If h(n) is defined as (1 + f(n))(1 - g(n)), what is h(1) + h(2) + . +

Question

f(n) and g(n) are defined as follows:
f(n) = {0 if n is even 1 if n is odd} and g(n) = {0 if n is a multiple of 5 1 if n is not a multiple of 5}

If h(n) is defined as (1 + f(n))(1 - g(n)), what is h(1) + h(2) + ... + h(1900)?

A. 550
B. 560
C. 570
D. 580
E. 590

gmatophobia · Answer

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h(n) = (1 + f(n))*(1 - g(n))

We can have four cases

1. n is even & a multiple of 5 
  h(n) = (1 + f(n))*(1 - g(n)) = (1+0)(1-0) = 1  
2. n is even & not a multiple of 5
  h(n) = (1 + f(n))*(1 - g(n)) = (1+0)(1-1) = 0  
3. n is odd & a multiple of 5
  h(n) = (1 + f(n))*(1 - g(n)) = (1+1)(1-0) = 2  
5. n is odd & not a multiple of 5
  h(n) = (1 + f(n))*(1 - g(n)) = (1+1)(1-1) = 0

After, solving for each of these cases we can summarize h(n) as -

\

Between 1 and 1900, the number of multiple of 5 =

\frac{1900 - 5 }{ 5} + 1  = 380

Out of these 380, 190 are even multiples and 190 are odd multiples.

Sum = (190*2) + 190 = 380 + 190 = 570

Option C

ArjunKumar25 · Answer

Reading this explanation is giving me gmatphobia. 
Is there a simpler and faster method to do this? I did it on the basis of the correct answer being a multiple of 3. It was probably by fluke I got it right.

ankitgoswami · Answer

h(n) = (1 + f(n))(1 - g(n))

We have to find h(1) + h(2) + ... + h(1900)

First see the term (1 - g(n)). We can eliminate terms where g(n) becomes 1 making (1 - g(n)) = 0. These will make h(n) = 0.

These terms are non multiples of 5. Eliminate them

Now we are left with

h(5) + h(10) + ... + h(1900)

Now h(odd 5,15,25...) = 2 and h(even 10,20,30...) = 1

Calculate no of even and odd terms

Even and odd each are 190 in number

So total sum = 190 * 3 = 570

Ans  C

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nasgmatbag · Answer

Quick and simple approach

Pattern is as follows, for every number other than a multiple of 5 the answer will be 0. Notice the pattern below for even and odd multiples of 5:

h(5) = (1 + 1)(1 - 0) = 2
h(10) = (1 + 0)(1 - 0) = 1
h(15) = (1 + 1)(1 - 0) = 2
h(20) = (1 + 0)(1 - 0) = 1

h(5) + h(10) = 3. To get from h(10) to h(1900) we gotta do this 190 times. So (3)(190) = 570

paritoshmahajan · Answer

h(n) = (1 + f(n)) (1 - g(n))

we need to add h(n) for n ranging from 1 to 1900.

The first thing I did was, to find out for how many n, will I get g(n) = 1. Because if g(n) = 1, then h(n) = (1 + f(n) * 0 = 0
Since g(n) is 1 for all non multiples of 5, we need to only calculate for all n which are multiples of 5, where h(n) = (1+f(n)) * 1

To calculate the number of multiples of 5, we can do 1900/5 = 380

Now, within those, if f(n) is odd, then h (n) = 1 + 1 = 2 ; else h(n) = 1 + 0 = 1

Now, since multiples of 5 will be odd when they aren't multiples of 10

h(n) = 2 for all multiples of 5 and not 10
h(n) = 1 for all multiples of 10

multiples of 10 = 1900/10 = 190

hence answer = 2*(no. of multiples of only 5) + 1* (no of multiples of 10) = 2*(190) + 1*190 = 570

bumpbot · Answer

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If h(n) is defined as (1 + f(n))(1 - g(n)), what is h(1) + h(2) + . +

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If h(n) is defined as (1 + f(n))(1 - g(n)), what is h(1) + h(2) + . +

Prep Toolkit

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