Sep 22 08:00 PM PDT  11:00 PM PDT A Revolutionary OnDemand GRE Prep Course with Target Test Prep. Try for $1 Sep 23 04:00 PM PDT  06:00 PM PDT Join my MyGuru for Free GMAT Math Refresher is the best workshop to learn about the basics and the advanced strategies required to get a 700+ GMAT score. Sep 23 08:00 PM PDT  09:00 PM PDT Learn how to evaluate your profile, skills, and experiences to determine if, when, and where you should apply to graduate school. Sep 27 08:00 PM PDT  09:00 PM PDT Working in collaboration with examPAL we will provide you with a unique online learning experience which will help you reach that higher score. Start your free 7 day trial today.
Author 
Message 
TAGS:


Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
WE: Business Development (Energy and Utilities)
Followers: 171
Kudos [?]:
2914
[5]
, given: 394

QOTD #8 When the decimal point of a certain positive decimal [#permalink]
03 Aug 2016, 17:08
5
This post received KUDOS
Question Stats:
58% (01:20) correct
41% (01:42) wrong based on 101 sessions
When the decimal point of a certain positive decimal number is moved six places to the right, the resulting number is 9 times the reciprocal of the original number. What is the original number? enter your valuePractice Questions Question: 21 Page: 154
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test




Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
WE: Business Development (Energy and Utilities)
Followers: 171
Kudos [?]:
2914
[6]
, given: 394

Re: QOTD #7 When the decimal point of a certain positive decimal [#permalink]
03 Aug 2016, 17:13
6
This post received KUDOS
ExplanationMoving the decimal point of a positive decimal number, n, six places to the right is equivalent to multiplying n by \(10^6\). In the question, you are given that the result of such a change is 9 times the reciprocal of the original number, or \(9(\frac{1}{n})\). Therefore \(n(10^6)=9(\frac{1}{n})\). You can solve this equation for n as follows. \(n(10^6)=9(\frac{1}{n})\) \(n^2=\frac{9}{(10^6)}\) \(n=0.003\).
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test



GRE Instructor
Joined: 10 Apr 2015
Posts: 3826
Followers: 148
Kudos [?]:
4471
[1]
, given: 69

Re: QOTD #7 When the decimal point of a certain positive decimal [#permalink]
24 Aug 2016, 11:14
1
This post received KUDOS
sandy wrote: Explanation
Moving the decimal point of a positive decimal number, n, six places to the right is equivalent to multiplying n by \(10^6\). In the question, you are given that the result of such a change is 9 times the reciprocal of the original number, or \(9(\frac{1}{n})\). Therefore \(n(10^6)=9(\frac{1}{n})\). You can solve this equation for n as follows.
\(n(10^6)=9(\frac{1}{n})\)
\(n^2=\frac{9}{(10^6)}\)
\(n=0.003\) Sandy's explanation is perfect. For anyone wondering about the last step, I might add two steps in between to get: \(n(10^6)=9(\frac{1}{n})\) \(n^2=\frac{9}{10^6}\) \(n^2=\frac{3}{10^3} * \frac{3}{10^3}\) \(n=\frac{3}{1000}\) \(n=0.003\)
_________________
Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course.
Sign up for GRE Question of the Day emails



Intern
Joined: 07 Jan 2019
Posts: 38
Followers: 0
Kudos [?]:
25
[1]
, given: 11

Re: QOTD #8 When the decimal point of a certain positive decimal [#permalink]
09 May 2019, 20:24
1
This post received KUDOS
I have a confusion: Given explanation: Moving the decimal point of a positive decimal number, n, six places to the right is equivalent to multiplying n by 10^6. My logic: Moving the decimal point of a positive decimal number, n, six places to the right is equivalent to multiplying n by 10^6.
Please explain.



Founder
Joined: 18 Apr 2015
Posts: 13310
Followers: 286
Kudos [?]:
3372
[0], given: 12174

Re: QOTD #8 When the decimal point of a certain positive decimal [#permalink]
10 May 2019, 02:24
What you said is incorrect. Multiply a number for \(10^{6}\) is equal to multiply the same number for \(\frac{1}{10^6}\) which is not the stem is asking you. Ask if something is still unclear to you Regards
_________________
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.



Intern
Joined: 07 Jan 2019
Posts: 38
Followers: 0
Kudos [?]:
25
[1]
, given: 11

Re: QOTD #8 When the decimal point of a certain positive decimal [#permalink]
10 May 2019, 07:56
1
This post received KUDOS
Thank u for d explanation. Suppose we have a positive decimal number: 0.123456 As per question, When the decimal point of a positive decimal number is moved six places to the right of the decimal point, we have 123456 * 10 ^ 6. Am I proceeding correctly? Posted from my mobile device



Founder
Joined: 18 Apr 2015
Posts: 13310
Followers: 286
Kudos [?]:
3372
[0], given: 12174

Re: QOTD #8 When the decimal point of a certain positive decimal [#permalink]
10 May 2019, 10:40
If you do have for instance a decimal number such as 0.1 * 10^6 = 0.1 * 1,000,000 = 100,000 See the GC book for reference Attachment: Regards
_________________
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.



Intern
Joined: 07 Jan 2019
Posts: 38
Followers: 0
Kudos [?]:
25
[1]
, given: 11

Re: QOTD #8 When the decimal point of a certain positive decimal [#permalink]
11 May 2019, 08:35
1
This post received KUDOS
Thank u for the clearcut explanation. Posted from my mobile device



GRE Instructor
Joined: 10 Apr 2015
Posts: 3826
Followers: 148
Kudos [?]:
4471
[2]
, given: 69

Re: QOTD #8 When the decimal point of a certain positive decimal [#permalink]
02 Jun 2020, 13:09
2
This post received KUDOS
sandy wrote: When the decimal point of a certain positive decimal number is moved six places to the right, the resulting number is 9 times the reciprocal of the original number. What is the original number? enter your valuePractice Questions Question: 21 Page: 154 A student asked me to solve this question. So here goes.... First we need to understand what must occur to move a decimal point 6 spaces to the RIGHT. Check out these examples: \((1.234567)(10^2) = 123.4567\). So, multiplying a number by \(10^2\) results in moving the decimal point 2 spaces to the RIGHT. \((6.73215333)(10^3) = 6,732.15333\). So, multiplying a number by \(10^3\) results in moving the decimal point 3 spaces to the RIGHT. \((9.865294501)(10^6) = 9,865,294.501\). So, multiplying a number by \(10^6\) results in moving the decimal point 6 spaces to the RIGHT. Let \(n\) = the original number This means \(\frac{1}{n}\) = the reciprocal of the original number GIVEN: When the decimal point of a certain positive decimal number is moved six places to the right, the resulting number is 9 times the reciprocal of the original number.We can reword this as: When \(n\) is multiplied by \(10^6\), the resulting number is 9 times \(\frac{1}{n}\) So our equation is: \((10^6)(n) = (9)(\frac{1}{n})\) Multiply both sides of the equation by \(n\) to get: \((10^6)(n^2) = 9\) Divide both sides of the equation by \(10^6\) to get: \(n^2 = \frac{9}{10^6}\) Rewrite the righthand side as follows: \(n^2=(\frac{3}{10^3})(\frac{3}{10^3}\)) In other words, \(n^2=(\frac{3}{10^3})^2\) This means: \(n = \frac{3}{10^3}=\frac{3}{1000}=0.003\) Answer: \(0.003\) Cheers, Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course.
Sign up for GRE Question of the Day emails



Intern
Joined: 04 Aug 2020
Posts: 1
Followers: 0
Kudos [?]:
0
[0], given: 1

Re: QOTD #8 When the decimal point of a certain positive decimal [#permalink]
04 Sep 2020, 13:05
GreenlightTestPrep wrote: sandy wrote: When the decimal point of a certain positive decimal number is moved six places to the right, the resulting number is 9 times the reciprocal of the original number. What is the original number? enter your valuePractice Questions Question: 21 Page: 154 A student asked me to solve this question. So here goes.... First we need to understand what must occur to move a decimal point 6 spaces to the RIGHT. Check out these examples: \((1.234567)(10^2) = 123.4567\). So, multiplying a number by \(10^2\) results in moving the decimal point 2 spaces to the RIGHT. \((6.73215333)(10^3) = 6,732.15333\). So, multiplying a number by \(10^3\) results in moving the decimal point 3 spaces to the RIGHT. \((9.865294501)(10^6) = 9,865,294.501\). So, multiplying a number by \(10^6\) results in moving the decimal point 6 spaces to the RIGHT. Let \(n\) = the original number This means \(\frac{1}{n}\) = the reciprocal of the original number GIVEN: When the decimal point of a certain positive decimal number is moved six places to the right, the resulting number is 9 times the reciprocal of the original number.We can reword this as: When \(n\) is multiplied by \(10^6\), the resulting number is 9 times \(\frac{1}{n}\) So our equation is: \((10^6)(n) = (9)(\frac{1}{n})\) Multiply both sides of the equation by \(n\) to get: \((10^6)(n^2) = 9\) Divide both sides of the equation by \(10^6\) to get: \(n^2 = \frac{9}{10^6}\) Rewrite the righthand side as follows: \(n^2=(\frac{3}{10^3})(\frac{3}{10^3}\)) In other words, \(n^2=(\frac{3}{10^3})^2\) This means: \(n = \frac{3}{10^3}=\frac{3}{1000}=0.003\) Answer: \(0.003\) Cheers, Brent Brent, could you show how this would work with plugging in numbers? I started with N = 3 3,000,000 = 1/3 * 9 All I end up with is 3,000,000 / 3. I'm struggling to understand where I went wrong in plugging in numbers. Thank you



GRE Instructor
Joined: 10 Apr 2015
Posts: 3826
Followers: 148
Kudos [?]:
4471
[1]
, given: 69

Re: QOTD #8 When the decimal point of a certain positive decimal [#permalink]
16 Sep 2020, 04:36
1
This post received KUDOS
rendition3 wrote: Brent, could you show how this would work with plugging in numbers?
I started with N = 3
3,000,000 = 1/3 * 9
All I end up with is 3,000,000 / 3. I'm struggling to understand where I went wrong in plugging in numbers.
Thank you We can't solve this question by plugging in numbers, since there's only one number that satisfies the given information. This means we would have to keep testing numbers until we get the one number that satisfies all of the given information. Let me first show you why the answer must be 0.003 (and then we'll take a look at your approach) If we move the decimal place 6 places to the right we get: 3000Since 0.003 = 3/1000, the reciprocal of 0.003 is 1000/3Notice that 3000 is 9 times the reciprocal, 1000/3That is, (9)( 1000/3) = 3000So, the correct answer must be n = 0.003 If we start testing numbers (as you have done), we'll find that all numbers (other than 0.003) won't satisfy the given information. For example, if n = 3, then we get 3,000,000 when we move the decimal point six spaces to the right The reciprocal of 3 is 1/3Since 3,000,000 does NOT equal (9)( 1/3), we can be certain the answer is NOT n = 3 Does that help?
_________________
Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course.
Sign up for GRE Question of the Day emails




Re: QOTD #8 When the decimal point of a certain positive decimal
[#permalink]
16 Sep 2020, 04:36





