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Manager  Joined: 06 Feb 2010
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Schools: University of Dhaka - Class of 2010
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If k is an integer  [#permalink]

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Question Stats: 76% (01:15) correct 24% (01:30) wrong based on 1735 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
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: $$0.0025*0.025*0.00025*10^{12}=25*25*25=integer$$

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Manager  Joined: 11 Sep 2013
Posts: 104
Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,  [#permalink]

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

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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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4
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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Originally posted by GMATinsight on 27 Oct 2015, 05:29.
Last edited by GMATinsight on 25 Jan 2020, 00:03, edited 1 time in total.
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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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2
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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Joined: 19 Apr 2016
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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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2
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: $$0.0025*0.025*0.00025*10^{12}=25*25*25=integer$$

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,  [#permalink]

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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: $$0.0025*0.025*0.00025*10^{12}=25*25*25=integer$$

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.

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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 i want to remove decimal from 0.025, won't i do 25/1000..?
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,  [#permalink]

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saurabh1407 wrote:
If i want to remove decimal from 0.025, won't i do 25/1000..?

_______________
Yes, that's correct.
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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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1
 Convert to Scientific Notation

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

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

 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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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
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Joined: 12 Sep 2015
Posts: 4226
Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,  [#permalink]

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Top Contributor
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, $$k = 12$$

Cheers,
Brent
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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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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

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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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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.

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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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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GMAT 1: 690 Q50 V34 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

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]

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because the final number of the product is not 10, we can not reduce any time of 10. for example
if we have
0.5*0.002 *k^x
we do not need k^4, we need only K^3 because 5*2=10
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Posts: 2
Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,  [#permalink]

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can someone please help me understand the OG explanation. It says that "since the unit digit of (25)^3 is 5, it follows that if K=11, then the 10th digit of N would be 5, and thus N would not be an integer; and if K=12, then N would be (25)^3 x (10)^0, which is an integer". what do they mean by this?? won't (25)^3 also be an integer?? Re: If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer,   [#permalink] 13 Nov 2019, 08:51

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