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

Question

The product P of two prime numbers is between 9 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then P =

A. 15
B. 33
C. 34
D. 46
E. 51

AR15J · Answer

Suppose there are two prime numbers a and b then 9 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

AR15J · 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

SI777 · Answer

E

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

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

Abhishek009 · Answer

Prime numbers greater than 2 but less than 6 = { 3 , 5 }
Prime numbers greater than 13 but less than 25 = { 17 , 19 , 23 }

Product P of two prime numbers between 9 and 55 is 51 ( ie, 3*17 )
  
Hence, aswer will be (E)

ScottTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

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

MathRevolution · Answer

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

KarishmaB · Answer

Eliminate possibilities as you go along to reduce the calculations involved. We know here that there is only one value of P (the way the question is framed) but in a DS question, that may not be the case.

2 < PrimeNumber1 < 6

Hence, PrimeNumber1 = 3 or 5
Since product is between 9 and 55, the other prime number can at most be 11 if PrimeNumber1 = 5. 
But 13 < PrimeNumber2 < 25 and hence PrimeNumber2 cannot be 11. Hence PrimeNumber1 cannot be 5.

So PrimeNumber1 = 3

The first prime number greater than 13 is 17. 
Since 3*17 = 51 (less than 55 but just about) so PrimeNumber2 = 17.
No other case is possible

Answer (E)

ArtemNYC · Answer

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.

vasu1104 · Answer

say first prime number a, other is b
2<a<6
13<b<25

product 9<ab<55
since in the given range prime numbers are odd, the product would be odd too.
so C, D are easy to eliminate.
A cant be true because of the given range. also they share different range constraint. and only way when to prime num get 15 is through but 3 and 5 is not possible.
B is not possible as 11 is not in any given range.
so only left E. 51. (17*3)

vasu1104 · Answer

say first prime number a, other is b
2<a<6
13<b<25

product 9<ab<55
since in the given range prime numbers are odd, the product would be odd too.
so C, D are easy to eliminate.
A cant be true because of the given range. also they share different range constraint. and only way when to prime num get 15 is through but 3 and 5 is not possible.
B is not possible as 11 is not in any given range.
so only left E. 51. (17*3)

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

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