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

It is currently 19 Nov 2019, 13:03

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

Set A consists of all distinct prime numbers which are 2 mor

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59147
Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 17 Feb 2014, 03:54
3
18
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (02:19) correct 60% (02:21) wrong based on 412 sessions

HideShow timer Statistics

Set A consists of all distinct prime numbers which are 2 more than a multiple of 3. If set B consists of distinct integers, is set B a subset of set A?

(1) Set B consist of two positive integers whose product is 10.
(2) The product of reciprocals of all elements in set B is a terminating decimal

_________________
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59147
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 17 Feb 2014, 03:54
3
7
SOLUTION

Set A consists of all distinct prime numbers which are 2 more than a multiple of 3. If set B consists of distinct integers, is set B a subset of set A?

According to the definition set A = {2, 5, 11, 17, 23, 29, 41, ...}

(1) Set B consist of two positive integers whose product is 10. 10 can be broken into the product of two integers in two ways: 10 = 1*10 and 10 = 2*5. If set B = {1, 10}, then the answer to the question is NO but if set B = {2, 5}, then the answer to the question is YES. Not sufficient.

(2) The product of reciprocals of all elements in set B is a terminating decimal. If set B = {4, 8}, then the answer to the question is NO but if set B = {2, 5}, then the answer to the question is YES. Not sufficient.

(1)+(2) Both possible sets from (1) meet the condition stated in the second statement: \(\frac{1}{1}*\frac{1}{10}=\frac{1}{10}=0.1= terminating \ decimal\) and \(\frac{1}{2}*\frac{1}{5}=\frac{1}{10}=0.1= terminating \ decimal\). Thus we still have two sets, which give two different answers to the question. Not sufficient.

Answer: E.
_________________
General Discussion
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 654
Location: India
GPA: 3.21
WE: Business Development (Other)
Reviews Badge
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 17 Feb 2014, 04:19
Bunuel wrote:
Set A consists of all distinct prime numbers which are 2 more than a multiple of 3. If set B consists of distinct integers, is set B a subset of set A?

(1) Set B consist of two positive integers whose product is 10.
(2) The product of reciprocals of all elements in set B is a terminating decimal


Sol: Possible values of Set A ={5,11,17,23,29,41,47...}

St 1: Possible combination with multiple of 10 ( 1,10) (2,5) -----> Clearly not a subset of A
So sufficient

St 2: Since the reciprocal is a terminating decimal so the terms will be of of 1/ (2^a*5^b) where a and b are integers
So possible value are {2,5,10, 20,125.....}
If Set B has only 1 element let us say {5} then B is subset otherwise not

Ans is A
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59147
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 17 Feb 2014, 04:23
WoundedTiger wrote:
Bunuel wrote:
Set A consists of all distinct prime numbers which are 2 more than a multiple of 3. If set B consists of distinct integers, is set B a subset of set A?

(1) Set B consist of two positive integers whose product is 10.
(2) The product of reciprocals of all elements in set B is a terminating decimal


Sol: Possible values of Set A ={5,11,17,23,29,41,47...}

St 1: Possible combination with multiple of 10 ( 1,10) (2,5) -----> Clearly not a subset of A
So sufficient

St 2: Since the reciprocal is a terminating decimal so the terms will be of of 1/ (2^a*5^b) where a and b are integers
So possible value are {2,5,10, 20,125.....}
If Set B has only 1 element let us say {5} then B is subset otherwise not

Ans is A


Like many GMAT Club's questions, this one is tricky... Set A is missing an important element.
_________________
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 654
Location: India
GPA: 3.21
WE: Business Development (Other)
Reviews Badge
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 17 Feb 2014, 04:47
Bunuel wrote:
WoundedTiger wrote:
Bunuel wrote:
Set A consists of all distinct prime numbers which are 2 more than a multiple of 3. If set B consists of distinct integers, is set B a subset of set A?

(1) Set B consist of two positive integers whose product is 10.
(2) The product of reciprocals of all elements in set B is a terminating decimal


Sol: Possible values of Set A ={5,11,17,23,29,41,47...}

St 1: Possible combination with multiple of 10 ( 1,10) (2,5) -----> Clearly not a subset of A
So sufficient

St 2: Since the reciprocal is a terminating decimal so the terms will be of of 1/ (2^a*5^b) where a and b are integers
So possible value are {2,5,10, 20,125.....}
If Set B has only 1 element let us say {5} then B is subset otherwise not

Ans is A


Like many GMAT Club's questions, this one is tricky... Set A is missing an important element.



Yes it is.
Possible values in Set A ={2,5,11,17,23,29,41....}
So if Set B={2,5} then yes but Set B={1,10} then No

So A and D ruled out

St2 : If Set B {2},{5} or {10} or {2,5} then yes otherwise no. So St 2 is ruled out

Combining we get Set B ={ 2,5}

Ans C
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Director
Director
User avatar
V
Joined: 27 May 2012
Posts: 937
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 23 Feb 2014, 06:01
1
really tricky one !

Let set B = {2,5} then yes , B is a subset of of A

let B = {1,10} Then no, B is not a subset of A

Answer E.
_________________
- Stne
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59147
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 23 Feb 2014, 06:05
1
SOLUTION

Set A consists of all distinct prime numbers which are 2 more than a multiple of 3. If set B consists of distinct integers, is set B a subset of set A?

According to the definition set A = {2, 5, 11, 17, 23, 29, 41, ...}

(1) Set B consist of two positive integers whose product is 10. 10 can be broken into the product of two integers in two ways: 10 = 1*10 and 10 = 2*5. If set B = {1, 10}, then the answer to the question is NO but if set B = {2, 5}, then the answer to the question is YES. Not sufficient.

(2) The product of reciprocals of all elements in set B is a terminating decimal. If set B = {4, 8}, then the answer to the question is NO but if set B = {2, 5}, then the answer to the question is YES. Not sufficient.

(1)+(2) Both possible sets from (1) meet the condition stated in the second statement: \(\frac{1}{1}*\frac{1}{10}=\frac{1}{10}=0.1= terminating \ decimal\) and \(\frac{1}{2}*\frac{1}{5}=\frac{1}{10}=0.1= terminating \ decimal\). Thus we still have two sets, which give two different answers to the question. Not sufficient.

Answer: E.
_________________
Manager
Manager
avatar
B
Joined: 19 Aug 2016
Posts: 73
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 22 Sep 2017, 10:16
Bunuel wrote:
SOLUTION

Set A consists of all distinct prime numbers which are 2 more than a multiple of 3. If set B consists of distinct integers, is set B a subset of set A?

According to the definition set A = {2, 5, 11, 17, 23, 29, 41, ...}

(1) Set B consist of two positive integers whose product is 10. 10 can be broken into the product of two integers in two ways: 10 = 1*10 and 10 = 2*5. If set B = {1, 10}, then the answer to the question is NO but if set B = {2, 5}, then the answer to the question is YES. Not sufficient.

(2) The product of reciprocals of all elements in set B is a terminating decimal. If set B = {4, 8}, then the answer to the question is NO but if set B = {2, 5}, then the answer to the question is YES. Not sufficient.

(1)+(2) Both possible sets from (1) meet the condition stated in the second statement: \(\frac{1}{1}*\frac{1}{10}=\frac{1}{10}=0.1= terminating \ decimal\) and \(\frac{1}{2}*\frac{1}{5}=\frac{1}{10}=0.1= terminating \ decimal\). Thus we still have two sets, which give two different answers to the question. Not sufficient.



Answer: E.



Hi Bunuel

How will we get 2 in set A? can u pls explain..

As per my understanding, 2 more than a multiple of 3 means..It starts with {5,11,17...}

Pls help
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59147
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 22 Sep 2017, 10:22
1
1
zanaik89 wrote:
Bunuel wrote:
SOLUTION

Set A consists of all distinct prime numbers which are 2 more than a multiple of 3. If set B consists of distinct integers, is set B a subset of set A?

According to the definition set A = {2, 5, 11, 17, 23, 29, 41, ...}

(1) Set B consist of two positive integers whose product is 10. 10 can be broken into the product of two integers in two ways: 10 = 1*10 and 10 = 2*5. If set B = {1, 10}, then the answer to the question is NO but if set B = {2, 5}, then the answer to the question is YES. Not sufficient.

(2) The product of reciprocals of all elements in set B is a terminating decimal. If set B = {4, 8}, then the answer to the question is NO but if set B = {2, 5}, then the answer to the question is YES. Not sufficient.

(1)+(2) Both possible sets from (1) meet the condition stated in the second statement: \(\frac{1}{1}*\frac{1}{10}=\frac{1}{10}=0.1= terminating \ decimal\) and \(\frac{1}{2}*\frac{1}{5}=\frac{1}{10}=0.1= terminating \ decimal\). Thus we still have two sets, which give two different answers to the question. Not sufficient.



Answer: E.



Hi Bunuel

How will we get 2 in set A? can u pls explain..

As per my understanding, 2 more than a multiple of 3 means..It starts with {5,11,17...}

Pls help


0 is a multiple of 3 (0 is a multiple of every positive integer) so 2 is 2 more than a multiple of 3.
_________________
Intern
Intern
avatar
B
Joined: 01 Nov 2018
Posts: 7
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 09 Dec 2018, 05:33
Hi! Sorry but how do you know from statement 2 that set B has only 2 values? Is it because of the reciprocity given in the question stem?
Senior Manager
Senior Manager
User avatar
P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 440
Premium Member
Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 26 May 2019, 14:05
lukevol123 we don't know that it only has two. It's just a simple example picking numbers to see a pattern.

Given: {A} is pn = 3q+2 so multiples of 3 + 2 that are prime... so A is {2, 5, 11 ...}
{B} = some non-repeating amount of ints
Question: are all ints in {B} in {A}?

(1) Set B consist of two positive integers whose product is 10.
10 = 1*10 or 2*5
If B is {1,10} ... NO
If B is {2,5} ... YES
Insufficient.

(2) The product of reciprocals of all elements in set B is a terminating decimal
If it's a terminating decimal then the reciprocals of the ints have to only have 2s, 5s or 10s.
If B is {1,10} then it's 1/1 * 1/10 = 1/10, a terminating decimal... NO
If B is {2,5} then it's 1/2 * 1/5 = 1/10, a terminating decimal... YES

(3) Combining both doesn't add any new information.
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1272
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

Show Tags

New post 28 Jul 2019, 07:38
1
Asked vide a PM : Why are we skipping prime numbers 7 and 19 , what does this line actually mean, Set A consists of all distinct prime numbers which are 2 more than a multiple of 3"

Response:


it means we need to consider all numbers in the form of N= 3n+2 , which are prime.
putting n = 0,1,2,3,4..., we get N = 2,5,8,11,14,17...
Now we need to select the numbers which are prime.
So the Set A = {2,5,11,17...}
_________________
GMAT Club Bot
Re: Set A consists of all distinct prime numbers which are 2 mor   [#permalink] 28 Jul 2019, 07:38
Display posts from previous: Sort by

Set A consists of all distinct prime numbers which are 2 mor

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne