Average

[Kritagya93]

The average score on the surprise quiz was 7 out of 10. Three students earned a 0, two earned only 1, one earned a 2 and rest of the students scored an integer. No student earned a perfect score. What is the least number of students there could have been in the class ?

(A) 5
(B) 11
(C) 23
(D) 25
(E) 100

Please kindly mention the solution with explanation too. Thanks

[SisyphusDilemma]

D. 25

let x be the number of students and t (2<t<10) be the score of the other students, then 0*3+2*1+1*2+(x-6)t=7x or
4+(x-6)t=7x or x=(4-6t)/(7-t). Since x>0 one must have t>7 or t<2/3 hence t=8,9. Now if t=8, x=44 and if t=9, x=25.
So the least x=25.