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

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

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26 Nov 2016, 02:11
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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

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Re: The product P of two prime numbers is between 9 and 55. If one of the  [#permalink]

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26 Nov 2016, 03:42
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
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The product P of two prime numbers is between 9 and 55. If one of the  [#permalink]

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26 Nov 2016, 03:53
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
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Re: The product P of two prime numbers is between 9 and 55. If one of the  [#permalink]

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26 Nov 2016, 07:55
E

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

only 17 * 3 = 51 will be with in the limit 9<p<55
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Re: The product P of two prime numbers is between 9 and 55. If one of the  [#permalink]

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26 Nov 2016, 10:07
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Bunuel wrote:
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

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)

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Re: The product P of two prime numbers is between 9 and 55. If one of the  [#permalink]

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27 Feb 2018, 09:34
Bunuel wrote:
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

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.

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Re: The product P of two prime numbers is between 9 and 55. If one of the   [#permalink] 27 Feb 2018, 09:34