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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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.

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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If your alternate approach is followed then option B is the answer is'int it

No, answer is still the same.

\(2\frac{2}{3}=\frac{8}{3}\).
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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

Wheree can I find the concepts related to such topic.. I need to dig more

Il PDF attached.
Regards

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I just went through it and I must say, it is insightful. KUDOS I am thankful to you.

Soon we will have our own PDF GREPrepclub
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I await that day. I really hope to have it soon.

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
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Thanks a lot Brent your method is quite intelligible . Kudos.

Good questions :D

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

**

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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kudos