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# The decimal r = 2.666666 continues forever in that repeating

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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
[Reveal] Spoiler: OA

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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Expert's post
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.
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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
Expert's post
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... = $$\frac{1739}{99}$$.
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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: 26-2/9 = 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
Attachments

GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]

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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]  23 May 2018, 23:13
Expert's post
Soon we will have our own PDF GREPrepclub
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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]  24 May 2018, 02:00
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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]  26 May 2018, 10:16
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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 + 2/3

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

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 + 2/3

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

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.

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Re: The decimal r = 2.666666 continues forever in that repeating [#permalink]  16 Jul 2018, 20:47
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]  17 Jul 2018, 04:37
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Re: The decimal r = 2.666666 continues forever in that repeating   [#permalink] 17 Jul 2018, 04:37
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