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

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

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New post 01 Nov 2019, 05:08
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The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 100 and n is not prime, what is the greatest possible value of f(n)?

(A) 99
(B) 95
(C) 91
(D) 87
(E) 78


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

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New post 01 Nov 2019, 05:42
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Bunuel wrote:
The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 100 and n is not prime, what is the greatest possible value of f(n)?

(A) 99
(B) 95
(C) 91
(D) 87
(E) 78


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f(n)= the product of the distinct prime factors of n
for given options
99 ; 3^2*11 ; 33
95 ; 5*19 ; 95
91 ; 7*13 ; 91
87 ; 3*29 ; 87
78 ; 2*3*13 ; 78
IMO B ; 95
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Re: The function f is defined for all positive integers n by the following  [#permalink]

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New post 02 Nov 2019, 06:59
Bunuel wrote:
The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 100 and n is not prime, what is the greatest possible value of f(n)?

(A) 99
(B) 95
(C) 91
(D) 87
(E) 78


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(A) 99 = 9*11 = 3^2*11 --> Product of distinct prime factors = 3*11 = 33
(B) 95 = 19*5 --> Product of distinct prime factors = 5*19 = 95
(C) 91 = 13*7 --> Product of distinct prime factors = 13*7 = 91
(D) 87 = 3*29 --> Product of distinct prime factors = 3*29 = 87
(E) 78 = 2*3*13 --> Product of distinct prime factors = 2*3*13 = 78

IMO Option B
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Re: The function f is defined for all positive integers n by the following   [#permalink] 02 Nov 2019, 06:59
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