Last visit was: 31 Oct 2024, 16:38 It is currently 31 Oct 2024, 16:38
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 31 Oct 2024
Posts: 96,533
Own Kudos:
673,099
 [3]
Given Kudos: 87,883
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,533
Kudos: 673,099
 [3]
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
User avatar
freedom128
Joined: 30 Sep 2017
Last visit: 01 Oct 2020
Posts: 943
Own Kudos:
1,296
 [2]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Products:
GMAT 1: 720 Q49 V40
Posts: 943
Kudos: 1,296
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
CareerGeek
Joined: 20 Jul 2017
Last visit: 28 Oct 2024
Posts: 1,297
Own Kudos:
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
GMAT 1: 690 Q51 V30
Posts: 1,297
Kudos: 3,726
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Kinshook
User avatar
GMAT Club Legend
Joined: 03 Jun 2019
Last visit: 31 Oct 2024
Posts: 5,400
Own Kudos:
4,481
 [1]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,400
Kudos: 4,481
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Asked: Let an infinite sequence of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite sequence M "pure"?

(1) M contains only prime numbers.
Prime numbers include 3 & 7.
M = {3, 7, 11, 13, 17, ....} - Not "Pure"
M = {11, 13, 17, .... } - "Pure"
NOT SUFFICIENT

(2) The units digit of all members of M is either 3 or 7.
M = {3, 7, 11, 13, 17, ....} - Not "Pure"
M = {13, 17, 23.... } - "Pure"
NOT SUFFICIENT

(1) + (2)
(1) M contains only prime numbers.
(2) The units digit of all members of M is either 3 or 7.
M = {3, 7, 11, 13, 17, ....} - Not "Pure"
M = {13, 17, 23.... } - "Pure"
NOT SUFFICIENT

IMO E
User avatar
exc4libur
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,710
Own Kudos:
1,383
 [1]
Given Kudos: 607
Location: United States
Posts: 1,710
Kudos: 1,383
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
Let an infinite sequence of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite sequence M "pure"?

(1) M contains only prime numbers.
(2) The units digit of all members of M is either 3 or 7.

(1) insufic

not pure primes: {2,3,5,7…}
pure primes: {2,5,11…}

(2) insufic

not pure: {3,7,13,17…}
pure: {13,17,23…}

(1/2) insufic

not pure primes: {3,7,13,17…}
pure primes: {13,17,23…}

Ans (E)
User avatar
Archit3110
User avatar
GMAT Club Legend
Joined: 18 Aug 2017
Last visit: 31 Oct 2024
Posts: 8,099
Own Kudos:
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Focus 1: 545 Q79 V79 DI73
Posts: 8,099
Kudos: 4,406
Kudos
Add Kudos
Bookmarks
Bookmark this Post
#1
M contains only prime numbers.
cannot be pure as 3,7 are prime and are divisible by 3 and 7 or may not be there as well; insufficient

#2
The units digit of all members of M is either 3 or 7.

again no ; can be 13,37 ; so the sequence is not Pure or can be pure if 27,63 are present
insufficient
nothing in common
IMO E


Let an infinite sequence of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite sequence M "pure"?

(1) M contains only prime numbers.
(2) The units digit of all members of M is either 3 or 7.
User avatar
unraveled
Joined: 07 Mar 2019
Last visit: 31 Oct 2024
Posts: 2,712
Own Kudos:
Given Kudos: 764
Location: India
WE:Sales (Energy)
Posts: 2,712
Kudos: 1,978
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let an infinite sequence of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite sequence M "pure"?

If no number divisible by 3 or 7 is present then sequence is pure
If a number divisible by either 3 or 7 is present then sequence is not pure

(1) M contains only prime numbers.
3 and 7 are present. Thus not pure.

SUFFICIENT.

(2) The units digit of all members of M is either 3 or 7.
Since its an infinite sequence it can contain
Case I: 3, 7 or 33, 27 - its not a pure sequence.
Case II: 13, 17, 23, 37, 43, 47 - its a pure sequence.


INSUFFICIENT.

Answer A.
avatar
chaitralirr
Joined: 17 Mar 2019
Last visit: 07 Oct 2021
Posts: 364
Own Kudos:
285
 [1]
Given Kudos: 35
Location: India
Concentration: Healthcare, General Management
Schools:
GPA: 3.75
WE:Pharmaceuticals (Healthcare/Pharmaceuticals)
Schools:
Posts: 364
Kudos: 285
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let an infinite sequence of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite sequence M "pure"?

(1) M contains only prime numbers.
(2) The units digit of all members of M is either 3 or 7.

Statement 1

If M contains only prime numbers it can contain 3 or 7 both are prime number hence statement 1 is insufficient.

Statement 2:

The units digit of all members of M is either 3 or 7

eg 23 Yes then M is pure
if it has 3 or 7 only then M sequence is not pure.

Hence statement 2 is insufficient.

Combining 1 and 2 still insufficient as we don't know if 3 or 7 alone are part of the sequence.

IMO E
Moderator:
Math Expert
96533 posts