Question

In a Math test taken by 35 students, the average score of 15 girls is 10 and that of 20 boys is also 10. Which of the following can be calculated based on the above data?
A. The highest score in the class.
B. The lowest score among the boys in the class.
C. The sum of the scores of the 35 students of the whole class.
D. All of the above.

Answer 1

Hint: We will first write down the data already provided to us and then evaluate whatever is possible from it and see which of the options we could evaluate.

Complete step-by-step answer:
We are given that the total number of students who gave the test were 35.
The average score of 15 girls is 10 and that of 20 boys is also 10.
The average is the sum of all the numbers obtained by each of the students divided by the number of students.
Therefore, the average score of 15 girls is 10.
We now know that the sum of all the numbers obtained by each of the 15 girls divided by 15 is equal to 10.
Let ${s_g}$ denote the sum of marks obtained by 15 girls.
So, $\dfrac{{{s_g}}}{{15}} = 10$
Taking the 15 from denominator of LHS to numerator in RHS, we will get:-
$ \Rightarrow {s_g} = 10 \times 15 = 150$
This means that the sum of all the numbers obtained by the 15 girls is 150. …….(1)
This data is none of the options.
Now coming to the next information provided to us that the average score of 20 boys is 10.
This means that the sum of all the numbers obtained by each of the 20 boys divided by 20 is equal to 10.
Let ${s_b}$ denote the sum of marks obtained by 20 boys.
So, $\dfrac{{{s_b}}}{{20}} = 10$
Taking the 20 from denominator of LHS to numerator in RHS, we will get:-
$ \Rightarrow {s_b} = 10 \times 20 = 200$
This means that the sum of all the numbers obtained by the 20 boys is 200. ………..(2)
This data is none of the options.
But if we club (1) and (2), we will have sum of boys’ marks and girls’ marks.

So, the correct answer is “Option C”.

Additional Information: A calculated "central" value of a set of numbers is known as mean in easier terms.


Note: The students might make the mistake of not trying to club the two information we deduced and thus reach none of the option, if available in the question.