Question

Ten students sit a test consisting of 20 questions. Two students get 8 questions correct and one student gets 9 questions correct. The remaining seven students all get at least 10 questions correct and the average number of questions answered correctly by these seven students is an integer. If the average number of questions answered correctly by all ten students is also an integer, then that integer is

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

Answer 1

14

Explanation:

That equation, with the given constraints, is easily solved using logical reasoning.10y is a multiple of 5, and 25 is a multiple of 5; that means 7x is a multiple of 5.And we know x is a number between 10 and 20. So x has to be 14