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For a positive integer n, f(n) and g(n) are defined as follows

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by Max@Math Revolution » Mon Mar 30, 2020 12:18 am

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[GMAT math practice question]

For a positive integer n, f(n) and g(n) are defined as follows

f(n)={0 , (n is a multiple of 5) 1 , (n is not a multiple of 5)
g(n)={0 , (n is a multiple of 7) 1 , (n is not a multiple of 7)

Moreover, h(n) is defined as (1 - f(n))(1 - g(n)).
What is the value of h(3) + h(6) + h(9) + … + h(2004) + h(2007)?

A. 13
B. 19
C. 38
D. 57
E. 152
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Re: For a positive integer n, f(n) and g(n) are defined as follows

by Max@Math Revolution » Wed Apr 01, 2020 1:04 am
=>

h(n) = 0 when f(n)=1 or g(n) = 1
h(n) = 1 when f(n)=0 and g(n)=0
Thus, we have h(n) = 1 when n is a multiple of both 5 and 7. It means we have h(n) = 1 when n is a multiple of 35.

3, 6, 9, … , 2016, 2019 are multiples of 3.
The function values of h for those numbers is 1 when they are multiples of 105 = 35*3.
2019 = 105*19 + 24
Thus, we have 19 multiples of 105 between 1 and 2007, inclusive.

Therefore, B is the answer.
Answer: B
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