As promised, after Ketaki and Roshni solved the "Magic Square", a ghost was assigned to guide them in the quest to get into their dream B-schools. They waited with bated breath to see who their new mentor would be. They found it strangely exciting, waiting to be tutored by a ghost. While they were arranging their paraphernalia which was just strewn about the place, as usual, the lights went off. They expected something strange to happen, but for around 10 minutes nothing happened. Then, suddenly, random coloured lights started flashing intermittently. A very catchy and oddly familiar tune started playing. The sound of sticks clicking could be heard and in came Jayshri - The Ghost of CAT Present - dancing to the tune, dandiyas in hand. She introduced herself to the girls and told them she had just come back from dancing with her friends while celebrating Navratri.
"I'm very impressed that you girls are continuing your CAT prep despite this very distracting time period. However, I only help those who are worthy of my help. I have two numbers greater than 1 in my mind. Ketaki, come here. The product of the two numbers is..." And she whispered the product into her ear. "Roshni, the sum of the numbers is..." And she whispered the sum into her ear. "Both of you need to tell me what the numbers are without disclosing the sum and product to each other. If you'll tell each other more than what's required, I shall make sure your computers hang when you'll submit your answers for CBT CAT 2009. Hahahaha!! Just kidding! I shall be back soon. Till then, Happy Dusshera!!!"
After she left, the girls had the following conversation:
Ketaki: I have no idea what the sum is.
Roshni: I figured that out. When we add the two numbers, we arrive at a number less than 14.
Ketaki: I kinda knew that. But, now, I also know the numbers.
Roshni: Ha ha ha! Even I know the numbers now.
You need to deduce the two numbers. Provide a detailed explanation along with your answer.