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What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?

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What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post 17 Dec 2018, 02:30
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What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post 17 Dec 2018, 04:36
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Archit3110 wrote:
Bunuel wrote:
What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?

A. 3/56
B. 2/21
C. 11/91
D. 12/77
E. 55/77



chetan2u :
Hi could you please suggest a <2 min way to determine the largest and smallest value from the given set : "2/3, 8/11, 5/8, 4/7, 9/13"


Thats a great question as the main point here is to find the largest and smallest value in the least time..

There are various ways..
Here, the first step would be to find some similarity in numerators or denominators.

(I) get them into same numerator or same denominator
There are three numbers with multiple of 2, and 8 is the maximum, so get all in terms of 8..
\(\frac{2}{3}=\frac{2*4}{3*4}; \frac{8}{11}; \frac{4}{7}=\frac{4*2}{2*7}\)...
when numerators are same, bigger the denominator, smaller the number..
So, \(14>12>11..... \frac{8}{11}>\frac{2}{3}=\frac{2*4}{3*4}>\frac{4}{7}=\frac{4*2}{2*7}\)..

Let me check 5/8 with 4/7 and 8/11 by second way..
(II) Get the fractions in form of \(\frac{a+x}{b+x}\)
all three fractions have a difference of 3 in numerator and denominator that is d-n=3..
so let me write all of them in same terms.. \(\frac{4}{7};\frac{4+1}{7+1};\frac{4+4}{7+4}\)....
In these three if the gap is same bigger the number, bigger the fraction so \(\frac{4}{7}<\frac{4+1}{7+1}<\frac{4+4}{7+4}\)

Now you have largest as 8/11 and smallest as 4/7 and we have to compare 9/13...
when you compare 4/7, you can convert it into 4*2/7*2=8/14 ... now 8/14 has a bigger numerator and a smaller denominator than 9/13, so 8/14 is smaller..
(III) Cross-multiply - You can cross-multiply too to find the answer .. 8/11 vs 9/13 .. 8*13 vs 9*11 = 104 vs 99 .. since 104 is bigger, 8/11 is bigger as 104 represents the numerator 8.

so range = \(\frac{8}{11} - \frac{4}{7}=\frac{56-44}{77}=\frac{12}{77}\)

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Re: What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post 17 Dec 2018, 02:33
Range = 8/11 -4/7 = 12/77

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Re: What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post 17 Dec 2018, 04:11
Bunuel wrote:
What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?

A. 3/56
B. 2/21
C. 11/91
D. 12/77
E. 55/77



chetan2u :
Hi could you please suggest a <2 min way to determine the largest and smallest value from the given set : "2/3, 8/11, 5/8, 4/7, 9/13"
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Re: What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post 17 Dec 2018, 04:28
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2/3 > 1/2.
If the difference between numerator and denominator is same same in two fractions, the fraction with highest numerator is greater in value than that of the fraction with lowest.
By that logic, among 4/7, 5/8 and 8/11, 8/11 is the largest.

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Re: What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post 17 Dec 2018, 04:31
nazeernaren wrote:
2/3 > 1/2.
If the difference between numerator and denominator is same same in two fractions, the fraction with highest numerator is greater in value than that of the fraction with lowest.
By that logic, among 4/7, 5/8 and 8/11, 8/11 is the largest.

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nazeernaren : agreed but then how will you negate for other two 2/3 and 9/13?
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What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post Updated on: 17 Dec 2018, 04:40
It is advisable to keep in mind the decimals for fractions of the form 1/x, for 1 <x<=12. That way we can estimate a fraction value in decimal and decide quickly. Hope this is helpful.

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Originally posted by nazeernaren on 17 Dec 2018, 04:35.
Last edited by nazeernaren on 17 Dec 2018, 04:40, edited 1 time in total.
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What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post Updated on: 01 Mar 2019, 07:43
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I don't know if this is the best way but you can estimate if you don't remember all the fraction to decimal conversions.

2/3 = .66

For these, I knew that 1/8 = .125 and 1/11 = .09
8/11 = .72
5/8 = .625

I forgot these two, so I got them close to denominator of 100.
4/7*(14/14) = 56/98, (actual is .57)
9/13*(8/8) = 72/104 (actual is .69)

Now I can see that 8/11 is largest and 4/7 is the smallest.
Use LCD 8/11-4/7 = 56/77 - 44/77 = 12/77

Originally posted by energetics on 12 Feb 2019, 17:01.
Last edited by energetics on 01 Mar 2019, 07:43, edited 1 time in total.
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Re: What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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New post 12 Feb 2019, 18:16
by percent conversion,

we get the smallest 4/7 and the greatest 8/11

So the range is the difference of these two .

The answer is 12/77 option D

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Re: What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?   [#permalink] 12 Feb 2019, 18:16
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