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The decimal r = 2.666666 continues forever in that repeating
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Updated on: 20 Feb 2017, 10:04
Updated on: 20 Feb 2017, 10:04
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The decimal r = 2.666666 continues forever in that repeating decimal pattern. When written as a fraction in lowest terms, r = a/b, where a and b are positive numbers.
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A |
Quantity B |
a + b |
10 |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Originally posted by leonidbasin1 on 19 Feb 2017, 21:55.
Last edited by Carcass on 20 Feb 2017, 10:04, edited 1 time in total.
Last edited by Carcass on 20 Feb 2017, 10:04, edited 1 time in total.
Edited by Carcass
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
20 Feb 2017, 05:04
20 Feb 2017, 05:04
7
Expert Reply
2
Bookmarks
Explanation
We have r = 2.666666......
So 10r = 26.666666....
We can write \(10r - r = 26.66666... - 2.666666.. = 24\)
So \(9r = 24\) or \(r =\frac{24}{9}=\frac{8}{3}\).
Hence a= 8 and b = 3. Thus \(a+b = 11\)
Hence clearly Quantity A is greater.
Alternatively you can remember .666666 .... is actually \(\frac{2}{3}\). So \(2.6666....\) is \(2\frac{2}{3}\).
The method above would work with any number of repeating decimals.
_________________
We have r = 2.666666......
So 10r = 26.666666....
We can write \(10r - r = 26.66666... - 2.666666.. = 24\)
So \(9r = 24\) or \(r =\frac{24}{9}=\frac{8}{3}\).
Hence a= 8 and b = 3. Thus \(a+b = 11\)
Hence clearly Quantity A is greater.
Alternatively you can remember .666666 .... is actually \(\frac{2}{3}\). So \(2.6666....\) is \(2\frac{2}{3}\).
The method above would work with any number of repeating decimals.
_________________
Sandy
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General Discussion
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
20 Feb 2017, 10:35
20 Feb 2017, 10:35
sandy wrote:
Explanation
We have r = 2.666666......
So 10r = 26.666666....
We can write \(10r - r = 26.66666... - 2.666666.. = 24\)
So \(9r = 24\) or \(r =\frac{24}{9}=\frac{8}{3}\).
Hence a= 8 and b = 3. Thus \(a+b = 11\)
Hence clearly Quantity A is greater.
Alternatively you can remember .666666 .... is actually \(\frac{2}{3}\). So \(2.6666....\) is \(2\frac{2}{3}\).
The method above would work with any number of repeating decimals.
We have r = 2.666666......
So 10r = 26.666666....
We can write \(10r - r = 26.66666... - 2.666666.. = 24\)
So \(9r = 24\) or \(r =\frac{24}{9}=\frac{8}{3}\).
Hence a= 8 and b = 3. Thus \(a+b = 11\)
Hence clearly Quantity A is greater.
Alternatively you can remember .666666 .... is actually \(\frac{2}{3}\). So \(2.6666....\) is \(2\frac{2}{3}\).
The method above would work with any number of repeating decimals.
Thank you! But I am still feel confused. What am I missing? I get the first step and perhaps the second step, but then I get confused.
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
20 Feb 2017, 12:36
20 Feb 2017, 12:36
1
Expert Reply
The object is to get rid of .666666 or any other recurring decimal
So if a number has 7.66666 multiply by 10 and subtract the original number.
Example
17.56565656..... can be
100 * 17.5656... =1756.565656565...
(-) 17.5656... = 17.565656....
99 * 17.5656.. = 1739
17.5656... = \(\frac{1739}{99}\).
_________________
So if a number has 7.66666 multiply by 10 and subtract the original number.
Example
17.56565656..... can be
100 * 17.5656... =1756.565656565...
(-) 17.5656... = 17.565656....
99 * 17.5656.. = 1739
17.5656... = \(\frac{1739}{99}\).
_________________
Sandy
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Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE:Information Technology (Computer Software)
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
18 May 2018, 03:30
18 May 2018, 03:30
sandy wrote:
Explanation
We have r = 2.666666......
So 10r = 26.666666....
We can write \(10r - r = 26.66666... - 2.666666.. = 24\)
So \(9r = 24\) or \(r =\frac{24}{9}=\frac{8}{3}\).
Hence a= 8 and b = 3. Thus \(a+b = 11\)
Hence clearly Quantity A is greater.
Alternatively you can remember .666666 .... is actually \(\frac{2}{3}\). So \(2.6666....\) is \(2\frac{2}{3}\).
The method above would work with any number of repeating decimals.
We have r = 2.666666......
So 10r = 26.666666....
We can write \(10r - r = 26.66666... - 2.666666.. = 24\)
So \(9r = 24\) or \(r =\frac{24}{9}=\frac{8}{3}\).
Hence a= 8 and b = 3. Thus \(a+b = 11\)
Hence clearly Quantity A is greater.
Alternatively you can remember .666666 .... is actually \(\frac{2}{3}\). So \(2.6666....\) is \(2\frac{2}{3}\).
The method above would work with any number of repeating decimals.
If your alternate approach is followed then option B is the answer is'int it
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
18 May 2018, 03:47
18 May 2018, 03:47
1
Expert Reply
No, answer is still the same.
\(2\frac{2}{3}=\frac{8}{3}\).
_________________
\(2\frac{2}{3}=\frac{8}{3}\).
_________________
Sandy
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Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
18 May 2018, 09:16
18 May 2018, 09:16
1
The faster way if you know the rule.
put all the number without commas and subtract the periodical part and divide by so many 9 does the periodical part has: 26-2/9 = 24/9 = 8/3
put all the number without commas and subtract the periodical part and divide by so many 9 does the periodical part has: 26-2/9 = 24/9 = 8/3
Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE:Information Technology (Computer Software)
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
21 May 2018, 06:39
21 May 2018, 06:39
Wheree can I find the concepts related to such topic.. I need to dig more 
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
22 May 2018, 12:07
22 May 2018, 12:07
2
Expert Reply
Il PDF attached.
Regards
Regards
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GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]
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Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE:Information Technology (Computer Software)
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
23 May 2018, 19:07
23 May 2018, 19:07
1
Carcass wrote:
Il PDF attached.
Regards
Regards
I just went through it and I must say, it is insightful. KUDOS I am thankful to you.
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
23 May 2018, 23:13
23 May 2018, 23:13
1
Expert Reply
Soon we will have our own PDF GREPrepclub 
Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE:Information Technology (Computer Software)
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
24 May 2018, 02:00
24 May 2018, 02:00
1
Carcass wrote:
Soon we will have our own PDF GREPrepclub
I await that day. I really hope to have it soon.
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
26 May 2018, 10:16
26 May 2018, 10:16
6
Expert Reply
leonidbasin1 wrote:
The decimal r = 2.666666 continues forever in that repeating decimal pattern. When written as a fraction in lowest terms, r = a/b, where a and b are positive numbers.
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A |
Quantity B |
a + b |
10 |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Given: r = 2.666666....
We know that 2/3 = 666666....
So, 2.666666.... = 2 + 2/3
Let's combine 2 + 2/3 into ONE fraction
2 + 2/3 = 6/3 + 2/3 = 8/3
Since the fraction 8/3 is in lowest terms, we can say that r = 2.666666... = 8/3 = a/b
So, a = 8 and b = 3
We get:
Quantity A: 8 + 3
Quantity B: 10
Evaluate:
Quantity A: 11
Quantity B: 10
Answer: A
Cheers,
Brent
_________________
Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE:Information Technology (Computer Software)
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
26 May 2018, 21:11
26 May 2018, 21:11
1
GreenlightTestPrep wrote:
leonidbasin1 wrote:
The decimal r = 2.666666 continues forever in that repeating decimal pattern. When written as a fraction in lowest terms, r = a/b, where a and b are positive numbers.
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A |
Quantity B |
a + b |
10 |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Given: r = 2.666666....
We know that 2/3 = 666666....
So, 2.666666.... = 2 + 2/3
Let's combine 2 + 2/3 into ONE fraction
2 + 2/3 = 6/3 + 2/3 = 8/3
Since the fraction 8/3 is in lowest terms, we can say that r = 2.666666... = 8/3 = a/b
So, a = 8 and b = 3
We get:
Quantity A: 8 + 3
Quantity B: 10
Evaluate:
Quantity A: 11
Quantity B: 10
Answer: A
Cheers,
Brent
Thanks a lot Brent your method is quite intelligible . Kudos.
Re: The decimal r = 2.666666 continues forever in that repeating
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27 May 2018, 12:39
27 May 2018, 12:39
Good questions :D
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
16 Jul 2018, 17:32
16 Jul 2018, 17:32
1
leonidbasin1 wrote:
The decimal r = 2.666666 continues forever in that repeating decimal pattern. When written as a fraction in lowest terms, r = a/b, where a and b are positive numbers.
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A |
Quantity B |
a + b |
10 |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
This is actually very simple and doesn't need a lot of work:
2.666666... -> Thats too long so lets just make it simple and make it 2.66
\(2.66 = \frac{a}{b}\)
\(2\frac{66}{100} = \frac{a}{b}\)
\(\frac{266}{100} = \frac{a}{b}\)
This literally is telling us that a=266 and b=100 and we already know that 266 + 100 will be bigger than 10. This same thing works whether we use 2.6 or 2.66666.
The answer A
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
16 Jul 2018, 20:47
16 Jul 2018, 20:47
2
leonidbasin1 wrote:
The decimal r = 2.666666 continues forever in that repeating decimal pattern. When written as a fraction in lowest terms, r = a/b, where a and b are positive numbers.
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A |
Quantity B |
a + b |
10 |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
**
For any recurring decimal if we need to convert in fraction, we dividie it by 9
Suppose let us take 0.3333333... = in fraction form it can be written as = \(\frac{3}{9}\)(since only 1 digit is repeating)
Let us take a number 0.53535353... = in fraction for = \(\frac{53}{99}\) (since 2 digits are repeating)
Let us take 0.129129129... = in fraction form = \(\frac{129}{999}\) (since 3 digits are repeating)
In this question we have the r = 2.666666....
so in fraction form it can be written as = \(2\frac6 9 = \frac8 3\)
Hence it is in a and b form so,
a + b = 8 + 3 = 11 > statement 2
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Re: The decimal r = 2.666666 continues forever in that repeating
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17 Jul 2018, 04:37
17 Jul 2018, 04:37
kudos
Re: The decimal r = 2.666666 continues forever in that repeating
[#permalink]
09 Jun 2021, 22:52
09 Jun 2021, 22:52
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