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# Given p is an integer and 0.00005*0.0005*0.005*10^p is an integer

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Math Expert
Joined: 02 Sep 2009
Posts: 58469
Given p is an integer and 0.00005*0.0005*0.005*10^p is an integer  [#permalink]

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20 Mar 2018, 22:48
00:00

Difficulty:

15% (low)

Question Stats:

91% (00:59) correct 9% (01:29) wrong based on 42 sessions

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Given p is an integer and $$0.00005*0.0005*0.005*10^p$$ is an integer, what is the least possible value of p?

(A) -12
(B) -9
(C) 0
(D) 9
(E) 12

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Re: Given p is an integer and 0.00005*0.0005*0.005*10^p is an integer  [#permalink]

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21 Mar 2018, 01:04
Bunuel wrote:
Given p is an integer and $$0.00005*0.0005*0.005*10^p$$ is an integer, what is the least possible value of p?

(A) -12
(B) -9
(C) 0
(D) 9
(E) 12

5 * 10^-5 * 5 * 10^-4 * 5 * 10^-3 * 10^p is an integer
125* 10^-12 * 10^p is an integer
125*10^(p-12) is int
p-12 >= 0
p>=12

Hence Option E.

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Given p is an integer and 0.00005*0.0005*0.005*10^p is an integer  [#permalink]

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23 Mar 2018, 10:42
Bunuel wrote:
Given p is an integer and $$0.00005*0.0005*0.005*10^p$$ is an integer, what is the least possible value of p?

(A) -12
(B) -9
(C) 0
(D) 9
(E) 12

The expression simply becomes,
$$125 * 10^-12 * 10^p$$

Or,$$125 * 10^ {-12 + p}$$

Or, $$125 * 10^{-12 + 12}$$

Or, $$125 * 10^0$$

$$125$$*$$1$$

Therefore, least value of "p" is 12 to keep the expression as integer.

(E)
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Given p is an integer and 0.00005*0.0005*0.005*10^p is an integer   [#permalink] 23 Mar 2018, 10:42
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