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Math Expert V
Joined: 02 Sep 2009
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Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

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Difficulty:   95% (hard)

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

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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

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

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3
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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.

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

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

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

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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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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

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- Stne
Math Expert V
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Posts: 59147
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

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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.

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

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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.

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 V
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Posts: 59147
Re: Set A consists of all distinct prime numbers which are 2 mor  [#permalink]

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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.

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

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

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

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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...}
_________________ Re: Set A consists of all distinct prime numbers which are 2 mor   [#permalink] 28 Jul 2019, 07:38
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