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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Fix core and project at their exact values, push specialization to its minimum of 10, then use the leftover credits for elective.
Step 1: Fix the two exact numbers first.
Core courses always use exactly 15 credits, and project always uses exactly 20 credits. Together these two fixed parts use $15+20=35$ credits no matter what.
Step 2: See what is left for the flexible parts.
The overall cap on total credits is 70. So whatever is left for specialization plus elective together cannot cross $70-35=35$.
Step 3: Remember specialization has its own floor.
The question sets a rule that specialization credits cannot go below 10. This 10 is credits that elective can never grab, because specialization must keep at least that much for itself.
Step 4: Give the rest fully to elective.
Out of the 35 credits shared between specialization and elective, at least 10 must sit with specialization. That leaves at most $35-10=25$ for elective.
Step 5: Verify with real numbers.
Take core 15, project 20, specialization 10, elective 25. Adding all four gives $15+20+10+25=70$, right at the allowed ceiling and respecting every stated minimum. So 25 is genuinely achievable, not just a theoretical bound.
Step 6: Why smaller answers are wrong.
Picking 10, 15, or 20 for elective would mean specialization is holding more than its required minimum of 10 credits without any rule forcing it to. That does not break any constraint, but it fails to reach the true maximum, since specialization can safely be trimmed down to exactly 10 to free up more room for elective.
