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Is the positive integer x a prime number? (1) x is even (2) 2< x < 19

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Is the positive integer x a prime number? (1) x is even (2) 2< x < 19  [#permalink]

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10 Jun 2018, 03:54
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Difficulty:

25% (medium)

Question Stats:

83% (00:30) correct 17% (00:19) wrong based on 31 sessions

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Is the positive integer x a prime number?

(1) x is even
(2) 2< x < 19

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Is the positive integer x a prime number? (1) x is even (2) 2< x < 19  [#permalink]

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Updated on: 10 Jun 2018, 17:03
We can substitute numbers to quickly figure this answer out.

With statement (1), 2 is a prime number, 4 is not. So not sufficient.
With statement (2), 3 is a prime number, 4 is not. So not sufficient.

Combined, with have something interesting. 2 is the only prime even number, and since we cannot include it, then all other even numbers we can think of will not be prime numbers. Regardless of whether x = 4, 6, 8, 10, 12, 14, 16, or 18, they'd all not be prime numbers. Hence together, statements (1) and (2) are sufficient. I.e. answer is C.

Another way to approach this question is to think back to the rules of prime numbers. Statement (1) cannot be sufficient because it includes both 2 and other even numbers, and we know 2 is a prime number while the others are not. Statement (2) include odd numbers, including a bunch that are definitely prime numbers, but also even numbers that are not. Combined, statement (2) actually only serves to rule out the number 2 as a possible even number for x. You don't and shouldn't even care about the fact that x has to be less than 19. The only time it'd matter is if x has to be < 4 or something, but that's not the case here, and I doubt would ever be the case in these sort of questions.
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Not a professional entity or a quant/verbal expert or anything. So take my answers with a grain of salt.

Originally posted by Azedenkae on 10 Jun 2018, 06:19.
Last edited by Azedenkae on 10 Jun 2018, 17:03, edited 1 time in total.
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Re: Is the positive integer x a prime number? (1) x is even (2) 2< x < 19  [#permalink]

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10 Jun 2018, 06:51
Stmt :1 says X is even,X can be 2 or 4 , may be Prime (2) or not a prime (4) Not sufficient

Stmt:2 2< x < 19 ,greater than 2 , lot of possible integers from 3 to 18 which can be prime no(3,5,7,11,13,17) and also non prime no(4,6,8 and so on) Not sufficient.

Combining 1& 2

Stmt 1 says X is even and stmt say x greater than 2 and less than 19,hence the x is non prime number ,only even prime no is 2.
Hence C,
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Re: Is the positive integer x a prime number? (1) x is even (2) 2< x < 19  [#permalink]

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10 Jun 2018, 10:48
We are given that x is a positive integer.

We have to analyze if x is a prime number or not.

(1): "x is even" - All even numbers with the exception of 2 are non-prime. We cannot be sure if x is prime or not. INSUFFICIENT.

(2): "2<x<19" - x can be any integer 2 and 19. There are both primes and non-primes in that range. INSUFFICIENT.

(1)+(2): " x is an even number greater than 2 and less than 19" - All possible values of x will be non-prime since 2 is the only prime even number and that is excluded from the range. Therefore, SUFFICIENT.

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Is the positive integer x a prime number? (1) x is even (2) 2< x < 19  [#permalink]

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10 Jun 2018, 18:44
Bunuel wrote:
Is the positive integer x a prime number?

(1) x is even
(2) 2< x < 19

Note:

1. x is a positive integer.
2. Need to fin out whether x is prime or not

Statement 1:

x is even. There are hundreds of even numbers . Among them only 2 is the prime. But no relevant information is given.

Not stuff.

Statement 2:

Range of numbers is given: 2<x<19

in this range prime and non prime numbers both are here. Suppose, 3 ,5 , 7 10 all fall under this range . but 10 is not prime.

Not stuff.

Both Statements Together:

1. it states that x is even
2. 2<x<19

There are several even numbers in this range but they are not prime. So, x is not a prime. we got the answer.

Thus, both statements together are sufficient. Thew correct answer is C.

Note: only 2 is the even prime on earth.
Is the positive integer x a prime number? (1) x is even (2) 2< x < 19 &nbs [#permalink] 10 Jun 2018, 18:44
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