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.
1 Like
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
1 Like
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.