Approximation--Someone please post an explanation

Question

If x > 0, which of the following best
approximates the value of x if  5^{23}  -  4^{11} = x^2  ?
(A)  5^{34}  
(B)  5^{12} 
(C)  5^{10} 
(D)  5^5 
(E)  5^3

YourDreamTheater · Answer

How is that OA correct?

5^{23} - 4^{11} = (5^{12})^2 = 5^{24}?

If A, B, and C are all positive, and if A - B = C, then A cannot be less than C.  5^{23}  cannot be less than the answer (which, in this case, is  (5^{12})^2 = 5^{24} )

YourDreamTheater · Answer

Well, I guess it's just an approximation... even still.

Where is this question from?

gurpreetsingh · Answer

C seems to be the only probable choice.

asch13 · Answer

I think you forgot the  x^2  on the other side if you got  5^{24}=x^2  then  x = 5^{12} 
I don't really follow how you got to  5^{24}  though

YourDreamTheater · Answer

I didn't. I looked at the OA (5^12) and I saw that it doesn't make any sense when plugged into the problem.

However, the scale of 4^11 is so small compared to 5^23 that 5^24 may indeed be the closest value.

asch13 · Answer

That makes sense, I would agree that  5^{10}  makes more sense, maybe the answer key is wrong. I got it from a pdf of problems from a one time tutor

Thanks

Approximation--Someone please post an explanation

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