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Quiz Average and Grades

XAT 2014 · Quantitative Ability & Data Interpretation · Medium · Averages

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Prof. Suman takes a number of quizzes for a course. All the quizzes are out of 100. A student can get an A grade in the course if the average of her scores is more than or equal to 90. Grade B is awarded to a student if the average of her scores is between 87 and 89 (both included). If the average is below 87, the student gets a C grade. Ramesh is preparing for the last quiz and he realizes that he will score a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will just manage a B. How many quizzes did Prof. Suman take?

  1. A.

    6

  2. B.

    7

  3. C.

    8

  4. D.

    9

  5. E.

    None of these

Answer

D

Explanation

Let nn be the total number of quizzes. Difference in Ramesh's last quiz score =97−70=27= 97 - 70 = 27. This difference changes his final average from the minimum for A grade (9090) to the minimum for B grade (8787), i.e., a change in overall average of 90−87=390 - 87 = 3. Thus, 3×n=27  ⟹  n=93 \times n = 27 \implies n = 9.

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