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Thread: Logical Reasoning

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    Logical Reasoning

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    Hey, can you please help me solve this quantitative problem?


    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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    An Urch Guru Pundit Swami Sage
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    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

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    GRE-GMAT Instructor Brent Hanneson's Avatar
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    Re: Logical Reasoning

    Quote Originally Posted by Ciara View Post
    Hey, can you please help me solve this quantitative problem?


    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:
    SPOILER: A

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