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

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Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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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
[Reveal] Spoiler: OA

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Re: Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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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.
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Re: Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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New post 17 Feb 2014, 03:19
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
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Re: Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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New post 17 Feb 2014, 03:23
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.
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Collection of Questions:
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Re: Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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New post 17 Feb 2014, 03:47
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
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Re: Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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New post 23 Feb 2014, 05:01
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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.
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Re: Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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New post 23 Feb 2014, 05:05
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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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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New post 22 Sep 2017, 09:16
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

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Re: Set A consists of all distinct prime numbers which are 2 mor [#permalink]

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New post 22 Sep 2017, 09:22
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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Set A consists of all distinct prime numbers which are 2 mor   [#permalink] 22 Sep 2017, 09:22
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