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# p is an integer between 10 and 99. Is p less than 80?

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p is an integer between 10 and 99. Is p less than 80?  [#permalink]

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26 May 2016, 11:11
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67% (01:54) correct 33% (01:53) wrong based on 186 sessions

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p is an integer between 10 and 99. Is p less than 80?

(1) The product of the two digits in p is a prime number.

(2) Each of the two digits has at most 2 factors.

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Re: p is an integer between 10 and 99. Is p less than 80?  [#permalink]

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26 May 2016, 11:31
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p is an integer between 10 and 99. Is p less than 80?

(1) The product of the two digits in p is a prime number.

(2) Each of the two digits has at most 2 factors.

Only from (1) : The product of the two digits in p is a prime number:
As per the definition of prime, it's only factors are 1 and itself, therefore if the number p's 2 digits are x and y, then x*y is a prime.Which implies, one of them is 1 and other could be 1 or another prime. so let's list the primes which has 1 in it.
{13, 17, 31, 71} exclude {41,61} since 4 and 6 are not primes as per given statement 1.
All the above are less than 80, So select A and D

Only from (2) : Each of the two digits has at most 2 factors :
As per this, the two digits can both be a single digit prime number and/or 1. which could be {11, 12, 13, 15, 17, 31, 71}.
All the above are less than 80, therefore select D.

Answer is therefore D, (D) each statement alone is sufficient
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Re: p is an integer between 10 and 99. Is p less than 80?  [#permalink]

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26 May 2016, 20:53
Bunuel wrote:
p is an integer between 10 and 99. Is p less than 80?

(1) The product of the two digits in p is a prime number.

(2) Each of the two digits has at most 2 factors.

Given: p is an integer between 10 and 99

Statement 1
The product of the two digits in p is a prime number. Prime number has 2 factors 1 and itself. So, one digit is 1 and other a prime.
p can at max be 71. Hence, p will always be less than 80.
Sufficient

Statement 2
Each of the two digits has at most 2 factors
This gives us following cases:
1. both digits are 1
2. one of the digits is 1 and other a prime
3. both the digits are prime.
so p can at max be 77. Hence, p will always be less than 80
Sufficient

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Re: p is an integer between 10 and 99. Is p less than 80?  [#permalink]

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26 May 2016, 21:05
For the number be to greater than 80, at least one of the digits should be greater than 8.

from statement 1, we can conclude that 8 and 9 cannot be one of the digits, as 8 and 9 are not primes themselves. A product of a composite and any number is a composite. Sufficient.

from Statement 2, we can conclude that 8 and 9 cannot be one of the digits. 8 and 9 both have more than 2 factors. 8's factors are 1, 2, 4, 8 and 9's factors are 1, 3, 9. Sufficient.

Each statement alone is sufficient, so, D.
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p is an integer between 10 and 99. Is p less than 80?  [#permalink]

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27 May 2016, 00:09
1
Statement 1
The product of the two digits in p is a prime number.
When is this possible. This is only possible when one of the digits is a prime number and other digit is 1. Now the greatest digit that is a Prime Number is 7.
71 is the greatest such number and it is less than 80. (Other such numbers are 12, 13, 15, 17, 21, 31, 51, and 71)

So everytime such number will be less than 80

So Statement 1 is sufficient

Statement 2

Each of the two digits has at most 2 factors. This essentially means that both of the digits are either prime numbers or 1.
Greatest number formed with above constraint (and given constraint that it is 2 digit number) is 77.
So such a number will always be less than 80

So Statement 2 is sufficient

Option D is correct choice
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Re: p is an integer between 10 and 99. Is p less than 80?  [#permalink]

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17 Aug 2017, 06:35
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Re: p is an integer between 10 and 99. Is p less than 80?   [#permalink] 17 Aug 2017, 06:35
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