There are at least three times as many boys as girls in a class.
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Updated on: 11 Feb 2023, 13:24
Let the average score of boys, B=78 and let the average score of girls, G=94
It is given that there are least three times as many boys as girls in a class. Since the average score of boys is lower than that of girls, the maximum class average will occur when the number of boys is the least possible.
If we assume there is only one girl in the class, then the least number of boys in the class will be 3.
Class average = (No. of boys x Average score of boys + No. of girls x Average score of girls)/(No. of boys + No. of girls)
Therefore, class average = (3 x 78 + 1 x 94)/(3 + 1) = (234 + 94)/4 = 328/4 = 82
84 cannot be an answer, so choices A and E are wrong.
Now, we need to check whether 80 can be the average score of the class for positive integer values of the number of boys and girls.
Let m be the number of boys and n be the number of girls.
Assuming the average is 80. Therefore, 80 = (m x 78 + n x 94)/(m + n)
Multiplying both sides by (m + n) we get, 80(m + n) = 78m + 94n, or 80m + 80n = 78m + 94n, or 2m=14n, or 1m=7n
For n=1,2,3,etc we get m=7,14,21,etc. As we have positive integer values for both m and n, the class average can take 80 as a value.
Both 82 and 80 are possible values. Therefore, choice D is correct
Originally posted by
g1006 on 09 Feb 2023, 11:13.
Last edited by
g1006 on 11 Feb 2023, 13:24, edited 1 time in total.