In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is
Explanation:
Let the number of students in section B is x and that in A is (x – 10). ⇒ (x-10)×32+x×602x-10 = integer
⇒ 92x-3202x-10 = integer
⇒ 46x-160x-5 = integer
⇒ 46(x-5)+70x-5 = integer
⇒ (x - 5) + 70x-5 = integer
⇒ 70x-5 should be an integer
∴ (x – 5) should be a factor of 70 while x > 10
⇒ Highest possible value of x = 75 while lowest possible value is 12
∴ Difference between highest and lowest values of x = 75 – 12 = 63.
Hence, 63.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.