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If k is an integer and 0.0010101*10^k is greater than 1,000,

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Bunuel
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If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink] New post   23 Dec 2013, 07:37
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If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
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E
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Bunuel
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Re: If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink] New post   24 Dec 2013, 03:30
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SOLUTION

If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

No algebraic manipulation is needed for this one. Consider this: when we multiply 0.0010101 by 10^k (where k is a positive integer), decimal point in 0.0010101 moves k decimal places to the right. The product to be more than 1000 we should move decimal point 6 places to the right to get 1010>1000, thus the least value of k is 6.

Answer: E.
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Re: If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink] New post   11 Sep 2014, 02:36
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\(0.0010101*10^6 = 1010.1\)

Answer = 6 = E
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Re: If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink] New post   22 May 2017, 18:38
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Quote:

If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


In order for 0.0010101*10^k to be greater than 1,000, we need to move the decimal point in 0.0010101 six places to the right so that we have 1,010.1, which is greater than 1,000. Thus, the minimum value of k is 6.

Answer: E
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Re: If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink] New post   31 Aug 2019, 07:37
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Problem Solving
Question: 4
Category: Arithmetic Operations on rational numbers
Page: 62
Difficulty: 500


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A number > 1000 in the form will be 1001

In 0.0010101*10^k the highlighted part represents that part....

So, 10^k will be 10^6 , Answer must be (E)
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Re: If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink] New post   25 Dec 2013, 03:34
My explanation (It's basically the same as Bunuel's)
0.0010101*10^k > 1000
--> (1010.1)*10^-6*10^k >1000*10^0
--> (1010.1)*10^(k-6) >1000*10^0
--> because 1010.1 > 1000, we just need 10^(k-6) >= 10^0 --> k-6 >= 0 --> k >= 6
--> min K = 6.
E is the answer.

Cheer!
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Re: If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink] New post   16 Sep 2019, 07:48
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Problem Solving
Question: 4
Category: Arithmetic Operations on rational numbers
Page: 62
Difficulty: 500


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?
0.0010101*10^k > 1000
.0010101 * 1000000 = 1010.1>1000; k =6

IMO E
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Re: If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink] New post   11 Dec 2022, 23:45
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Re: If k is an integer and 0.0010101*10^k is greater than 1,000, [#permalink]
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