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If A=15^12 and B=10^16 which of the following is true?

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If A=15^12 and B=10^16 which of the following is true?  [#permalink]  01 Mar 2007, 07:30
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If A=15^12 and B=10^16 which of the following is true?

(I) A>B
(II) When written in decimal notation, A+B has more digits than does the smaller of {A,B}.
(III) A+B is divisible by 10

(A) I only
(B) II only
(C) I and III
(D) II and III
(E) I and II
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I say B

I) B is clearly going to be bigger as it is to the 16th power rather than the 12th power. Sorry this isnt a good explanation its just kind of intuitive.

II) The smaller of the 2 is A and its going to have less digits than B, so when you add them together it is still going to have less digits.

III) 15 times itself any number of times will always end in 5. 10 times itself any number of times will always end in 0. Added together, it will end in 5 and not be divisible by 10.
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I say B too.

I think burningskulls explained II and III

To be sure on I and to calculate it fast...(so that we dont have rely on intuition)

I did it this way

15 ^ 12 = (10 ^ 12) * (1.5 ^ 12)
10 ^ 16 = (10 ^ 12) * (10 ^ 4 )

So effectively you cancel out (10 ^12)

1.5 ^ 12 = 2.25 ^ 6 = 4.xx ^ 3 which we know for sure is less than 10 ^ 4
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