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Xavier Aptitude Test 2014 Paper

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Question : 54 of 103

Marks: +1, -0

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 must 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?

6
7
8
9
None of these

Solution:

(d) Let the total number of quizzes = x

and score of previous quizzes = y

\therefore \frac{y+97}{x}=90, \frac{y+70}{x}=87

\Rightarrow \frac{y}{x}+\frac{97}{x}=90, \frac{y}{x}+\frac{70}{x}=87

\Rightarrow \frac{y}{x}=90-\frac{97}{x}

........(i)

\Rightarrow \frac{y}{x}=87-\frac{70}{x}

..........(ii)

From (i) and (ii)

\therefore 90-\frac{97}{x}=87-\frac{70}{x}

3=\frac{-70}{x}+\frac{97}{x}=\frac{27}{x}

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