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Set consists of the positive multiples of 5

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yasir9909
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Set consists of the positive multiples of 5 [#permalink] New post   Updated on: 29 Aug 2016, 02:16
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Set X consists of the positive multiples of 5 and set Y consists of odd prime numbers less than 20.If set Z consists of every distinct integer less than 100 that is the product of one element from set X and one element from set Y,then set Z consists of how many elements?

    A). 12
    B). 14
    C). 15
    D). 16
    E). 18
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B

Originally posted by yasir9909 on 27 Aug 2016, 07:04.
Last edited by Carcass on 29 Aug 2016, 02:16, edited 2 times in total.
Edited by Carcass
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Sonalika42
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Re: Set consists of the positive multiples of 5 [#permalink] New post   27 Aug 2016, 09:02
I think answer should be C
Set Q--->5,10,15,20,25,30
Set Y--->3,5,7,11,13,17,19
set Z--->5 multiplying it with all the numbers in set Y--->7
10 multiplying it with 3, 7, 5 in set Y--->3
15 multiplying it with 3,5 in set Y-->2
20 multiplying it with 3 in set Y --->1
25 multiplying it with 3 in set Y --->1
30 multiplying it with with 3 in set Y --->1
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yasir9909
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Re: Set consists of the positive multiples of 5 [#permalink] New post   28 Aug 2016, 02:10
@Sonalika42

I also think answer should be C but I am not able to asses why it is given to be B in 1007 Practice Questions by Princeton Review.

I have edited the post because Q stands for Question while it was Set X so you also replace Q with X in your post
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Re: Set consists of the positive multiples of 5 [#permalink] New post   Updated on: 28 Aug 2016, 02:52
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@Sonalika42

Here is my solution to this question:

Set X = {5,10,15,20,25,30,35,...}
Set Y = {3,5,7,11,13,17,19}
Set Z = {3*5,3*10,3*15,3*20,3*25,3*30,
5*5,5*10,5*15,
7*5,7*10,
11*5,
13*5,
17*5,
19*5}
Z = {15,30,45,60,75,90,25,50,75,35,70,55,65,85,95}

It seems like as 75 is repeated so it is counted as one element in set Z.

=> Thus Set Z has 14 elements instead of 15.This could be the only justification for answer to be 14 i.e. (B)

Originally posted by yasir9909 on 28 Aug 2016, 02:21.
Last edited by yasir9909 on 28 Aug 2016, 02:52, edited 1 time in total.
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Re: Set consists of the positive multiples of 5 [#permalink] New post   28 Aug 2016, 02:47
My perception about repetition of elements in a set is right.This is what mentioned on sets on page 138,under caption Sets,Lits and Sequences in Official Guide of GRE,2nd Edition by ETS:

"When the elements of a set are given,repetitions are not counted as additional elements and the order of the elements is not relevant.Elements are also called members"

So this proves that 75 which is repeated in Set Z would be counted as one element instead of counting it twice.

Difficult questions on actual GRE Exam pose such subtle conceptual twists that make the test taker commit mistake and lose points on GRE

regards
m.yasir
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Sonalika42
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Re: Set consists of the positive multiples of 5 [#permalink] New post   28 Aug 2016, 03:08
@Yasir

Oops my wrong...... you are right it should be 14 i mistakenly repeated 75.
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Set consists of the positive multiples of 5 [#permalink] New post   30 Jul 2021, 10:48
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yasir9909 wrote:
Set X consists of the positive multiples of 5 and set Y consists of odd prime numbers less than 20.If set Z consists of every distinct integer less than 100 that is the product of one element from set X and one element from set Y,then set Z consists of how many elements?

    A). 12
    B). 14
    C). 15
    D). 16
    E). 18

Set X = {5*(1+2+3...20 ... n); n positive multiples}
Set Y = {3, 5, 7, 11, 13, 17, 19}
There are
5*1 times 7 primes = 7 elements {15, 25, 35, 55, 65, 85, 95}
5*2 times 3 primes = 3 elements {30, 50, 70}
5*3 times 2 primes = 2 elements {45, 75}
5*4 times 1 prime = 1 element {60}
5*5 times 1 prime = 1 element {75} <---- repeated with 5*3 times 2 primes, exclude since elements are distinct in set Z
5*6 times 1 prime = 1 element {90}
In total 15-1 OR 14 elements in set Z. Answer is B.

fixed.
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Re: Set consists of the positive multiples of 5 [#permalink] New post   24 Dec 2021, 02:11
1
This question is NOT from any official GRE sources. It is from Princeton [ref.] [ref-2].
Kindly remove the deceptive tag - "Source: OG Big Book".
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Re: Set consists of the positive multiples of 5 [#permalink] New post   24 Dec 2021, 02:42
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Expert Reply
XavierAlexander wrote:
This question is NOT from any official GRE sources. It is from Princeton [ref.] [ref-2].
Kindly remove the deceptive tag - "Source: OG Big Book".


Thank you. Fixed
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Re: Set consists of the positive multiples of 5 [#permalink]
24 Dec 2021, 02:42
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