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Bunuel
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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Bunuel
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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Bunuel
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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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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Bunuel
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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