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

Question

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  \frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2}  ?

A. 13
B. 22
C. 107
D. 400
E. 1075

EgmatQuantExpert · Answer

Solution

Given:  
• Googol is the number written as 1 followed by 100 zeros
• It is represented by G

To find:  
• Sum of the digits of  \frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2}

Approach and Working:   
• The quotients in the divisions are as follows:
 o When G is divided by 8, quotient will be 125 followed by zeros 
 o When G is divided by 5, quotient will be 200 followed by zeros 
 o When G is divided by 4, quotient will be 250 followed by zeros 
 o When G is divided by 2, quotient will be 500 followed by zeros 
 o The final sum = 125 + 200 + 250 +500 = 1075 
• Therefore, the sum of the digits of the results = 1+0+7+5

As per the options, the correct answer is option A.

Answer: A

Tulkin987 · Answer

\frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2}   = 1.075G

Hence,  1+7+5=13 .

Answer: A

ScottTargetTestPrep · Answer

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

exc4libur · Answer

G=10^{100} 
 \frac{G}{8}  =10^{100}/2^{3}=10^{97}•5^3 
 \frac{G}{5}  =10^{100}/5=10^{99}•2 
 \frac{G}{4}  =10^{100}/2^{2}=10^{98}•5^2 
 \frac{G}{2}  =10^{100}/2=10^{99}•5 
 \frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2}=… 
 10^{97}•5^3+10^{99}•2+10^{98}•5^2+10^{99}•5…= 
 10^{97}(5^3+10^{2}•2+10•5^2+10^{2}•5)=… 
 10^{97}(125+200+250+500)=… 
 10^{97}(1075)=… 
 digits:1+7+5=13

Answer (A).

Kinshook · Answer

Given: A googol is the number that is written as 1 followed by 100 zeros.

Asked: if G represents a googol, what is the sum of the digits of  \frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2}  ?

G= 10^100 
 \frac{G}{8}= \frac{1000}{8} * 10^{97} = 125 * 10^{97} 
 \frac{G}{5} = \frac{1000}{5}* 10^{99} = 200 * 10^{97} 
 \frac{G}{4} = \frac{1000}{4} * 10^{98} = 250 * 10^{97} 
 \frac{G}{2} = \frac{1000}{2} * 10^{99} = 500 * 10^{97} 
 \frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2} = 1075 * 100^{97}

Sum of the digits of  \frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2}  = 1 + 0 + 7 + 5 = 13

IMO A

ShivamoggaGaganhs · Answer

It's simple,

write everything in powers of 10^98 as 100 is almost divided by all the denominators
Now, simplify,

you will get 107.5* 10^98
= 1075 * 10^97

This is 1075 followed by 97 zeroes

Upon adding all the digits you will get 13

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

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