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# How many positive prime numbers are less than the integer n?

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Intern
Joined: 27 Feb 2012
Posts: 37

Kudos [?]: 27 [0], given: 5

How many positive prime numbers are less than the integer n? [#permalink]

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26 Dec 2012, 23:50
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Difficulty:

15% (low)

Question Stats:

74% (01:00) correct 26% (00:40) wrong based on 96 sessions

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How many positive prime numbers are less than the integer n?

(1) 14 < n < 20
(2) 13 < n < 17
[Reveal] Spoiler: OA

Kudos [?]: 27 [0], given: 5

Manager
Joined: 08 Apr 2012
Posts: 128

Kudos [?]: 113 [0], given: 14

Re: how many positive prime numbers are less than the integer n? [#permalink]

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27 Dec 2012, 00:16
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jsphcal wrote:
How many positive prime numbers are less than the integer n?

(1) 14 < n < 20

(2) 13 < n < 17

Lets consider all the positive prime numbers less than 20:

2, 3, 5, 7, 11, 13, 17, 19

(1) 14<n<20 and n is an integer

Value of n |||||||| positive prime numbers less than n
15 |||||||| 6 (2, 3, 5, 7, 11, 13)
16
17
18 |||||||| 7 (2, 3, 5, 7, 11, 13, 17)
19

Since we get 2 different answers, (1) is not sufficient

(2) 13 < n < 17

Value of n |||||||| positive prime numbers less than n
14 |||||||| 6 (2, 3, 5, 7, 11, 13)
15 |||||||| 6 (2, 3, 5, 7, 11, 13)
16 |||||||| 6 (2, 3, 5, 7, 11, 13)

Since (2) gives a definitive answer that there are 6 positive prime numbers less than n (whether n = 14, 15, or 16), (2) is sufficient.

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Shouvik
http://www.Edvento.com

Kudos [?]: 113 [0], given: 14

Intern
Joined: 27 Feb 2012
Posts: 37

Kudos [?]: 27 [0], given: 5

Re: how many positive prime numbers are less than the integer n? [#permalink]

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27 Dec 2012, 13:01
Edvento,

thanks this helps me to better understand why we ruled out 1 and why 2 is correct

Kudos [?]: 27 [0], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 42630

Kudos [?]: 135844 [0], given: 12715

Re: How many positive prime numbers are less than the integer n? [#permalink]

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28 Dec 2012, 03:23
jsphcal wrote:
How many positive prime numbers are less than the integer n?

(1) 14 < n < 20
(2) 13 < n < 17

Similar question to practice: collection-of-12-ds-questions-85441-60.html#p809394
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Kudos [?]: 135844 [0], given: 12715

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Re: How many positive prime numbers are less than the integer n? [#permalink]

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30 Sep 2014, 09:41
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Re: How many positive prime numbers are less than the integer n?   [#permalink] 30 Sep 2014, 09:41
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