A man had an accident and was admitted into the hospital. When questioned by the police about the vehicle, he replied it is a Yamaha bike. It is red in color and the rider was wearing a black shirt. The police inspector said, that is all right, but tell me anything about the registration number. "For this the replied I do not remember the number but there is a peculiarity of the number. It has only two factors excluding 1 and itself. In addition, it is a four digit number with the first two digits forming a perfect square. Also, the next two digits form a number which is one more than a perfect square". Which of the following could be the number?

A) 3681

B) 1665

C) 2565

D) 2582


A 2 - digit number is such that the sum of its digits is 5 times the difference of the digits. If the number is neither a prime nor a perfect square, then how many such 2-digit numbers are possible?

A) 2

B) 3

C) 4

D) 6