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Is the two-digit positive integer P a prime number?

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Is the two-digit positive integer P a prime number?  [#permalink]

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New post 01 Feb 2020, 18:54
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Is the two-digit positive integer P a prime number?

(1) P has a factor f such that 1<f<P.
(2) Neither P− 2 nor P + 2 is prime.

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Re: Is the two-digit positive integer P a prime number?  [#permalink]

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New post 01 Feb 2020, 18:55

Official Solution:



Statement 1 P has a factor f such that 1<f<P.
A prime number can not have any factor except 1 or P itself.
Hence by definition of a prime number, P is not a prime number
SUFFICIENT

Statement 2: Neither P− 2 nor P + 2 is prime.
This is not sufficient
37 (35, 39 are not prime): prime
24 (22, 26 are not prime): not prime

hence NOT SUFFICIENT

Answer A
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Re: Is the two-digit positive integer P a prime number?  [#permalink]

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New post 01 Feb 2020, 19:37
1
1) All prime numbers have two factors: 1 and the number itself. However, this statement indicates that P has another factor f (1<f<P); therefore, P cannot be prime.
Clearly, this statement is sufficient.
2) All prime numbers above 3 are of the form 6n-1 or 6n+1. If P=6n-1, then P-2=6n-3=3(2n-1), which is divisible by 3 and; therefore, is not a prime number. Likewise, if P=6n+1, then P+2=6n+3=3(2n+1), which is divisible by 3 and; therefore, is not a prime number.
It follows from the analysis that P cannot be a prime number.
Clearly, this statement is sufficient.
Answer:D
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Re: Is the two-digit positive integer P a prime number?  [#permalink]

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New post 01 Feb 2020, 19:46
Is the two-digit positive integer P a prime number?

(1) P has a factor f such that 1<f<P.
(2) Neither P− 2 nor P + 2 is prime.

(1)P has a factor f such that 1<f<P.
Only factors of a prime number is 1 and itself. If a factor between 1 and the number itself, then the number is not a prime number.

Option A alone is sufficient. Eliminate B,C and E.

(2)Neither P− 2 nor P + 2 is prime.

We do not need to do any calculations for this option as there are many examples that comes to mind to prove P is not a prime.
For P-2, we can state 5 as example. 5 is a prime and 5-2=3 is also prime number.
For P+2, we can state same 5 as example as 5 is prime and 5+2 = 7 is also prime number.
So P is not a prime number.

Option B alone is sufficient. Eliminate A,C and E.

Ans: D
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Re: Is the two-digit positive integer P a prime number?  [#permalink]

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New post 01 Feb 2020, 20:43
Qs : Is the two-digit positive integer P a prime number?
Given : two digit integer and positive.

(1) P has a factor f such that 1<f<P.

the statement say that there will be always a factor for a number that will be less than that number and greater than 1. so that number will contain at-least 3 factors. if more than two factors are possible then the number is not prime. Hence sufficient to answer the question.
Example :
p=10, then factor= 1, 2, 5,10 so f= 2, 5 but 10 is not prime.
p=17, then factor = 1, 17 so no f is possible.

(2) Neither P− 2 nor P + 2 is prime.
consider the cases, if P= 23, then p-2= 21, p+2= 25 both are not prime. however P is prime.
if P= 28, then p-2= 26, p+2= 30 both are not prime. however P is not prime.
so no unique answer is possible. the condition is not sufficient.

Answer is A.

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Re: Is the two-digit positive integer P a prime number?  [#permalink]

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New post 01 Feb 2020, 21:51
Statement 1: P has a factor f which is >1 & <P, so it implies that P is not a prime number since a prime number can have only 2 factor, 1 and the number itself.
So Sufficient.

Statement 2: P-2 and P+2 are not primes.

Let P = 13,
11 is prime, whereas 15 not prime,

Let P = 83,
81 is not Prime, 85 is also not prime, so we cannot say anything for sure about P being a prime number. Statement is Insufficient.


Answer is A.
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Re: Is the two-digit positive integer P a prime number?  [#permalink]

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New post 01 Feb 2020, 21:58
Is the two-digit positive integer P a prime number?

(1) P has a factor f such that 1<f<P.
(2) Neither P− 2 nor P + 2 is prime.

Given : P is a 2 digit Positive integer.

Question: P is prime? Y or N.

(1) P has a factor f such that 1<f<P.

If P has any factor other than 1 and P then it is not a Prime number. Hence the answer is No.

Sufficient.

(2) Neither P− 2 nor P + 2 is prime.

If P is 23 then 21 and 25 are not Prime. Y.
If P is 97 then 95 and 99 are not Prime. Y.
But If P is 11 then 9 is not a Prime but 13 is a Prime. So even though P is prime but the statement is not true.

Not Sufficient.

Answer A
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Re: Is the two-digit positive integer P a prime number?  [#permalink]

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New post 02 Feb 2020, 01:31
Is the two-digit positive integer P a prime number?

(1) P has a factor f such that 1<f<P.
(2) Neither P− 2 nor P + 2 is prime

#1
no prime no can have any factor except no itself and 1 ; so f being a factor means p is not prime ; sufficient
#2
Neither P− 2 nor P + 2 is prime
test with P = 20 ; we get P is not prime and P = 23 ; yes is prime ; insufficient
IMO A
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Re: Is the two-digit positive integer P a prime number?   [#permalink] 02 Feb 2020, 01:31

Is the two-digit positive integer P a prime number?

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