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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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New post 12 Nov 2010, 21:47
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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

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Re: If k is an integer  [#permalink]

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New post 12 Nov 2010, 23:03
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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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New post 20 Oct 2015, 10:41
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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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New post 03 Mar 2017, 18:59
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1
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
1
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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New post 08 Dec 2017, 11:25
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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]

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New post 16 Dec 2018, 23:56
If i want to remove decimal from 0.025, won't i do 25/1000..?
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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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If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,  [#permalink]

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New post 06 Mar 2019, 17:10
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[1] Convert to Scientific Notation

\((25 \times 10^{-4}) (25 \times 10^{-3}) (25 \times 10^{-5}) (10^k)\)

\((25 \times 10^{-12})(10^k)\)

[2] Solve

To cancel out \(10^{-12}\), k must equal 12.

\(10^{-12} \times 10^{12} = 10^0 = 1\)

\(25 \times 1 = 25\)
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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 09 Mar 2019, 06:47
Hi,

Can someone explain why not C can be the correct answer? As 10^0 equals 1. So 0 is the least possible value of K

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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 08 May 2019, 06:44
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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


Another approach is to convert everything to fractions.

\((0.0025)(0.025)(0.00025)(10^k)\) is an integer

So, \((\frac{25}{10,000})(\frac{25}{1,000})(\frac{25}{100,000})(10^k)\) is an integer

Simplify to get: \((\frac{25^3}{1,000,000,000,000})(10^k)\) is an integer

To create an integer, we need \(1,000,000,000,000=10^k\)

So, \(k = 12\)

Answer: E

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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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New post 08 May 2019, 11:31
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


Simply, we will just count how many digits after decimal.

Here,

.0025=4
.025=3
.00025=5

Thus, 4+3+5=12 digits

And K must be 12 to get the least integer

Answer is E

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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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New post 28 Jul 2019, 14:29
ScottTargetTestPrep 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


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



I was able to solve the question, but just curious, Why can K not be Zero since if we raise any number to zero we get 1? and both 1 and 0 are integers.
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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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New post 02 Aug 2019, 09:04
Shef08 wrote:
Hi,

Can someone explain why not C can be the correct answer? As 10^0 equals 1. So 0 is the least possible value of K

Posted from my mobile device


Because if k=0, then \((0.0025)(0.025)(0.00025)*10^k\) is equal to \((0.0025)(0.025)(0.00025)*1\), which is not an integer.

See, \((0.0025)(0.025)(0.00025)\) is equal to \((25*10^-4)(25*10^-3)(25*10^-5)\) which is equal to \(25^3*10^-12\).

For it to be an integer by itself, then the numerator would have to be equal to or a multiple of the denominator and \(25^3\) is not equal to \(10^-12\).
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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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New post 16 Sep 2019, 07:59
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


If k is an integer and (.0025)(.025)(.00025)10^k is an integer, what is the least possible value of K?
\(25 * 10^{-4} * 25* 10^{-3} * 25*10^{-5} * 10^k = 25*25*25 * 10^{-4-3-5+k}\)
-4-3-5+k =0
k = 12

IMO E
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Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,   [#permalink] 16 Sep 2019, 07:59
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