In an engineering college of $10,000$ students, $1,500$ like neither their core branches nor other branches. The number of students who like their core branches is $1 / 4^{\text {th }}$ of the number of students who like other branches. The number of students who like both their core and other branches is $500$.
The number of students who like their core branches is
- $1,800$
- $3,500$
- $1,600$
- $1,500$
