Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Given Kudos: 0
WE:Business Development (Energy and Utilities)
Re: If 3x(52) is divided by 35(53), the quotient terminates with
[#permalink]
17 Aug 2018, 16:28
Explanation
When a non-multiple of 3 is divided by 3, the quotient does not terminate (for instance, \(\frac{1}{3}= 0.333\)…).
Since \(\frac{3^x(5^2)}{3^5(5^2)}\)does not repeat forever, x must be large enough to cancel out the \(3^5\) in the denominator.
Thus, x must be at least 5. Note that the question asks what must be true. Choice (D) must be true.
Choice (E), x = 5, represents one value that would work, but this choice does not have to be true.