Question:medium

A student needs to enroll for a minimum of 60 credits. A student cannot enroll for more than 70 credits. The credits are divided amongst project and three distinct sets of courses namely, core courses, specialization courses, and elective courses. It is compulsory for a student to enroll for exactly 15 credits of core courses and exactly 20 credits of project. In addition, a student has to enroll for a minimum of 10 credits of specialization courses. The maximum credits of elective courses that a student can enroll for is ______

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Maximize total credits and minimize specialization credits to leave the most room for electives.
Updated On: Jul 22, 2026
  • 10
  • 15
  • 20
  • 25
Show Solution

The Correct Option is D

Solution and Explanation

We want the maximum of E subject to the total-credit ceiling $15 + 20 + S + E \le 70$ and the specialization floor $S \ge 10$. Rearranging the ceiling condition gives $E \le 70 - 15 - 20 - S = 35 - S$. Since S can be pushed down to its floor value of 10 without violating any rule, the loosest (largest) bound on E occurs at $S=10$, giving $E \le 35 - 10 = 25$. So E cannot exceed 25 under any valid allocation. To confirm 25 is actually attainable, plug the numbers back: Core $15$ + Project $20$ + Specialization $10$ + Elective $25$ = $70$, which is within the allowed range $60 \le T \le 70$, and $S=10$ meets its own minimum. Since the bound is both derived and achieved, the maximum elective credit a student can enroll for is $E_{max}=25$. $\boxed{25}$
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