If x = 2^b - (8^8 + 8^6), for which of the following b values is x clo

Question

If  x = 2^b - (8^8 + 8^6) , for which of the following b values is x closest to zero?

(A) 20
(B) 24
(C) 25
(D) 30
(E) 42

Kinshook · Answer

Asked: If  x = 2^b - (8^8 + 8^6) , for which of the following b values is x closest to zero?

x = 2^b - 8^6(8^2 + 1) ~ 2^b - 2^18*2^6 ~ 2^b - 2^24 
For b=24, x is closest to 0.

IMO B

Showmeyaa · Answer

x = 2^b - (8^8 + 8^6) 
 x = 2^b - 8^6(8^2 + 1) 
 x = 2^b - 2^{3*6}(65) 
 x = 2^b - 2^{18}(65) 
 x = 2^b - 2^{18}* 2^6  (As, 65 ~ 2^6 + 1)
 x = 2^b - 2^{24} 
So, (B) IMO!

LerPrivet · Answer

Could smb please explain, why we write 2^b-2^18(2^6+1) instead of 2^b-2^24-2^18?

Isn't it 8^8=(2^3)^8 = 8^24 and so on?

Thnx

Showmeyaa · Answer

If I understood your question correctly, you want to understand why the question stem was broken down to 2^b-2^18(2^6+1) instead of 2^b - 2^24 - 2^18
That's because we are interested in finding the value of b which makes the value of x close to 0. Ideally, every base should be 2 so that we can easily find for what value of b would x be closest to zero.

2^b - 2^24 - 2^18 -> This form doesn't help explain what could be possible value of b whereas this form(2^b-2^18(2^6+1)) helps.

Let me know, in case you had a different question in mind!

Malar95 · Answer

I was just having fun with numbers and then I looked at the answer option and tadaaa, answer was there. Hope that helped. Hope its correct.
Was doing it directly from the book.

bumpbot · Answer

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If x = 2^b - (8^8 + 8^6), for which of the following b values is x clo

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If x = 2^b - (8^8 + 8^6), for which of the following b values is x clo

Prep Toolkit

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