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

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Lucky2783
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If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink] New post   01 Mar 2015, 01:07
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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?

19/36
12/25
6/11
5/11
8/18
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B
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Re: If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink] New post   24 Apr 2018, 07:37
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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 \(12/25\)

adkikani wrote:
Bunuel niks18 amanvermagmat gmatbusters chetan2u @veritasprepakarishma


Quote:
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?

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


Do we not make denominators same for comparing numerators in such a ratio problem?
What is the most efficient way to solve this?
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Re: If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink] New post   01 Mar 2015, 05:01
Lucky2783 wrote:
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?

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


+1 Kudos for correct answer and explaination.
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Re: If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink] New post   01 Mar 2015, 10:17
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Lucky2783 wrote:
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?

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


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!
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Re: If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink] New post   24 Apr 2018, 06:35
Bunuel niks18 amanvermagmat gmatbusters chetan2u @veritasprepakarishma


Quote:
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?

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


Do we not make denominators same for comparing numerators in such a ratio problem?
What is the most efficient way to solve this?
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Re: If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink] New post   24 Apr 2018, 07:40
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adkikani wrote:
Bunuel niks18 amanvermagmat gmatbusters chetan2u @veritasprepakarishma


Quote:
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?

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


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


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
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If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink] New post   05 Jul 2019, 16:06
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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)
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Re: If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink] New post   28 Nov 2022, 19:53
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
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Re: If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from [#permalink]
28 Nov 2022, 19:53
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