Question

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 ______

• A. 10
• B. 15
• C. 20
• D. 25

Hint:

Fix core and project at their exact values, push specialization to its minimum of 10, then use the leftover credits for elective.

Answer 1

The Correct Option is D

Step 1: List all the given constraints.
Total credits must be at least 60 and at most 70. Core courses take exactly 15 credits. Project takes exactly 20 credits. Specialization courses need a minimum of 10 credits. Elective courses can vary, and we need their maximum possible value.

Step 2: Write the total credits equation.
\[ \text{Total} = \text{Core} + \text{Project} + \text{Specialization} + \text{Elective} \]
\[ \text{Total} = 15 + 20 + \text{Specialization} + \text{Elective} = 35 + \text{Specialization} + \text{Elective} \]

Step 3: Apply the upper bound on total credits.
Since the total cannot go above 70,
\[ 35 + \text{Specialization} + \text{Elective} \leq 70 \]
\[ \text{Specialization} + \text{Elective} \leq 35 \]

Step 4: Push specialization to its lowest allowed value.
To make elective as large as possible, specialization should be as small as possible, since the two share the leftover 35 credits. The minimum allowed specialization is 10 credits, so
\[ \text{Elective} \leq 35 - 10 = 25 \]

Step 5: Confirm this value is reachable.
With core 15, project 20, specialization 10, and elective 25, the total becomes
\[ 15+20+10+25=70 \]
This exactly meets the maximum allowed total of 70 and does not break any minimum, so it is a valid enrollment plan.

Step 6: Check the other options.
10, 15 and 20 are all smaller than the true maximum. Each of these leaves specialization credits sitting higher than its required floor of 10, which is allowed but does not give the largest possible elective value. Only 25 pushes specialization down to its floor of 10 while keeping the total within the allowed cap.

Final Answer:
The maximum credits of elective courses a student can enroll for is 25. \[ \boxed{25} \]