This is problem number 32 from Divisibility and Primes, Manhattan 5lb

If 3^x(5^2) is divided by 3^5(5^3), the quotient terminates with one decimal digit. If x > 0, which of the following statements are true?

D. x >= 5

E. x = 5

(other options are not relevant)

So the doubt is regarding the solution in the book. According to the book option D is correct, as “Choice (E), x = 5, represents one value that would work, but this choice does not HAVE to be true”

if x = 5, the fraction would result in 1/5, which is 0.2. This IS true, so how is option (E) incorrect?

Usually, when you divide by 5 and 10 you get quotient terminating with one decimal digit.

Again, have you tried plugging in x=6 and see if it checks out? I just did and it does, indeed, check out. x=5 is only one case but plug in values greater than 5 and you’ll notice all of them will satisfy the given condition.

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The option does not say “one possible value of x is 5”, it says x = 5

The first statement is correct, the latter would be incorrect

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So, the point is that although x = 5 satisfies the condition, it implies that higher values of x won’t satisfy the condition. Thus, x >= 5 is a more general truth.