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# The function f is defined for all positive integers p by the following

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Math Expert
Joined: 02 Sep 2009
Posts: 55271
The function f is defined for all positive integers p by the following  [#permalink]

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10 Sep 2017, 04:56
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Difficulty:

65% (hard)

Question Stats:

68% (01:54) correct 32% (01:46) wrong based on 42 sessions

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The function f is defined for all positive integers p by the following rule: f(p) is the number of prime numbers, each of which is less than p and has no positive factor in common with p other than 1. What is f(h)?

(1) h < 10
(2) h is a perfect square.

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Posts: 7686
Re: The function f is defined for all positive integers p by the following  [#permalink]

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10 Sep 2017, 04:59
Bunuel wrote:
The function f is defined for all positive integers p by the following rule: f(p) is the number of prime numbers, each of which is less than p and has no positive factor in common with p other than 1. What is f(h)?

(1) h < 10
(2) h is a perfect square.

so f(p) means all prime number less than p..

lets see each statement..
(1) h<10..
if h is 2, ans is 0
if h is 5 ans is 3 ( 2,3,5)
insuff

(2) h is a perfect square..
h is 4.. ans is 2 ------- 2 ,3
h is 9.. ans is 4-------- 2,3,5,7
so insuff

combined..
h can be 4 or 9 and ans can be 2 or 4
insuff

E
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The function f is defined for all positive integers p by the following  [#permalink]

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10 Sep 2017, 09:50
f(p)= number of prime numbers less than p.
f(h)=?
Statement 1)
h < 10
There are total 4 prime numbers(2,3,5,7) which are less than 10.
h can take any value between 1 to 9.
lets take h=4 then f(h)=2
and if we take h=7,then f(h)=3
Hence Insufficient.

(2) h is a perfect square.
h=4 then f(h)=2
h=9 then f(h)=4
hence Insufficient.

Even after combining 1) and 2)
h=1,4,9 and hence f(h) will take different values.
The function f is defined for all positive integers p by the following   [#permalink] 10 Sep 2017, 09:50
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