among the following will definitely be in the same group?

- (a)
A and C

- (b)
B and K

- (c)
D and I

- (d)
B and H

Answer: Option D

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**Explanation** :

Consider the solution to first question of this set.

Since, H has to be part of a study group and the only way H can be part of a study group is when it is definitely with B.

Hence, option (d).

Workspace:

**PE 6 - Selection & Distribution | LR - Selection & Distribution**

If all the study groups have the same number of students, what is the minimum number of study groups that must be formed?

Answer: 4

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**Explanation** :

Consider the solution to first question of this set.

To minimize number of study groups we need to maximise number of students in each group.

Since H has to be in one of the groups and the largest group it can be part of is a 3 student group (when B is the monitor).

∴ Maximum number of students in each group = 3

⇒ Minimum number of groups = 12/3 = 4 i.e.,

HBK, GAC, DFI and LJE.

Hence, 4.

Workspace:

**PE 6 - Selection & Distribution | LR - Selection & Distribution**

If A, F and K must be in the same group, who among the following cannot be a monitor?

- (a)
F

- (b)
A

- (c)
D

- (d)
K

Answer: Option D

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**Explanation** :

Consider the solution to first question of this set.

If A is the monitor, all three i.e., K, A and F can be in the same group.

If F is the monitor, all three cannot be in the same group.

Similarly, if K is the monitor, all three cannot be in the same group.

∴ F and K definitely cannot be the monitors.

Hence, option (d).

Note: F and D can be monitors of other study groups.

Workspace:

**Answer the next 4 questions based on the information given below.**

Six flights – A to F, operate between cities – New York, France, Sydney, Beijing, Singapore and Bhopal. All six flights take-off from different cities and land in different cities. No two flights operate between the same pair of cities. Flight duration of each flight is a distinct integer between 3 and 11 (excluding both).

The following information is known about the origins, destinations and the travel times of the six flights:

- Flight A's destination matches Flight D's origin, but neither originates from nor travels to France.
- Flight E's travel duration exceeds Flight C's by two hours and is more than six hours.
- One flight departs from New York bound for Bhopal, with a travel duration of six hours.
- F, the flight to Sydney has a travel duration under ten hours, whereas the flight originating in Sydney lasts five hours.
- Flight B, starting from Singapore, has a travel duration equating to the average of flights originating from Beijing and Bhopal.
- The flight to France departs from Sydney; Flight D does not originate in Bhopal.

**PE 6 - Selection & Distribution | LR - Selection & Distribution**

Which flight lands at Bhopal?

- (a)
D

- (b)
E

- (c)
F

- (d)
Either A or E

Answer: Option A

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**Explanation** :

Hence, option (a).

Workspace:

**PE 6 - Selection & Distribution | LR - Selection & Distribution**

If each of the six flights starts from its origin city twice each day, once at 6:00 AM and once at 1:00 PM, what is the minimum number of hours required for a person to travel from Bhopal to Singapore using these six flights?

Answer: 31

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**Explanation** :

**Case 1**: One can start from Bhopal at 6 am.

Day 1: 6 am from Bhopal → Sydney at 2 pm

Day 2: 6 am from Sydney → France at 11 am

Day 2: 1 pm from France → Singapore at 8 pm.

The person starts at 6 am on Day 1 and reaches destination at 8 pm on Day 2.

∴ Total travel duration = 38 hours.

**Case 2**: One can start from Bhopal at 1 pm.

Day 1: 1 pm from Bhopal → Sydney at 9 pm

Day 2: 6 am from Sydney → France at 11 am

Day 2: 1 pm from France → Singapore at 8 pm.

The person starts at 1 pm on Day 1 and reaches destination at 8 pm on Day 2.

∴ Total travel duration = 31 hours.

Hence, 31.

Workspace:

**PE 6 - Selection & Distribution | LR - Selection & Distribution**

What is the travel time for flight starting from Beijing?

Workspace:

**PE 6 - Selection & Distribution | LR - Selection & Distribution**

The flight originating from Bhopal lands in which city?

- (a)
Beijing

- (b)
Sydney

- (c)
New York

- (d)
Cannot be determined

Workspace:

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