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If 3x(52) is divided by 35(53), the quotient terminates with
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12 Aug 2018, 15:50
12 Aug 2018, 15:50
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Question Stats:
66% (01:43) correct
33% (01:39) wrong based on 92 sessions
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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 must be true?
(A) x is even
(B) x is odd
(C) x < 5
(D) x ≥ 5
(E) x = 5
(A) x is even
(B) x is odd
(C) x < 5
(D) x ≥ 5
(E) x = 5
Re: If 3x(52) is divided by 35(53), the quotient terminates with
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16 Aug 2018, 00:22
16 Aug 2018, 00:22
2
\(\frac{3^x5^2}{3^55^3}\) = \(\frac{3^x}{3^55}\). Since \(\frac{1}{5}\) = 0.2. In order for a fraction to have a terminating decimal, the denominator should only consist of either 2s or 5s.
Hence x≥5.
D is the answer.
Hence x≥5.
D is the answer.
Re: If 3x(52) is divided by 35(53), the quotient terminates with
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17 Aug 2018, 16:28
17 Aug 2018, 16:28
2
Expert Reply
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.
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.
