If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from

Question

If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from least to greatest, which number would be in the middle?

A. 19/36
B. 12/25
C. 6/11
D. 5/11
E. 8/18

GMATBusters · Accepted Answer

Hii
There are many ways to compare fractions, some of the methods are discussed above.
I would like to present a different approach.
 For any positive fraction,  the higher the value of fraction, the lower is the value of its reciprocal.  
 Sometimes it is very easy to find the approximate value of reciprocal , which is the key factor to use this approach.
 If u want to find the highest fraction, the reciprocal would be lowest or vice versa. 
reciprocal of  19/36 = 36/19 =1.89.. 
reciprocal of  5/11= 11/5 = 2.2 
reciprocal of  12/25=25/12 =2.0.. 
reciprocal of  6/11 =11/6 =1.8... 
reciprocal of  8/18 =18/8 =2.25

Now if we want to arrange them in least to greatest, we have to arrange the reciprocal from greatest to least
hence the order of reciprocal would be:
2.25, 2.2, 2.0.., 1.89., 1.8..
hence the numbers order from least to greatest would be:
 8/18, 5/11, 12/25, 19/36, 6/11

Hence the middle term would be  12/25

tommyvarese · Answer

hi! all numbers are about 1/2 so you can separate those are bigger from those are smaller: 19/36 bigger than 18/36=1/2 12/25 smaller than 12/24=1/2 6/11 bigger than 6/12=1/2 5/11 smaller than 6/12=1/2 8/18=4/9 smaller than 4/8=1/2 now you have to choose 12/25, 5/11 or 4/9. you compare 4/9 and 5/11: the least common multiple between 9 and 11 is 99---> 44/99 < 45/99 you compare now 5/11 and 12/25: the LCM is 25*11=275---> 125/275 < 132/275 so answer is B! hope it's clear!

adkikani · Answer

Bunuel   niks18   amanvermagmat   gmatbusters   chetan2u  @veritasprepakarishma

Do we not make denominators same for comparing numerators in such a ratio problem?
What is the most efficient way to solve this?

chetan2u · Answer

Hi, each question would require a approach suiting it....

Here you can easily see 2 of them, 19/36 and 6/11, to be >1/2 and other three are less than 1/2..
So our answer is greatest of remaining three..
Some similarity in numerator of 12/25 and 8/18..
12=8*3/2..
So 8/18=(8*3/2)/(18*3/2)=12/27<12/25

Finally check between 5/11 and 12/25..
Here you can cross Multiply..
5*25=125 and 11*12=132..
132 is greater, so 12/25 is greater and the middle value

bebs · Answer

By scanning through the fractions, one can tell that two of them,  \frac{19}{36}  and  \frac{6}{11} , are slightly greater than  \frac{1}{2} , so we are left with  \frac{5}{11} ,  \frac{12}{25} , and  \frac{8}{18}  (same as  \frac{4}{9} )
We can quickly manipulate the three fractions to have the same numerator as follows:
 \frac{5}{11}  x  \frac{12}{12}  =  \frac{60}{132} 
 \frac{12}{25}  x  \frac{5}{5}  =  \frac{60}{125} 
 \frac{4}{9}  x  \frac{15}{15}  =  \frac{60}{135}

Therefore,  \frac{4}{9}  <  \frac{5}{11}  <  \frac{12}{25}  < ... < ... ====> Answer is  \frac{12}{25}  ( B )

Kinshook · Answer

Asked: If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from least to greatest, which number would be in the middle?

5/11 = 0.45555
19/36 = 0.503
12/25 = 0.48
6/11 = 0.54444
8/18 = 4/9 = .4444

8/18 < 5/11 < 12/25 < 19/36 < 6/11

IMO B

weez · Answer

I finally have a good solution that wasn't mentioned before so:

Greater than 1/2: 6/11, 19/36
Less than 1/2: 5/11, 12/25, 8/18

The answer is one of the values less than 1/2.

- 5/11 is 0.5/11 away from 1/2
- 12/25 is 0.5/25 away from 1/2
- 8/18 or 4/9 is 0.5/9 away from 1/2

12/25 is the least distance away from 1/2, so it's the middle number.

vishwathols · Answer

multiply the numerators by 2
38/36; 10/11; 24/25; 12/11; 16/18

Now group those fractions that are less than 1 and greater than 1

those < 1: 10/11; 24/25; 16/18
those > 1: 38/36; 12/11

now arrange them in order using the difference between the numerator and denominator

when the differences for two fractions are same, the fraction with the highest numerator is larger in value than the fraction with the lowest numerator

with that in mind, lets re-arrange only those < 1, coz those >1 will never be the middle one in the arrangement

those < 1: 16/18 < 10/11 < 24/25

Final ascending order: 16/18 < 10/11 < 24/25 < [38/36; 12/11]

Answer: 12/25

luisdicampo · Answer

Deconstructing the Question

We must arrange the fractions  \frac{19}{36} ,  \frac{5}{11} ,  \frac{12}{25} ,  \frac{6}{11} , and  \frac{8}{18}  from least to greatest and find the middle value.

Since there are   5   numbers, the middle number will be the third after sorting.

A fast GMAT approach is to approximate the fractions as decimals.

Step-by-step

First simplify  \frac{8}{18}

\frac{8}{18} = \frac{4}{9}

\frac{4}{9} \approx 0.444

Next approximate  \frac{5}{11}

\frac{5}{11} \approx 0.455

Convert  \frac{12}{25}

\frac{12}{25} = 0.48

Estimate  \frac{19}{36}

\frac{18}{36} = 0.5

So

\frac{19}{36} \approx 0.528

Now estimate  \frac{6}{11}

\frac{6}{11} \approx 0.545

Order from least to greatest

\frac{8}{18} \approx 0.444

\frac{5}{11} \approx 0.455

\frac{12}{25} = 0.48

\frac{19}{36} \approx 0.528

\frac{6}{11} \approx 0.545

The third number is  \frac{12}{25}

Answer B: 12/25

If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from

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