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The 400 students at Watermelon Sugar High School can choose up to 3 electives from the following classes: an art class, a business class, and a computer class. Half of the students chose the art class, half of the students chose the business class, and half of the students chose the computer class.
If 96 of the students have signed up for all three electives, select from the available options the least possible and greatest possible number of students who could have signed up for exactly two of the three electives. Make only two selections, one in each column.
  • a)
    Least: 8
    Greatest: 156
  • b)
    Least: 10
    Greatest: 200
  • c)
    Least: 12
    Greatest: 205
  • d)
    Least: 15
    Greatest: 250
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The 400 students at Watermelon Sugar High School can choose up to 3 el...
Total = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(A and C) - 2*P(A and B and C)
400 = 200 + 200 + 200 - P(A and B) - P(B and C) - P(A and C) - 2 * 96
P(A and B) + P(B and C) + P(A and C) = 8
This is the minimum value required to satisfy the given numbers.
To maximize, all singular selections set should be 0,
P(A) = P(singular A) + P(A and B) + P(A and C) + P(A and B and C)
200 = 0 + P(A and B) + P(A and C) + 96
P(A and B) + P(A and C) = 104 --- (1)
similarly,
P(B and C) + P(A and C) = 104 --- (2)
P(A and B) + P(B and C) = 104 --- (3)
From (1), (2) and (3), summing up,
2(P(A and B) + P(A and C) + P(B and C)) = 312
P(A and B) + P(A and C) + P(B and C) = 156
Hence, least value is 8 and greatest value is 156.
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The 400 students at Watermelon Sugar High School can choose up to 3 electives from the following classes: an art class, a business class, and a computer class. Half of the students chose the art class, half of the students chose the business class, and half of the students chose the computer class.If 96 of the students have signed up for all three electives, select from the available options the least possible and greatest possible number of students who could have signed up for exactly two of the three electives. Make only two selections, one in each column.a)Least: 8Greatest: 156b)Least:10Greatest: 200c)Least:12Greatest: 205d)Least:15Greatest: 250Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The 400 students at Watermelon Sugar High School can choose up to 3 electives from the following classes: an art class, a business class, and a computer class. Half of the students chose the art class, half of the students chose the business class, and half of the students chose the computer class.If 96 of the students have signed up for all three electives, select from the available options the least possible and greatest possible number of students who could have signed up for exactly two of the three electives. Make only two selections, one in each column.a)Least: 8Greatest: 156b)Least:10Greatest: 200c)Least:12Greatest: 205d)Least:15Greatest: 250Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 400 students at Watermelon Sugar High School can choose up to 3 electives from the following classes: an art class, a business class, and a computer class. Half of the students chose the art class, half of the students chose the business class, and half of the students chose the computer class.If 96 of the students have signed up for all three electives, select from the available options the least possible and greatest possible number of students who could have signed up for exactly two of the three electives. Make only two selections, one in each column.a)Least: 8Greatest: 156b)Least:10Greatest: 200c)Least:12Greatest: 205d)Least:15Greatest: 250Correct answer is option 'A'. Can you explain this answer?.
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