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05 Dec 2016, 02:29
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41%
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If p is an integer, is p + 4 a prime number less than 50?
(1) p + 1 is a prime number.
(2) p is a prime number.
(1) p + 1 is a prime number.
(2) p is a prime number.
05 Dec 2016, 03:00
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1) the only two prime numbers which are also consecutive integers are 2 and 3. Thus, since p+1=prime p=2 p+2=2+4=6 So, we can say that p+4 is not a prime number with certainty. SUFFIcient
2) lets see two cases:
p=2 p+4=2+6=6 not prime
p=7 p+4=7+4=11 prime
Thus we cannot say with certainty that p+4 is prime INSUFFICIENT
2) lets see two cases:
p=2 p+4=2+6=6 not prime
p=7 p+4=7+4=11 prime
Thus we cannot say with certainty that p+4 is prime INSUFFICIENT
05 Dec 2016, 03:16
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f p is an integer, is p + 4 a prime number less than 50?
(1) p + 1 is a prime number.
(2) p is a prime number.
(1) p+1 =2 --> p =1, p+4=5, prime less than 50
but p+1= 3 onwards (all odd prime) --> p= even, even + 4 = even, not a prime
-->(1) insufficient
(2) p is a prime number, p = 2, 2+4=6 not a prime less than 50
p=3, 3+4=7, a prime less than 50
-->(2) insufficient
(1)+(2), p is a prime and p+1 is a prime. That case can only be satisfied with p=2, 2+4 =6, not a prime --> sufficient. Answer is C
(1) p + 1 is a prime number.
(2) p is a prime number.
(1) p+1 =2 --> p =1, p+4=5, prime less than 50
but p+1= 3 onwards (all odd prime) --> p= even, even + 4 = even, not a prime
-->(1) insufficient
(2) p is a prime number, p = 2, 2+4=6 not a prime less than 50
p=3, 3+4=7, a prime less than 50
-->(2) insufficient
(1)+(2), p is a prime and p+1 is a prime. That case can only be satisfied with p=2, 2+4 =6, not a prime --> sufficient. Answer is C
