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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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If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

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New post 16 Jun 2016, 06:03
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A
B
C
D
E

Difficulty:

  65% (hard)

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60% (01:57) correct 40% (01:54) wrong based on 1393 sessions

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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

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New post 16 Jun 2016, 20:53
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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  [#permalink]

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New post 20 Nov 2016, 22:13
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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  [#permalink]

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New post 16 Jun 2016, 08:30
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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  [#permalink]

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New post 16 Jun 2016, 12:59
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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  [#permalink]

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New post 17 Jun 2016, 03:41
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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 = 6k-1
=> x = (6k-2)/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  [#permalink]

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New post 08 Dec 2016, 10:00
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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  [#permalink]

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New post 28 Mar 2017, 20:08
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  [#permalink]

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New post 15 Mar 2018, 20:11
Hi Bunuel,

Is there an alternative method to this where we do not have to plug in values at random?

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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

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New post 15 Mar 2018, 20:55
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

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New post 28 Mar 2018, 15:09
1
\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 prime

Let 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  [#permalink]

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New post 01 Nov 2018, 08:49
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  [#permalink]

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New post 14 Oct 2019, 21:40
Bunuel wrote:
If x is a positive integer, then is x prime?

(1) 3x + 1 is prime
(2) 5x + 1 is prime

Bunuel chetan2u
can u clear this confusion:
3x+1 is prime
so 3x+1=6k+1 or 3x+1=6k-1
x=2k ----(A) or x=2k-(2/3)-----(B)
eqn b can never be prime as it will always be decimal
so answer is no
eqn A can be prime if k=1 or cannot be prime if k=2
so cannot say
My question is
will the answer be common to both A and B which is No
or answer will be
if i prove in any case x can be prime then it will be yes
else no
so we are considering its insufficent
can u please claer this ?
how to interpret answer from both the statemnts
Say it had been and case
then answer will be No ,right?
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

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New post 15 Oct 2019, 00:09
This is an excellent question on the properties of Primes. I’d also use the Units digit concept to solve the question since there is a multiple of 5 mentioned in one of the statements.

‘x’ is a positive integer. This means that x can take any value from the set {1,2,3,4,5……}.

From statement I, we know that 3x + 1 is prime. Since x is a positive integer, we can say that the smallest value we can take for 3x is 3, which is to say that the smallest value for x is 1. Therefore, 3x + 1 cannot be equal to 2 or 3.

If 3x + 1 = 5, 3x = 4. x is not an integer here. If 3x + 1 = 7, 3x = 6 which gives us x = 2. This value of x answers the main question with a YES since 2 is prime.

Any prime number greater than 3 can be written as 6k – 1 or 6k + 1 where k is a positive integer. A careful analysis will tell us that when we equate 3x + 1 to 6k + 1, we get x to be an integer. That’s why we got x = 2 in the example above.

The next two prime numbers that can be written in the form of 6k + 1 are 13 and 19. If 3x + 1 = 13, x = 4; if 3x + 1 = 19, x = 6. 4 and 6 are not prime numbers and hence answer the main question with a NO.

Statement I is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, 5x + 1 is a prime. Again, the smallest prime of this form can be 11. Clearly we are dealing with odd primes. Therefore, 5x has to be even. In other words, 5x is a multiple of 5 with units digit ZERO and so 5x + 1 is a prime with units digit 1. This means that x can be 2 or 6 or 8. We again face a YES NO situation.

Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining the data given in the two statements, we have x = 2 and x = 6 satisfying both statements at the same time. The combination of statements is insufficient as well.

The correct answer option is E.

Hope that helps!
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Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x   [#permalink] 15 Oct 2019, 00:09
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