In a class of 30 students, each student reads exactly one newspaper

Question

In a class of 30 students, each student reads exactly one newspaper, with no more than nine students reading the same newspaper. Furthermore, each newspaper is read by a different number of students.

Select for  Maximum  the highest possible number of newspapers that could have been read by the class, and select for  Minimum  the lowest possible number of newspapers that could have been read by the class. Make only two selections, one in each column.

Bunuel · Accepted Answer

Official Solution: To maximize the number of different newspapers read by the class, we need to minimize the number of students reading each newspaper. Let 1 student read one newspaper, 2 students read another, 3 students read a third newspaper, and so on. This gives the sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + ... . Adding these, we see that 7 newspapers would account for a total of 28 students. We cannot exceed 7 newspapers because doing so would require more than 30 students. However, we can adjust the total from 28 to 30 by increasing the last group, reading the seventh kind of newspaper, from 7 students to 9 students. Thus, the distribution becomes 1 + 2 + 3 + 4 + 5 + 6 + 9 = 30 . Therefore, the maximum number of newspapers that could have been read by the class is 7. To minimize the number of different newspapers read by the class, we need to maximize the number of students reading each newspaper. Since no more than nine students can read the same newspaper, the first group of 9 students could read one newspaper, the next group of 8 could read another, the third group of 7 could read a third newspaper, and the fourth group of 6 could read a fourth newspaper. Adding these groups gives us 9 + 8 + 7 + 6 = 30 . Therefore, the minimum number of newspapers that could have been read by the class is 4. Correct answer: Maximum "7" Minimum "4" GMAT-Club-Forum-cv5ju23h.png

Aavesh · Answer

Can someone please provide explanation for above question

Dare Devil · Answer

Criteria
1. All different numbers
2. Max 9 can read same newspaper

Max:
So each newspaper should be read by minimum numbers so that no. of newspapers count become more => 1,2,3,4,5,6,9 (why last nine is if taken 7, 2 remains (30-28) and 2 will be repeated
Total count 7

Min:
So each newspaper should be read by Maximum numbers so that no. of newspapers count become less
9,8,7,6

Whoisdmx15 · Answer

In a class of 30 students, each student reads exactly one newspaper, with no more than nine students reading the same newspaper. Furthermore, each newspaper is read by a different number of students.

Minimum:
For minimizing the number of Newspapers, we need to Maximize the number of students who read 01 newspapaer.
Hence start with maximum possible newspapers,

9,8,7,6 (As no. of students reading each newspaper is distinct)
Therefore  04 newspape rs can be read by 30 students.

Maximum:
for maximizing, start with minimum no of students reading each newspaper:
1,2,3,4,5,6,7 = 28
As we cannot have another paper being read by 2 students,
we can increase 6->7 and 7->8 or only increase 7->9 to make it 30.
Hence, 30 students can read  max 7 newspapers .

bumpbot · Answer

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In a class of 30 students, each student reads exactly one newspaper

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