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# If 3x(52) is divided by 35(53), the quotient terminates with

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Joined: 07 Jun 2014
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If 3x(52) is divided by 35(53), the quotient terminates with [#permalink]  12 Aug 2018, 15:50
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Question Stats:

41% (01:34) correct 58% (01:17) wrong based on 12 sessions
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
[Reveal] Spoiler: OA

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Joined: 15 Aug 2018
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Re: If 3x(52) is divided by 35(53), the quotient terminates with [#permalink]  16 Aug 2018, 00:22
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KUDOS
$$\frac{3^x5^2}{3^55^3}$$ = $$\frac{3^x}{3^55}$$. 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.
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

Re: If 3x(52) is divided by 35(53), the quotient terminates with [#permalink]  17 Aug 2018, 16:28
Expert's post
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.
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Sandy
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Re: If 3x(52) is divided by 35(53), the quotient terminates with   [#permalink] 17 Aug 2018, 16:28
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