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A googol is the number that is written as 1 followed by 100

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A googol is the number that is written as 1 followed by 100 [#permalink] New post 03 Nov 2016, 21:09
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 May 2018, 03:19, edited 3 times in total.
Edited by carcass
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Re: Quantitative [#permalink] New post 04 Nov 2016, 00:03
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Hi

We can write G= \(1*10^1^0^0\) or \(1000*10^9^7\)

Now evaluating all the component number


\(\frac{G}{8}\) =\(\frac{1000*10^9^7}{8}\) =\(125 * 10^9^7\).

\(\frac{G}{5}\) =\(\frac{1000*10^9^7}{5}\) =\(200 * 10^9^7\).

\(\frac{G}{4}\) =\(\frac{1000*10^9^7}{4}\) =\(250 * 10^9^7\).

\(\frac{G}{2}\) =\(\frac{1000*10^9^7}{2}\) =\(500 * 10^9^7\).


Adding them up, we have

\(1075 * 10^9^7\).

Thus sum of digits are 1+0+7+5 =13. Hence option A is correct.


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Re: Quantitative [#permalink] New post 17 Nov 2016, 12:20
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Ciara wrote:
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

Answer:
[Reveal] Spoiler:
A


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Re: A googol is the number that is written as 1 followed by 100 [#permalink] New post 09 May 2018, 15:01
Expert's post
Ciara wrote:
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



We can get common denominators in our expression and we have:

5G/40 + 8G/40 + 10G/40 + 20G/40

43G/40

43/40 x G

1.075 x 10^100

1,075 x 10^97

We can see that the number is 1,075 followed by 97 zeros; thus, the sum of the digits is 1 + 7 + 5 = 13 (we don’t need to add any digits that are 0).

Answer: A
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Re: A googol is the number that is written as 1 followed by 100   [#permalink] 09 May 2018, 15:01
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