# PE 4 - Puzzles | LR - Puzzles

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

The following table gives the number of students across six different classes of BVN Higher Secondary School in the years 2020 & 2021.

It was known that:

- Students who fail in a class in a year will study in the same class next year.
- New students are admitted only in class 1.
- No student leaves the school before passing out class 6.

**PE 4 - Puzzles | LR - Puzzles**

What is the minimum possible number of students who could have joined the school in 2020?

Answer: 48

**Explanation** :

To minimise the number of students who could have joined the school in 2021, we need to minimise the number of students that exit the school in 2021.

∴ We need to maximise the number of students failing in class 6.

If all 33 students in class 6 fail in 2020, these 33 students will remain in class 6 in 2021.

Hence, out of 48 students enrolled in class 6 in 2021, 33 of them were those who failed previous year and hence remained in class 6.

It means (48 - 33 =) 15 students of class 6 in 2021 were those who passed in class 5 in 2020.

Similarly, we can draw the following chart.

Hence, minimum number of students who could have joined the school in 2021 is 48.

Hence, 48.

Workspace:

**PE 4 - Puzzles | LR - Puzzles**

What is the maximum possible number of students who could have joined the school in 2020?

Answer: 77

**Explanation** :

To maximise the number of students who could have joined the school in 2021, we need to maximise the number of students that exit the school in 2021.

∴ We need to minimise the number of students failing in class 6.

There are 48 students in class 6 in 2021. Out of these 48, maximum 44 could have passed in class 5 and moved to class 6. Hence, minimum 4 students need to fail in class 6.

Now, since all 44 students passed from class 5 to class 6, no student failed in class 5 in 2020.

Now in 2021 all 49 students in class 5 could have come from passing class 4.

Hence, out of 59 students in class 4 in 2020, at most 49 passed to next class and hence at least 10 failed and stayed in class 4.

Similarly, we can draw the following chart.

Hence, maximum number of students who could have joined the school in 2021 is 77.

Hence, 77.

Workspace:

**PE 4 - Puzzles | LR - Puzzles**

In 2020, which of the following was not a possible pass percentage of Class 3?

- A.
27.54%

- B.
33.33%

- C.
69.57%

- D.
None of these

Answer: Option D

**Explanation** :

Consider the solution to first 2 questions of this set.

Minimum students that could have passed class 3 in 2020 = 19

∴ Minimum pass percentage = 19/69 × 100% = 27.54%

Maximum students that could have passed class 3 in 2020 = 48

∴ Maximum pass percentage = 48/69 × 100% = 69.57%

∴ Pass percentage for class 3 can be between 27.54% and 69.57%.

Hence, option (d).

Workspace:

**PE 4 - Puzzles | LR - Puzzles**

In 2020, if the pass percentage in Class 2 was 50%, then what was the pass percentage in Class 5?

- A.
78.39%

- B.
85%

- C.
86.36%

- D.
44.44%

Answer: Option C

**Explanation** :

Since 50% students passed in class 2, hence out of 64 students in class 3 next year 37 came from class 2.

It means (64 - 37 =) 27 students must have failed and remaind in class 3.

Since 27 students failed in class 3, hence (69 - 27 =) 42 students passed from class 3 to class 4.

Out of 58 students in class 4 in 2021, 42 came from class 3, hence (58 - 42 =) 16 failed in class 4 in 2020.

Since 16 students failed in class 4 in 2020, hence (59 - 16 =) 43 students passed from class 4 to class 5.

Out of 49 students in class 5 in 2021, 43 came from class 4, hence (49 - 43 =) 6 failed in class 5 in 2020.

Since 6 students failed in class 5 in 2020, hence (44 - 6 =) 38 students passed from class 4 to class 5.

Similarly, we can draw the following chart.

∴ pass % for class 5 = 38/44 × 100% = 86.36%.

Hence, option (c)..

Workspace:

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