Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 06 Jun 2020, 07:04

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 n is a positive integer greater than 16, is n a prime

Author Message
TAGS:

Hide Tags

Intern
Joined: 22 Mar 2012
Posts: 5
If n is a positive integer greater than 16, is n a prime  [#permalink]

Show Tags

Updated on: 29 Mar 2012, 13:09
3
00:00

Difficulty:

65% (hard)

Question Stats:

63% (02:09) correct 37% (02:00) wrong based on 198 sessions

HideShow timer Statistics

If n is a positive integer greater than 16, is n a prime number?

(1) n is odd
(2) The remainder when n is divided by 3 is 1, and the remainder when n is divided by 7 is 1.

Originally posted by Jakevmi80 on 29 Mar 2012, 12:49.
Last edited by Bunuel on 29 Mar 2012, 13:09, edited 1 time in total.
Moved to DS subforum
Math Expert
Joined: 02 Sep 2009
Posts: 64318

Show Tags

29 Mar 2012, 13:08
1
2
If n is a positive integer greater than 16, is n a prime number?

(1) n is odd. An odd number can be prime as well as non-prime. Not sufficient.

(2) The remainder when n is divided by 3 is 1, and the remainder when n is divided by 7 is 1:
$$n=3q+1$$, so $$n$$ can be; (1, 4, 7, 10, 13, 16), 19, 22, ... (numbers greater than 16)
$$n=7p+1$$, so $$n$$ can be; (1, 8, 15), 22, 29...

General formula of $$n$$ based on the above two conditions would be $$n=21t+22$$, divisor will be the least common multiple of above two divisors 3 and 7, hence 21 and the remainder will be the first common integer in above two patterns, hence 22 (for more on this check: manhattan-remainder-problem-93752.html?hilit=derive#p721341 and when-positive-integer-n-is-divided-by-5-the-remainder-is-90442.html?hilit=derive#p722552).

Next, from $$n=21t+22$$ $$n$$ can be: 22, 43, 64, 85, 106, 127, ... We can see that $$n$$ ca be prime (for example 43) as well as non-prime (for example 85). Not sufficient.

(1)+(2) $$n$$ can still be a prime as well as non-prime, for example 43 or 85. Not sufficient.

P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.
_________________
Director
Joined: 03 Aug 2012
Posts: 648
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Re: If n is a positive integer greater than 16, is n a prime  [#permalink]

Show Tags

11 Aug 2013, 08:15
n>0 (Integer)
n> 16

Is n prime?

(1).

n=odd so n can be 17,19,21 ....
Here 17 is prime. However, 21 is not. And hence INSUFFICIENT.

(2).

n = 3A +1 19,22,25,28,31,34,37,40,43
n= 7B + 1 22,29,36,43

Combining series n = 21A + 43

So Numbers 43,64,85
Here 43 is prime . However, 64 isnt Hence INSUFFICIENT

Combining (1) and (2).

43,85.............While 85 isn't prime 43 is .

Insufficient Hence (E) it is
Intern
Joined: 26 Jan 2010
Posts: 20
Location: chile
WE 1:
WE 2:
WE 3:
Re: If n is a positive integer greater than 16, is n a prime  [#permalink]

Show Tags

30 Nov 2014, 14:23
They indicate that n is greater than 16 and asked if n is Prime?

With condition 1) N is odd, there are many odd older than 16 who are not prime numbers, example numbers: 21, 25 and more. Eye and there are also many odd greater than 16, that if are prime numbers for example: 17, 19, and more.

Given the situation that there is both Prime and non-prime numbers, we conclude that the condition 1) is not enough.

Condition 2) rest 1, is obtained by dividing N by 3, and rest 1 is obtained by dividing N by 7.
This results in N = 3 K + 1 and N = 7 p + 1, given that N is unique and that 3 and 7 are prime numbers, we can conclude that N to be divided by (7 x 3) 21, also gets rest 1, since N must be divisible simultaneously for 3 and 7 for rest 1.

So N = 21J + 1, then N may be 22, 43, and other values, given that 22 is even and 43 is prime number, there is ambiguity, then 2) is not enough.

Let’s see if it is enough 1) and 2).

1) N = 17, 19, 21, 25,..., 43,..., 85,...

(2) N = 22, 43, 64, 85...

There we can see two values that satisfy both conditions 43 and 85, and as 43 is a prime number and 85 it is not a prime number, again produced ambiguity and we conclude that the two conditions together nor we can affirm or deny, initial sentence.

_________________
Private lessons GMAT QUANT GRE QUANT SAT QUANT
Classes group of 4 students GMAT QUANT GRE QUANT SAT QUANT
Distance learning courses GMAT QUANT GRE QUANT SAT QUANT

Website http://www.gmatchile.cl
Email clasesgmatchile@gmail.com
Skype: clasesgmatchile@gmail.com
Address Avenida Hernando de Aguirre 128 Of 904, Tobalaba Metro Station, Santiago Chile.
Non-Human User
Joined: 09 Sep 2013
Posts: 15104
Re: If n is a positive integer greater than 16, is n a prime  [#permalink]

Show Tags

03 Apr 2018, 07:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If n is a positive integer greater than 16, is n a prime   [#permalink] 03 Apr 2018, 07:45