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Is x a prime number?

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Bunuel
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Is x a prime number? [#permalink] New post   16 Feb 2015, 06:47
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E

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45% (medium)

Question Stats:

65% (01:37) correct 35% (01:42) wrong based on 226 sessions
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Is x a prime number?

(1) 14-x is prime
(2) x is not a multiple of 3
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E
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sterling19
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Is x a prime number? [#permalink] New post   16 Feb 2015, 08:25
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Statement 1: x could be 1, 3, 7, 12
Statement 2: x could 0, 1, 2, 4, 5, 7, 8, 11, 13 ...

If we combine both statements, x could be 1 or 7.
14 - 1 = 13, which is prime
14 - 7 = 7, which is prime

The correct answer is E.
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Re: Is x a prime number? [#permalink] New post   16 Feb 2015, 11:45
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Is x a prime number?

Statement 1
(1) 14-x is prime = Set of prime numbers less than 14 { 2 ,3 ,5 ,7 , 11, 13 }
Therefore X = { 1 ,2 ,7 ,11 , 12 } , X may or may not be prime not sufficient

Statement 2 :
(2) X is not a multiple of 3
X can be { 1 , 2 ,4 ,5 , 7 , 8 .... } May or may not be prime .

Combining both statements also the answer may or may not be prime .

Hence E
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Re: Is x a prime number? [#permalink] New post   22 Feb 2015, 11:08
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Bunuel wrote:
Is x a prime number?

(1) 14-x is prime
(2) x is not a multiple of 3


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: E

Applying the information found in statement 1, we find that 1, 3, 7, 9, 11, and 12 each satisfy the statement. 3, 7, and 11 are prime, but 1, 9, and 12 are not. Therefore, statement 1 is insufficient. Statement 2, by itself, leaves an infinite number of potential values, both prime and not, so it is also insufficient. When taken together, only 1, 7, and 11 are potential values of x. 7 and 11 are prime, but 1 is not. Accordingly, there is not sufficient information to determine whether x is prime, and the correct answer is E.
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Re: Is x a prime number? [#permalink] New post   07 Jun 2016, 04:25
Bunuel wrote:
Is x a prime number?

(1) 14-x is prime
(2) x is not a multiple of 3


Statement 1

say x =1; 14-1 = 13; 13 is a prime number. But x --> not prime (1 is not prime number).
say x =3; 14-3 = 11; 11 is a prime number. x = 3 --> a prime number

Not sufficient.

Statement 2

say x =8; x is not a multiple of 3. x is not a prime number.
say x =7; x is not a multiple of 3. x is a prime number.

Not sufficient.

Combining Statement 1 and 2
say x =1; x is not a multiple of 3 ; 14-1 = 13; 13 is a prime number.
x --> not prime (1 is not prime number).

say x =7; x is not a multiple of 3 ; 14-7 = 7; 7 is a prime number.
x --> prime

Not sufficient.

E is the answer.
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Re: Is x a prime number? [#permalink] New post   07 Jun 2016, 09:22
Bunuel wrote:
Is x a prime number?

(1) 14-x is prime
(2) x is not a multiple of 3


Statement 1= prime numbers below 14 are 13 (14-1) , 11 (14-3) , 7 (14-7) , 5 (14-9) , 3 (14-11) , 2 (14-12)

So x is prime if 3, 7, 11
and not prime if x is 1, 9, 12
Not Sufficient

Statement 2= x is not a multiple of 3
it can be any number not a multiple of 3
Not sufficient

Combining statement 1 and 2
X is not 9 or 12, but it can be 1, 3, 7, 9. Not sufficient since 1 is not a prime number and others are.

E is the answer
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Re: Is x a prime number? [#permalink] New post   16 Oct 2016, 03:42
We need to get if x is prime or not
Statement 1 => 14-x=prime
hence x=14-prime
=> x can be 14-2=12 => not a prime
x can be => 14-7=7 => prime number
Not suff
Statement 2 => x => not a multiple of 3
x=2=> prime
x=70=> not a prime
combining the two statements
x=> 14-prime
14-2
14-3
14-5
14-7
14-11
14-13
14-17
14-19
etc.
Hence x may be prime => 7
or it may not be prime => 1 or -3 (since negatives can never be prime)
Hence E

Why isn't anyone considering the possibility of negative values.
Remember Primes can never be negative
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Is x a prime number? [#permalink] New post   16 Oct 2016, 04:31
Bunuel wrote:
Is x a prime number?

(1) 14-x is prime
(2) x is not a multiple of 3


FROM STATEMENT - I ( INSUFFICIENT )

P = 14 - x

If x is odd -

If x is odd P can be prime 14 - 1 = 13 ( Prime )
If x is odd P may not be prime 14 - 5 = 9 ( Not a Prime )

If x is even -

If x is even P may not be prime 14 - 10 = 4 ( Not a Prime )
If x is even P may be prime 14 - 12= 2 ( Prime )

So, We can not state if 14 - x will be prime from statement 1....


FROM STATEMENT - II ( INSUFFICIENT )

If x is not a multiple of 3 , it can be a multiple of some other number ( Prime or Non Prime )

So, we can not state x is prime from statement II as well...

COMBINE STATEMENT I AND II [b]( INSUFFICIENT )

[/b]We can not state x is prime...

Hence answer will be (E), Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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Is x a prime number? [#permalink]
16 Oct 2016, 04:31
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Bunuel
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