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# Set X consists of all prime numbers less than 60. Set Y consists of al

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Joined: 09 Jul 2018
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Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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Updated on: 01 Sep 2018, 07:57
1
00:00

Difficulty:

75% (hard)

Question Stats:

45% (01:37) correct 55% (01:41) wrong based on 85 sessions

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Set X consists of all prime numbers less than 60. Set Y consists of all integers which have a remainder of 2 when divided by 7. How many integer values are part of both sets?

A. None
B. One
C. Two
D. Three
E. Four

Originally posted by harshitagarg on 30 Aug 2018, 12:30.
Last edited by Bunuel on 01 Sep 2018, 07:57, edited 2 times in total.
Renamed the topic and edited the OA.
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Posts: 7
Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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30 Aug 2018, 12:31
1
The official explanation provided is:
If the members of Set Y have a remainder of 2 when divided by 7, this means that they are each 2 more than a multiple of 7. Therefore, the members of Set Y are {9, 16, 23, 30, 37, 44, 51,58, …} The only members of Set Y that are prime numbers less than 60 are 23 and 37.

The correct answer is choice C.

CAN ANYONE CLARIFY WHY IS 2 NOT INCLUDED IN SET Y? THE REMAINDER WHEN 2 IS DIVIDED BY 7 IS 2 SO IT SHOULD BE INCLUDED IN THE SET?
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Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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30 Aug 2018, 12:45
harshitagarg wrote:
Set X consists of all prime numbers less than 60. Set Y consists of all integers which have a remainder of 2 when divided by 7. How many integer values are part of both sets?

A. None
B. One
C. Two
D. Three
E. Four

prime nos set X = [2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59]

Now divide by each number by 7 and see what the remainder is. 23-7*3=2, 37-7*5=2, so set Y has [23, 37].
Only 2 numbers are common in set X and Y, so answer is C.
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Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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30 Aug 2018, 12:48
1
harshitagarg wrote:
The official explanation provided is:
If the members of Set Y have a remainder of 2 when divided by 7, this means that they are each 2 more than a multiple of 7. Therefore, the members of Set Y are {9, 16, 23, 30, 37, 44, 51,58, …} The only members of Set Y that are prime numbers less than 60 are 23 and 37.

The correct answer is choice C.

CAN ANYONE CLARIFY WHY IS 2 NOT INCLUDED IN SET Y? THE REMAINDER WHEN 2 IS DIVIDED BY 7 IS 2 SO IT SHOULD BE INCLUDED IN THE SET?

I agree with you my friend. 2 is a prime number and $$\frac{2}{7}$$ = 0 remainder 2

Therefore, I believe the answer should be D. Three

Set X: 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59
Set Y: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65.....
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Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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30 Aug 2018, 12:57
MikeScarn wrote:
harshitagarg wrote:
The official explanation provided is:
If the members of Set Y have a remainder of 2 when divided by 7, this means that they are each 2 more than a multiple of 7. Therefore, the members of Set Y are {9, 16, 23, 30, 37, 44, 51,58, …} The only members of Set Y that are prime numbers less than 60 are 23 and 37.

The correct answer is choice C.

CAN ANYONE CLARIFY WHY IS 2 NOT INCLUDED IN SET Y? THE REMAINDER WHEN 2 IS DIVIDED BY 7 IS 2 SO IT SHOULD BE INCLUDED IN THE SET?

I agree with you my friend. 2 is a prime number and $$\frac{2}{7}$$ = 0 remainder 2

Therefore, I believe the answer should be D. Three

Set X: 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59
Set Y: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65.....

I believe because result of $$\frac{2}{7}$$ is not an integer.
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Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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30 Aug 2018, 13:06
Math Expert
Joined: 02 Sep 2009
Posts: 56371
Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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30 Aug 2018, 21:06
ammuseeru wrote:
Set X consists of all prime numbers less than 60. Set Y consists of all integers which have a remainder of 2 when divided by 7. How many integer values are part of both sets?

A. None
B. One
C. Two
D. Three
E. Four

Primes less than 60: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59. (17 primes)
Integers which have a remainder of 2 when divided by 7: 2, 9, 16, 23, 30, 37, 44, 51, 58, ...

There are three numbers in common of these two sets.

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Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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30 Aug 2018, 21:09
1
Bunuel wrote:
ammuseeru wrote:
Set X consists of all prime numbers less than 60. Set Y consists of all integers which have a remainder of 2 when divided by 7. How many integer values are part of both sets?

A. None
B. One
C. Two
D. Three
E. Four

Primes less than 60: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59. (17 primes)
Integers which have a remainder of 2 when divided by 7: 2, 9, 16, 23, 30, 37, 44, 51, 58, ...

There are three numbers in common of these two sets.

OA says C
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Joined: 02 Sep 2009
Posts: 56371
Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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30 Aug 2018, 21:13
ammuseeru wrote:
Bunuel wrote:
ammuseeru wrote:
Set X consists of all prime numbers less than 60. Set Y consists of all integers which have a remainder of 2 when divided by 7. How many integer values are part of both sets?

A. None
B. One
C. Two
D. Three
E. Four

Primes less than 60: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59. (17 primes)
Integers which have a remainder of 2 when divided by 7: 2, 9, 16, 23, 30, 37, 44, 51, 58, ...

There are three numbers in common of these two sets.

OA says C

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OA is wrong. Edited.
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Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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31 Aug 2018, 06:03
harshitagarg wrote:
Set X consists of all prime numbers less than 60. Set Y consists of all integers which have a remainder of 2 when divided by 7. How many integer values are part of both sets?

A. None
B. One
C. Two
D. Three
E. Four

If we write X = qXd+r and substitute q = 0,1, 2, 3, 4, ..... , then we would get X = 2, 9, 16, 23.... .
And number 2 is the smallest even prime number? So, why isn't 2 involved in the set ?
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Re: Set X consists of all prime numbers less than 60. Set Y consists of al  [#permalink]

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31 Aug 2018, 09:01
1
harshitagarg wrote:
Set X consists of all prime numbers less than 60. Set Y consists of all integers which have a remainder of 2 when divided by 7. How many integer values are part of both sets?

A. None
B. One
C. Two
D. Three
E. Four

OA: D

Set X :{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59}
Set Y :{2, 9, 16, 23, 30, 37, 44, 51, 58,..............}

$$3$$ integers i.e $$2,23,37$$ are part of both the sets.
Re: Set X consists of all prime numbers less than 60. Set Y consists of al   [#permalink] 31 Aug 2018, 09:01
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