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Director
Joined: 16 May 2014
Posts: 592
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GRE 1: Q165 V161
If S1 = {1, 2, 3, 4, ... , 23} and S2
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17 Mar 2016, 07:08
17 Mar 2016, 07:08
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Question Stats:
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If S1 = {1, 2, 3, 4, ... , 23} and S2 = {207, 208, 209, 210, 211, ... , 691}, how many elements of the set S2 are divisible by at least four distinct prime numbers that are elements of the set S1?
(a) 9
(b) 8
(c) 11
(d) 12
(e) 7
(a) 9
(b) 8
(c) 11
(d) 12
(e) 7
Director
Joined: 16 May 2014
Posts: 592
Given Kudos: 0
GRE 1: Q165 V161
Re: If S1 = {1, 2, 3, 4, ... , 23} and S2
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17 Mar 2016, 07:14
17 Mar 2016, 07:14
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Explanation
If a number of the set S2 is divisible by at least four distinct prime numbers of the set S1, then it will be divisible by their product as well.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 7, i.e. 210 = 3.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 11, i.e. 330 = 2.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 13, i.e. 390 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 17, i.e. 510 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 19, i.e. 570 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 23, i.e. 690 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 7 and 11, i.e. 462 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 7 and 13, i.e. 546 = 1.
numbers in set S1 that divides any of the elements of set S2.
Hence, the required number of elements = 11.
General Discussion
Re: If S1 = {1, 2, 3, 4, ... , 23} and S2
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14 Dec 2018, 07:13
14 Dec 2018, 07:13
1
soumya1989 wrote:
Explanation
If a number of the set S2 is divisible by at least four distinct prime numbers of the set S1, then it will be divisible by their product as well.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 7, i.e. 210 = 3.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 11, i.e. 330 = 2.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 13, i.e. 390 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 17, i.e. 510 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 19, i.e. 570 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 5 and 23, i.e. 690 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 7 and 11, i.e. 462 = 1.
- The number of numbers in S2 divisible by the product of 2, 3, 7 and 13, i.e. 546 = 1.
numbers in set S1 that divides any of the elements of set S2.
Hence, the required number of elements = 11.
Why 11? I see you listed 8 elements divisible by 4 or more primes in set S1.
