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There were 60 questions to be answered in a mathematical competition. The average number of questions answered correctly by all the participants was 44. The average number of questions answered correctly by the top 75% of the participants was 48. What was the average number of questions that were answered incorrectly by the bottom 25% of the participants?

Apr 20, 2021

#1
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75/100 = 3/4

44 * 4 = 176

176 - 3 * 48 = 32

32 was the average number

Apr 20, 2021
#2
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Let  there  be  100  contestants  and let  each  question  be  worth  1 point  for a correct answer

The total points possible of correct answers =  100  * 44  = 4400

Let  x  be  the average  number of questions  that  were  answered correctly by the bottom  25%

So   we  have

75 peolple with 48 correct answers each + 25 people with x correct answers each =  4400

75( 48)   +   25 (x)    =   4400

3600  +  25x  =  4400

25x =  4400 - 3600

25x = 800

x = 32   =  the  avg no.  of  questions answered correctly  by the  bottom 25%

So     60  -  32   =   28  = avg no. of  questions answerd incorrectly by the bottom 25%   Apr 20, 2021