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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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Math Expert
Joined: 02 Sep 2009
Posts: 52294
What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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17 Dec 2018, 01:30
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Difficulty:

55% (hard)

Question Stats:

69% (02:49) correct 31% (02:53) wrong based on 32 sessions

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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

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Joined: 12 Dec 2018
Posts: 19
Location: India
Concentration: Finance, Operations
Schools: ISB '20
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WE: Information Technology (Computer Software)
Re: What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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17 Dec 2018, 01:33
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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17 Dec 2018, 03:11
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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17 Dec 2018, 03:28
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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17 Dec 2018, 03:31
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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Updated on: 17 Dec 2018, 03:40
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, 03:35.
Last edited by nazeernaren on 17 Dec 2018, 03:40, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7204
What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ?  [#permalink]

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17 Dec 2018, 03:36
2
1
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 = $$\frac{8}{11} - \frac{4}{7}=\frac{56-44}{77}=\frac{12}{77}$$

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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What is the range of the set 2/3, 8/11, 5/8, 4/7, 9/13 ? &nbs [#permalink] 17 Dec 2018, 03:36
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