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Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is
  • a)
    20
  • b)
    22
  • c)
    21
  • d)
    24
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Five students, including Amit, appear for an examination in which poss...
To find the difference between the highest and lowest possible marks of Amit, let's consider the given conditions step by step:

Step 1: Amit got the least marks among the five students.
This means that the minimum marks Amit can get is 0.

Step 2: The average marks for all the students is 38.
The sum of the marks obtained by all the students is 38 * 5 = 190.

Step 3: Exactly three students got more than 32.
Since Amit got the least marks, he cannot be one of the three students who got more than 32. Therefore, Amit's marks should be less than or equal to 32.

Step 4: No two students got the same marks.
Since Amit got the least marks, the other four students must have distinct marks. Let's assume the marks of the other four students are a, b, c, and d in ascending order.

So, the sum of the marks obtained by the remaining four students is a + b + c + d.

Step 5: The sum of the marks obtained by all the students is 190.
From Step 4, we know that the sum of the marks obtained by the remaining four students is a + b + c + d. Adding Amit's marks, we get:
a + b + c + d + Amit's marks = 190

Step 6: Exactly three students got more than 32.
Since Amit's marks should be less than or equal to 32, the sum of the marks obtained by the remaining three students (a, b, and c) should be greater than 32.

Step 7: The maximum marks that the remaining three students can get is 50 + 49 + 48 = 147.
So, a + b + c ≤ 147.

Step 8: The minimum marks that the remaining three students can get is 33 + 34 + 35 = 102.
So, a + b + c ≥ 102.

Now, let's calculate the possible range of Amit's marks:

- From Step 2, we know that the sum of the marks obtained by all the students is 190.
- From Step 5, we have the equation: a + b + c + d + Amit's marks = 190.
- From Step 7, we have the inequality: a + b + c ≤ 147.
- From Step 8, we have the inequality: a + b + c ≥ 102.

By substituting the values of a, b, c, and d in the equation and inequalities, we can calculate the possible range of Amit's marks.

The difference between the highest and lowest possible marks of Amit is 32 - 0 = 32.

Therefore, the correct answer is option 'A' - 32.
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Community Answer
Five students, including Amit, appear for an examination in which poss...
The average marks for all the students is 38.
Sum = 5*38 = 190
To find the minimum marks scored by Amit, we need to maximise the score of remaining students.
Maximum scores sum of remaining students = 50 + 49 + 48 + 32 = 179
Minimum possible score of Amit = 190 - 179 = 11
It is given, Amit scored least. This implies maximum possible score of Amit is 31.
Difference = 31 - 11 = 20
Hence Option A is correct.
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Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit isa)20b)22c)21d)24Correct answer is option 'A'. Can you explain this answer?
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Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit isa)20b)22c)21d)24Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit isa)20b)22c)21d)24Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit isa)20b)22c)21d)24Correct answer is option 'A'. Can you explain this answer?.
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