CareerCup

Can make use of Observer Design Pattern.
Here is a simple implementation of the Publisher/Subscriber model for StockMarket. As and when interviewer pose with some more questions, we can add on to it.

Publisher Interface:

public interface Publisher {
  public void setStockValue(int value);
  public void registerObserver(Observer observer);
  public void unRegisterObserver(Observer observer);
  public void notifyAllObservers();
}

Subscriber(Observer) Interface:

public interface Observer {
   public void update(int newValue);
   public void display();
   public void unSubscribe();
}

StockMarket Class which implements the Publisher interface:

public class StockMarket : Publisher {
  Set<Observer> observers;
  int newValue;

  public StockMarket() {
	observers = new HashSet<Observer>();
	newValue = 0;
  }  
  
  public void setStockValue(int value){
    newValue = value;
  }
  
  public void registerObserver(Observer observer){
    observers.add(observer);
  }

  public void unRegisterObserver(Observer observer){
    if(observer != null && observer instanceof Observer){
	    observers.remove(observer);
	}
  }

  public void notifyAllObservers(){
	Iterator<Observer> observerIterator = observers.iterator();
	while(observerIterator.hasNext()){
		Observer observer = observerIterator.next();
		observer.update(this, null);
	}
  }
}

As a sample i will implement the PayPalStock which implements the Observer Interface. This inturn maintains a reference to the Publisher.

public class PayPalStock : Observer {
   Publisher stockMarket;
   int latestValue;

   public PayPalStock (Publisher subject){
   	latestValue = 0;
    stockMarket = subject;
    stockMarket.registerObserver(this); // Self-Registering to the Publisher
   }

   public void update(int newValue){
    latestValue = newValue;
    display();
   }

   public void display(){
     System.out.println("Latest Stock Price = " + latestValue);
   }

   public void unSubscribe(){
     stockMarket.unRegisterObserver(this);
   }
}

A more detailed design can be looked up at: http://read.pudn.com/downloads152/doc/663610/Software%20Design.pdf

A market is a place where buy and sell happens real-time or in a batch. depending on the service... The code above won't cut....

Stock Market System is about a "Market" - i.e. Buying and Selling.
Your solution should talk about how you will satisfy the order, will that be atomically satisfied or not, How will you avoid starvation of orders, What happens to huge orders?, Strategy for that... All that would matter in a potential solution.