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# Logical Reasoning

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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

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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

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• 2 weeks later...

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

A

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