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The decimal r = 2.666666 continues forever in that repeating [#permalink]
19 Feb 2017, 21:55
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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.
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
Last edited by Carcass on 20 Feb 2017, 10:04, edited 1 time in total.
Edited by Carcass




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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
20 Feb 2017, 05:04
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ExplanationWe 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.
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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
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. 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.



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
20 Feb 2017, 12:36
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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. Example17.56565656..... can be 100 * 17.5656... =1756.565656565... () 17.5656... = 17.565656.... 99 * 17.5656.. = 1739 17.5656... = \(\frac{1739}{99}\).
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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
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. If your alternate approach is followed then option B is the answer is'int it



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
18 May 2018, 03:47
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No, answer is still the same. \(2\frac{2}{3}=\frac{8}{3}\).
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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
18 May 2018, 09:16
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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: 262/9 = 24/9 = 8/3



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
21 May 2018, 06:39
Wheree can I find the concepts related to such topic.. I need to dig more



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
22 May 2018, 12:07
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Il PDF attached. Regards
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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
23 May 2018, 19:07
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Carcass wrote: Il PDF attached. Regards I just went through it and I must say, it is insightful. KUDOS I am thankful to you.



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
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Carcass wrote: Soon we will have our own PDF GREPrepclub I await that day. I really hope to have it soon.



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
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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.
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 + 2/3Let'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
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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
26 May 2018, 21:11
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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.
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 + 2/3Let'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.



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
27 May 2018, 12:39
Good questions :D



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
16 Jul 2018, 17:32
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.
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



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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]
16 Jul 2018, 20:47
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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.
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 [#permalink]
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