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If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,

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If k is an integer [#permalink]

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If k is an integer and (.0025)(.025)(.00025)10^k is an integer, what is the least possible value of K?

(A) -12
(B) -6
(C) 0
(D) 6
(E) 12
[Reveal] Spoiler: OA

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Re: If k is an integer [#permalink]

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monirjewel wrote:
If k is an integer and (.0025)(.025)(.00025)10^k is an integer, what is the least possible value of K?

(A) -12
(B) -6
(C) 0
(D) 6
(E) 12


Given: \(0.0025*0.025*0.00025*10^k=integer\)

There are 4 decimal places after zero in 0.0025, 3 decimal places after zero in 0.025 and 5 decimal places after zero in 0.00025 so in order the product to be an integer k must be at least 4+3+5=12 to convert all these fractions into the integers, in this case: \(0.0025*0.025*0.00025*10^{12}=25*25*25=integer\)

Answer: E.
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Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer, [#permalink]

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New post 18 Oct 2015, 13:12
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Bunuel wrote:
If k is an integer and (0.0025)(0.025)(0.00025) × 10k is an integer, what is the least possible value of k?

(A) −12
(B) −6
(C) 0
(D) 6
(E) 12

Kudos for a correct solution.


It should be 10^k, not 10k

If so, Ans: E

(0.0025)(0.025)(0.00025) × 10^k = 10^k/(2^6*10^6).

=> k=6+6=12
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Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer, [#permalink]

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(0.0025)(0.025)(0.00025) × 10k
\((25*10^-^4*25*10^-^3*25*10^-^5)*10^k\)
\((25*10^-^1^2)*10^k\)

Answer E = 12
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Re: If k is an integer [#permalink]

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New post 27 Oct 2015, 05:29
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monirjewel wrote:
If k is an integer and (.0025)(.025)(.00025)10^k is an integer, what is the least possible value of K?

(A) -12
(B) -6
(C) 0
(D) 6
(E) 12



(.0025)(.025)(.00025)10^k = Integer

{25*10^(-4)}{25*10^(-3)}{25*10^(-5)}×10^k = Integer

(25^3)*10^(k-12) = Integer

I.e. (k-12) = Integer
I.e. Min (k-12)=0
I.e. (k)min = 12

Ans: Option E
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Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer, [#permalink]

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New post 11 Dec 2015, 12:12
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since 25 to the power any integer will always yield last digit as 5 and not yield any 0, k is just summation of number of places we need to move the decimal point to get each individual number to be an integer i.e. 4+3+5=12
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If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer, [#permalink]

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Bunuel wrote:
monirjewel wrote:
If k is an integer and (.0025)(.025)(.00025)10^k is an integer, what is the least possible value of K?

(A) -12
(B) -6
(C) 0
(D) 6
(E) 12


Given: \(0.0025*0.025*0.00025*10^k=integer\)

There are 4 decimal places after zero in 0.0025, 3 decimal places after zero in 0.025 and 5 decimal places after zero in 0.00025 so in order the product to be an integer k must be at least 4+3+5=12 to convert all these fractions into the integers, in this case: \(0.0025*0.025*0.00025*10^{12}=25*25*25=integer\)

Answer: E.



Hi. Can you please explain why it's not 10^-12? I understand how you get to 12, but have issues with how to know if it should be negative or positive.
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Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer, [#permalink]

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New post 04 Mar 2017, 02:15
Expert's post
mhill5446 wrote:
Bunuel wrote:
monirjewel wrote:
If k is an integer and (.0025)(.025)(.00025)10^k is an integer, what is the least possible value of K?

(A) -12
(B) -6
(C) 0
(D) 6
(E) 12


Given: \(0.0025*0.025*0.00025*10^k=integer\)

There are 4 decimal places after zero in 0.0025, 3 decimal places after zero in 0.025 and 5 decimal places after zero in 0.00025 so in order the product to be an integer k must be at least 4+3+5=12 to convert all these fractions into the integers, in this case: \(0.0025*0.025*0.00025*10^{12}=25*25*25=integer\)

Answer: E.



Hi. Can you please explain why it's not 10^-12? I understand how you get to 12, but have issues with how to know if it should be negative or positive.


10^(-12) = 1/10^12

It's not 10^(-12) because if you substitute this value there you won't get an integer.

You can check easier example: 0.12*10^(-2) = 0.12*1/10^2=0.0012 but 0.12*10^2 = 12.
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Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer, [#permalink]

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monirjewel wrote:
If k is an integer and (.0025)(.025)(.00025)10^k is an integer, what is the least possible value of K?

(A) -12
(B) -6
(C) 0
(D) 6
(E) 12


We are given the expression:

0.0025 x 0.025 x 0.00025 x 10^k = integer

To determine the least possible value of k, we want to use our rules of multiplication with decimals. When multiplying decimals, the final product has an equal number of decimal places to the decimal places of the numbers being multiplied. Let’s start by counting the number of decimal places.

0.0025 has 4 decimal places

0.025 has 3 decimal places

0.00025 has 5 decimal places

Thus, the result of 0.0025 x 0.025 x 0.00025 will have 12 decimal places.

In order for 0.0025 x 0.025 x 0.00025 x 10^k = integer, k would have to be at least 12, since 10^12 times any number with 12 decimal places would move the decimal point of that number 12 places to the right, making it an integer.

Answer: E
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Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,   [#permalink] 08 Dec 2017, 11:25
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