1. ## Logical Reasoning

A googol is the number that is written as 1 followed by 100 zeros. if G represents a googol, what is the sum of the digits of G/8 + G/5 + G/4 + G/2 ?

a. 13
b. 22
c. 107
d. 400
e. 1075  Reply With Quote

2. ## Re: Logical Reasoning

This is made much simpler by understanding that you will still end up with mostly 0s. I think the answer is identical if you are dealing with 1000 instead of G.

G/8 = 125...
G/5= 200...
G/4 = 250....
G/2= 500...

so 1+ 2+ 5 + 2 +2 +5 +5 = 22  Reply With Quote

3. ## Re: Logical Reasoning Originally Posted by Ciara A googol is the number that is written as 1 followed by 100 zeros. if G represents a googol, what is the sum of the digits of G/8 + G/5 + G/4 + G/2 ?

a. 13
b. 22
c. 107
d. 400
e. 1075
G = 10^100
We can rewrite this as follows: G = (10^3)(10^97)
Or we can say G = (1000)(10^97)

So, G/8 = (1000)(10^97)/8 = (125)(10^97)
G/5 = (1000)(10^97)/5 = (200)(10^97)
G/4 = (1000)(10^97)/4 = (250)(10^97)
G/2 = (1000)(10^97)/2 = (500)(10^97)

So, G/8 + G/5 + G/4 + G/2 = (125)(10^97) + (200)(10^97) + (250)(10^97) + (500)(10^97)
= (10^97)(125 + 200 + 250 + 500)
= (10^97)(1075)
This evaluates to be 1075 followed by 97 zeros
So, the sum of the digits = 1 + 0 + 7 + 5 + a bunch of zeros
= 13

SPOILER: A  Reply With Quote