The product P of two prime numbers is between 9 and 55. If one of the

If it would be a DS ques as given below, we had to check for other possible values as well.

Question :The product P of two prime numbers is between 9 and 55. What is the value of P.

1. If the first prime number is greater than 2 but less than 6.
2. If the second prime number is greater than 13 but less than 25.

Solution :

Suppose there are two prime numbers a and b then 9<ab<55.
1. 2< a<6 --> a can be 3 or 5

2. 13< b<25 --> b can be 17,19,23

It can be checked easily that either of the statements is not sufficient alone.
Taking them together

a) Check for a=3, b=17: 17*3=51, 9<51<55

b) Check for a=3, b=19: 19*3=57, 57>55, so we don't have to check for a=3, b=23 because of the condition does not hold true for b=19, it will certainly be not true for b=23 when a remains same

c) check for a=5, b=17; 17*5=85, 85>55, so we don't have to check for a=5, b=19 or a=5, b=23

In this case, C will be correct answer