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# If P is a set of integers from 2 to 100 (Inclusive)

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Director
Joined: 18 Jul 2018
Posts: 679
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
If P is a set of integers from 2 to 100 (Inclusive)  [#permalink]

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10 Oct 2018, 17:54
2
00:00

Difficulty:

55% (hard)

Question Stats:

55% (02:26) correct 45% (02:22) wrong based on 23 sessions

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If P is a set of integers from 2 to 100 (Inclusive) and Q is another set of integers from 101 to 200 (Inclusive). Then how many elements of Q are there such that Q doesn't have any elements of P as factors?

a) 21
b) 22
c) 23
d) 24
e) 25

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Manager
Joined: 08 Sep 2008
Posts: 123
Location: India
Concentration: Operations, General Management
Schools: ISB '20
GPA: 3.8
WE: Operations (Transportation)
Re: If P is a set of integers from 2 to 100 (Inclusive)  [#permalink]

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10 Oct 2018, 18:02
Afc0892 wrote:
If P is a set of integers from 2 to 100 (Inclusive) and Q is another set of integers from 101 to 200 (Inclusive). Then how many elements of Q are there such that Q doesn't have any elements of P as factors?

a) 21
b) 22
c) 23
d) 24
e) 25

Basically question is asking how many prime number is there between 101 to 200.

Total:21 prime numbers.

I have counted and it took long time. Any shorter way to reach the answer?

Sent from my iPad using GMAT Club Forum mobile app
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Vishal

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Director
Joined: 18 Jul 2018
Posts: 679
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If P is a set of integers from 2 to 100 (Inclusive)  [#permalink]

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10 Oct 2018, 18:10
vishalkazone wrote:
Afc0892 wrote:
If P is a set of integers from 2 to 100 (Inclusive) and Q is another set of integers from 101 to 200 (Inclusive). Then how many elements of Q are there such that Q doesn't have any elements of P as factors?

a) 21
b) 22
c) 23
d) 24
e) 25

Basically question is asking how many prime number is there between 101 to 200.

Total:21 prime numbers.

I have counted and it took long time. Any shorter way to reach the answer?

Sent from my iPad using GMAT Club Forum mobile app

There are 25 primes between 1-100 and 46 primes between 1-200.

168 primes between 1 to 1000. This info is enough for GMAT
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Re: If P is a set of integers from 2 to 100 (Inclusive)   [#permalink] 10 Oct 2018, 18:10
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