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If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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16 Jun 2016, 05:03
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59% (01:24) correct 41% (01:21) wrong based on 1195 sessions
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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16 Jun 2016, 19:53
There is one variable (x) in the original condition. So we need 1 equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the correct answer. The condition 1) has x=2 yes, x=6 no not suffi. The condition 2) has x=2 yes, x=6 no not suffi. Since the condition 1) and the condition 2) have x=2 yes, x=6 no not suffi, the correct answer is E.  For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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20 Nov 2016, 21:13
A quick trick: plug in only even numbers in \(x\). Remember that with the exception of 2, prime numbers are odd.
For the equation \(3x + 1\) and \(5x + 1\) to have an odd prime result, we need to plug in even numbers 2, 4, 6 to \(x\).
Because combining both A and B gives us \(x = 2\) (prime) and \(x = 6\) (not prime), our answer is E.




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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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16 Jun 2016, 07:30
Bunuel wrote: If x is a positive integer, then is x prime?
(1) 3x + 1 is prime (2) 5x + 1 is prime x = +ve integer (1) 3x + 1 is prime if 3x+1 = 7 = prime => x= 2 , which is prime if 3x+1 = 19 = prime => x = 6 , which is not a prime Not sufficient (2) 5x + 1 is prime if 5x + 1 = 11 = prime => x = 2 , which is prime if 5x + 1 = 31 = prime => x = 6 , which is not a prime Not sufficient Combining 1 and 2 , we get Still Not sufficient Answer E
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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16 Jun 2016, 11:59
Bunuel wrote: If x is a positive integer, then is x prime?
(1) 3x + 1 is prime (2) 5x + 1 is prime Statement 1: If x is 2, 4 , 6.... then 3x + 1 is prime if x is 1, 3, 5.... then 3x + 1 is not prime Not sufficient as x may or may not be prime. Statement 2: If x is 1, 3, 5... then 5x + 1 is not prime if x is 2, 6... then 5x + 1 is prime. Not sufficient as x may or may not be prime. Both statements combined together do not give a unique solution. Hence the answer is E
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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17 Jun 2016, 02:41
Bunuel wrote: If x is a positive integer, then is x prime?
(1) 3x + 1 is prime (2) 5x + 1 is prime primes > 3 are always of the form 6k +/ 1 1) 3x + 1 = 6k+1 => x = 6k/3 = 2k 2k can be prime (2) or not (4,6,8,...) insufficient 2) 5x+1 = 6k+1 => x = 6k/5 here x cannot be a prime 5x+1 = 6k1 => x = (6k2)/5 if k=2, then x=2 (prime) if k=7, then x=8 (not a prime) insufficient (1)+(2) x=2 or x=8 (more common values might exist but i am not bothering to calculate since this is enough to answer) insufficient. Hence, E.
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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08 Dec 2016, 09:00
Bunuel wrote: If x is a positive integer, then is x prime?
(1) 3x + 1 is prime (2) 5x + 1 is prime We are given that x is a positive integer and must determine whether x is prime. Statement One Alone: 3x + 1 is prime. Using the information in statement one, x does not necessarily have to be prime. For instance, if x = 2, then 3x + 1 = 7 is prime, or if x = 4, then 3x + 1 = 13 is prime. In the former case, x = 2 is prime; however, in the latter case, x = 4 is not prime. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D. Statement Two Alone:5x + 1 is prime. Using the information in statement two, x does not necessarily have to be prime. For instance, if x = 2, then 5x + 1 = 11 is prime, or if x = 6, then 5x + 1 = 31 is prime. In the former case, x = 2 is prime; however, in the latter case, x = 6 is not prime. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B. Statements One and Two Together:Using the information from statements one and two, we still cannot determine whether x is prime. For instance, if x = 2, then both 3x +1 = 7 and 5x + 1 = 11 are prime, or if x = 12, then both 3x + 1 = 37 and 5x + 1 = 61 are prime. In the former case, x = 2 is prime; however, in the latter case, x = 12 is not prime. Answer: E
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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28 Mar 2017, 19:08
Plug in prime numbers as a result of the equation 1) 3x+1=7 x=2 (prime)
3x+1=19 x=6 (not prime); hence NS
2) 5x+1=11 x=2 (prime)
5x+1=31 x=6 (not prime) ; hence NS
1) & 2) x=2 or x= 6 and both equations would still yield a prime number.
Correct answer E)



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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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15 Mar 2018, 19:11
Hi Bunuel,
Is there an alternative method to this where we do not have to plug in values at random?
Best Amit



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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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15 Mar 2018, 19:55



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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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28 Mar 2018, 14:09
\sqrt{} Bunuel wrote: If x is a positive integer, then is x prime?
(1) 3x + 1 is prime (2) 5x + 1 is prime (1) 3x + 1 is primeLet x =2........3 + 1 =7........Answer is Yes Let x =6........18 + 1 =19........Answer is No Insufficient (2) 5x + 1 is prime Let x =2........10+ 1 =11........Answer is Yes Let x =6........30 + 1 =31........Answer is No Insufficient Combine 1 & 2 Use same examples..........No certain answer. Insufficient Answer: E



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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x
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01 Nov 2018, 07:49
Bunuel wrote: If x is a positive integer, then is x prime?
(1) 3x + 1 is prime (2) 5x + 1 is prime Answer: E 1) Given: 3x+1 is prime, also since x>=1 , 3x+1 cant be 2, this implies 3x+1 is an odd prime, thus 3x is even, Thus x is even. Now x>=1, so x can be 2 (prime) and greater than 2(Not prime). Insufficient 2) We can use the similar explanation for 5x+1. Insufficient. Combining both is also insufficient.
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x &nbs
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