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18 Aug 2014, 07:59
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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42% (02:11) correct
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Is the positive integer P a prime number?
(1) (P+2) and (P+4) are prime
(2) (P-2) and (P-4) are prime
Source: 4Gmat
(1) (P+2) and (P+4) are prime
(2) (P-2) and (P-4) are prime
Source: 4Gmat
18 Aug 2014, 08:41
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Is the positive integer P a prime number?
(1) (P+2) and (P+4) are prime. If p = 1, then the answer is NO but if p = 3, then the answer is YES. Not sufficient.
(2) (P-2) and (P-4) are prime. If p = 9, then the answer is NO but if p = 7, then the answer is YES. Not sufficient.
(1)+(2) Since (P-4), (P-2), (P+2), and (P+4) are primes, then all of them must be odd numbers. This means that (P-4), (P-2), P, (P+2), and (P+4) are 5 consecutive odd numbers. Since there are no 5 consecutive odd primes, then P cannot be a prime (out of 5 consecutive odd numbers one must be a multiple of 3 and another a multiple of 5. There are only one prime, which is a multiple of 3, 3 itself and there are only one prime, which is a multiple of 5, 5 itself but P can be neither 3 or 5 since this violate (P-4), (P-2), (P+2), and (P+4) being primes). Sufficient.
Answer: C.
Hope it's clear.
(1) (P+2) and (P+4) are prime. If p = 1, then the answer is NO but if p = 3, then the answer is YES. Not sufficient.
(2) (P-2) and (P-4) are prime. If p = 9, then the answer is NO but if p = 7, then the answer is YES. Not sufficient.
(1)+(2) Since (P-4), (P-2), (P+2), and (P+4) are primes, then all of them must be odd numbers. This means that (P-4), (P-2), P, (P+2), and (P+4) are 5 consecutive odd numbers. Since there are no 5 consecutive odd primes, then P cannot be a prime (out of 5 consecutive odd numbers one must be a multiple of 3 and another a multiple of 5. There are only one prime, which is a multiple of 3, 3 itself and there are only one prime, which is a multiple of 5, 5 itself but P can be neither 3 or 5 since this violate (P-4), (P-2), (P+2), and (P+4) being primes). Sufficient.
Answer: C.
Hope it's clear.
General Discussion
18 Aug 2014, 08:38
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For Stat1
P can be equal to 3 and can be equal to 9. So not sufficient
For STAT2
P can be equal to 7 and can be equal to 9. So not sufficient
STAT1 and STAT2 together
p-4, p-2,p, p+2, p+4
If P is prime then P must be odd (as only even prime is 2 and p-4 will not be prime then)
if p is odd then p cannot be prime as
p-4,p-2,p,p+2,p+4 make a series of 5 consecutive odd numbers and NO pair of 5 consecutive odd numbers are prime
So, p is NOT a prime number.
So, Answer will be C
Hope it helps!
P can be equal to 3 and can be equal to 9. So not sufficient
For STAT2
P can be equal to 7 and can be equal to 9. So not sufficient
STAT1 and STAT2 together
p-4, p-2,p, p+2, p+4
If P is prime then P must be odd (as only even prime is 2 and p-4 will not be prime then)
if p is odd then p cannot be prime as
p-4,p-2,p,p+2,p+4 make a series of 5 consecutive odd numbers and NO pair of 5 consecutive odd numbers are prime
So, p is NOT a prime number.
So, Answer will be C
Hope it helps!
(edited)
