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

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

Check for a=3, b=17: 17*3=51, 9<51<55
E is the answer

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

E

x = 3,5
y=17,19,23

only 17 * 3 = 51 will be with in the limit 9<p<55

The primes greater than 2 but less than 6 are 3 and 5.

The primes greater than 13 but less than 25 are 17, 19, and 23.

Thus, we see that P could only be 3 x 17 = 51. Increasing either factor in this product would result in a number that is greater than 55.

Answer: E

We have 2 < a < 6 The prime numbers are 3 and 5.

This Statement automatically eliminates options C (2 x 17) and D (2 x 23), as the product cannot be an even number without 2.


We also have 13 < b < 25.

With this Option A (3 x 5) is eliminated as both prime numbers cannot be less than 6 and Option B (3 x 11) gets eliminated as 11 cannot be a valid prime number.


Therefore Option E

Arun Kumar

Product P(two prime numbers): 9 < P < 55.

One of the prime numbers is greater than '2' but less than '6': 3 or 5

Other is greater than '13' but less than '25': 17, 19 or 23

=> P = Only 3 * 17 = 51 is in between '9' and '55'.

Answer E

I tried to find prime numbers in the results:
1. 15 = 3*5
2. 33 = 3*11
3. 34 = 2*17
4. 46 = 2*23
5. 51 = 3*17

While keeping the conditions in mind, I quickly eliminate options 3 and 4, and then realize that the large number only appears in the fifth answer choice (and it doesn't break down further) - that's the answer. It took 15 sec max.