GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 00:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58438
If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

16 Jun 2016, 06:03
3
60
00:00

Difficulty:

65% (hard)

Question Stats:

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

### HideShow timer Statistics

If x is a positive integer, then is x prime?

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

_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8029
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

16 Jun 2016, 20:53
3
19
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.
Attachments

variable approach's answer probability.jpg [ 219.74 KiB | Viewed 18801 times ]

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Status: Gaja!
Joined: 26 Aug 2014
Posts: 49
Location: United States (CA)
GMAT 1: 700 Q49 V36
GMAT 2: 680 Q49 V34
GMAT 3: 740 Q50 V40
GPA: 3.6
WE: Consulting (Consulting)
If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

20 Nov 2016, 22:13
11
1
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.
##### General Discussion
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2401
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

16 Jun 2016, 08:30
2
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
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Current Student
Joined: 18 Oct 2014
Posts: 801
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

16 Jun 2016, 12:59
1
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
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Manager
Joined: 22 Jan 2014
Posts: 170
WE: Project Management (Computer Hardware)
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

17 Jun 2016, 03:41
2
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.
_________________
Illegitimi non carborundum.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8137
Location: United States (CA)
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

08 Dec 2016, 10:00
3
1
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 08 Mar 2016
Posts: 2
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

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.

Intern
Joined: 10 Nov 2014
Posts: 17
Location: United Kingdom
WE: Information Technology (Consulting)
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

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?

Best-
Amit
Math Expert
Joined: 02 Sep 2009
Posts: 58438
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

15 Mar 2018, 20:55
Amit989 wrote:
Hi Bunuel,

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

Best-
Amit

For this particular question you have to test values. There is no purely algebraic way.
_________________
SVP
Joined: 26 Mar 2013
Posts: 2341
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

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

Insufficient

Intern
Joined: 03 Sep 2018
Posts: 19
WE: Analyst (Consulting)
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

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

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.
_________________
Regards,
Bashdeep

Let's study and grow together
If the answer helped you, be generous and hit +1 Kudos
Manager
Joined: 17 Jul 2017
Posts: 193
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

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
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
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?
CrackVerbal Quant Expert
Joined: 12 Apr 2019
Posts: 268
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x  [#permalink]

### Show Tags

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!
_________________
Re: If x is a positive integer, then is x prime? 1) 3x + 1 is prime 2) 5x   [#permalink] 15 Oct 2019, 00:09
Display posts from previous: Sort by