Mean or average based question ?

A group of 210 students appeared in a test. 

The mean of 1/3 of the students is found to be 60. 

The mean of the remaining students is found to be 78. 

The mean of the whole group will be?

Total students = 210

1/3 of 210 = 70 students

Mean marks of 70 students = 60

Let the sum of marks of 70 students be x

Mean = x/Number of students

60 = x/70

x = 70*60

⇒ Sum of marks of 70 students = 4200

Remaining students = 210 - 70 = 140 students

Mean of 140 students = 78

Sum of marks of 78 students = 140*78 = 10920

Total marks of 210 students = 4200 + 10920

= 15120

Mean of the whole group = 15120/210

= 72 marks

Answer.

That doesn't make sense. If the mean score of the 210 students is 60, then are are no "remaining students".