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Re: Your Opponent is the exponent [#permalink]
16 Mar 2013, 09:27

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3,276,800,000 = 32,768 x 100,000 = 2^15 x 100,000 = 2^15 x 5^5 x 2^5 = 2^20 x 5^5

Therefore x =0, y =10, z = 5

xy/z = 0

The answer is B. Although this detailed explanation has been provided, you can straightaway reach the answer by realizing that x=0 since the large number given does not have 3 as a factor, and so xy/z has to be 0. _________________

Re: Your Opponent is the exponent [#permalink]
16 Mar 2013, 10:22

GyanOne wrote:

3,276,800,000 = 32,768 x 100,000 = 2^15 x 100,000 = 2^15 x 5^5 x 2^5 = 2^20 x 5^5

Therefore x =0, y =10, z = 5

xy/z = 0

The answer is B. Although this detailed explanation has been provided, you can straightaway reach the answer by realizing that x=0 since the large number given does not have 3 as a factor, and so xy/z has to be 0.

Thanks but how did you get that the big number = 2^15? and why the absence of 3 from the factors would lead the fraction to be = zero? _________________

Re: Your Opponent is the exponent [#permalink]
16 Mar 2013, 14:02

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If we know that 3,276,800,000 is not divisible by 3 (which by the way you can quickly test by adding the digits of the number together and seeing whether they are divisble by 3) , this implies that when it is expressed in the form (3^x) (4^y) (5^z) the x=0. Hence xy/z =0 Concerning the 2^15, either you know the powers of 2 or you don't. This one is indeed very high so it seems unlikely to know it by heart. But if you divide 32768 by 8 for example you land on 4096 (which is 2^12) so you eventually figure out that it's 2^15. But again, this was not necessary in order to solve the question.

Re: For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,0 [#permalink]
07 Sep 2013, 12:48

'x' is the easiest to check here.. just add the digits of the number, sum is 26, thus this is not a multiple of 3.. since 'x' is an integer it must be '0'.. now neither of 'y' or 'z' could be '0' because just by looking we see that this number has trailing zeroes so it must have both 2 and 5...

so simply since 'x' is '0' the given solution is '0'. Hence B

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