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In Cracku, 60% of the enrolled students read newspaper A, 50% of the enrolled students read newspaper B, 30% of the enrolled students read newspaper C, 40% of the enrolled students read newspaper D. While a particular student may read more than one newspaper, each student must read at least one newspaper. It is known that no one reads 2 or 3 newspapers, which of the following is a possible number of enrolled students in Cracku?
  • a)
    30030
  • b)
    15015
  • c)
    20020
  • d)
    More than one of the above
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In Cracku, 60% of the enrolled students read newspaper A, 50% of the e...
I + II + III + IV = 100%
I + 2 II + 3 III + 4 IV = 60 + 50 + 30 + 40 = 180%
Hence, the additional 80% should be distributed among II + 2 III + 3 IV.
It is mentioned that II = 0, III = 0
Hence, IV = 80/3%
Now, IV has to be natural number since it is the number of students.

Hence, n must be a multiple of 15.
But, we have not yet considered the people who only follow one newspaper.
People who only follow A = 
People who only follow B = 
People who only follow C =
People who only follow D = 
Hence, n must be divisible by 30 as well.
Hence, 30030 is the only possible alternative.
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Most Upvoted Answer
In Cracku, 60% of the enrolled students read newspaper A, 50% of the e...
Given information:
- 60% of the enrolled students read newspaper A.
- 50% of the enrolled students read newspaper B.
- 30% of the enrolled students read newspaper C.
- 40% of the enrolled students read newspaper D.
- No one reads 2 or 3 newspapers.
- Each student must read at least one newspaper.

To determine the possible number of enrolled students in Cracku, we can use the concept of sets and Venn diagrams.

Let's assume:
- Set A represents the students who read newspaper A.
- Set B represents the students who read newspaper B.
- Set C represents the students who read newspaper C.
- Set D represents the students who read newspaper D.
- Set E represents the students who read none of the newspapers.

Using the given information, we can draw the Venn diagram as follows:

```
A
___/ \___
__/ \__
/ \
| E |
\ /
\__ __/
\__ __/
\___/
B C
```

From the Venn diagram, we can make the following observations:

1. The total number of students enrolled in Cracku is given by:
100% - % of students who read none of the newspapers.

2. Since no one reads 2 or 3 newspapers, the following regions are empty:
- A ∩ B
- A ∩ C
- B ∩ C
- A ∩ B ∩ C

3. The remaining regions represent the students who read only one newspaper:
- A - (A ∩ B ∩ C)
- B - (A ∩ B ∩ C)
- C - (A ∩ B ∩ C)
- D - (A ∩ B ∩ C)

4. The students who read at least one newspaper can be represented as the union of all these regions:
- Students who read at least one newspaper = (A - (A ∩ B ∩ C)) ∪ (B - (A ∩ B ∩ C)) ∪ (C - (A ∩ B ∩ C)) ∪ (D - (A ∩ B ∩ C))

To find the possible number of enrolled students in Cracku, we need to find a common multiple of the percentages 60%, 50%, 30%, and 40%.

The least common multiple (LCM) of 60, 50, 30, and 40 is 300. This means that there are 300 students in total.

Therefore, the possible number of enrolled students in Cracku is 30030 (LCM of 300 and 100).

Hence, the correct answer is option A) 30030.
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In Cracku, 60% of the enrolled students read newspaper A, 50% of the enrolled students read newspaper B, 30% of the enrolled students read newspaper C, 40% of the enrolled students read newspaper D. While a particular student may read more than one newspaper, each student must read at least one newspaper. It is known that no one reads 2 or 3 newspapers, which of the following is a possible number of enrolled students in Cracku?a)30030b)15015c)20020d)More than one of the aboveCorrect answer is option 'A'. Can you explain this answer?
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