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Which of the following fractions is the largest?

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Which of the following fractions is the largest? [#permalink]

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New post 06 Aug 2016, 12:54
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Which of the following fractions is the largest?

A) 5/6
B) 11/14
C) 12/15
D) 17/21
E) 29/35
[Reveal] Spoiler: OA

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Re: Which of the following fractions is the largest? [#permalink]

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New post 06 Aug 2016, 14:03
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EBITDA wrote:
Which of the following fractions is the largest?

A) 5/6
B) 11/14
C) 12/15
D) 17/21
E) 29/35


Although unlikely to be a general method, I found inverting the fractions and finding the smallest to be useful and fast.

\(\text{(A) }\frac{1}{6} = \frac{3}{18} = 0.1\bar{6}\\
\text{(B) }\frac{3}{14}\\
\text{(C) }\frac{3}{15}\\
\text{(D) }\frac{4}{21}\\
\text{(E) }\frac{6}{35} = \frac{3}{17.5}\)

By setting the numerator to 3, we can eliminate all but one \(\Big(\frac{3}{18} < \frac{3}{17.5} < \frac{3}{15} < \frac{3}{14}\Big)\).

We are left with \(\frac{4}{21}\text{ and }\frac{1}{6}\). \(\frac{1}{6} = \frac{4}{24}\).

Therefore \(\frac{1}{6}\) is the smallest. \(\frac{5}{6}\) is therefore the largest.
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Re: Which of the following fractions is the largest? [#permalink]

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New post 06 Aug 2016, 19:47
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A) 5/6 = 25/30 = 30/36 = 35/42

B) 11/14 - knowing fractions (adding one to each numerator and denominator) this is known to be less than choice C and can be eliminated

C) 12/15 = 24/30 so less than choice A

D) 17/21 = 34/42 so also less than choice A

E) 29/35 - same as choice B, we know this is less than 30/36 which is choice A

Therefore the answer is A.

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Re: Which of the following fractions is the largest? [#permalink]

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New post 06 Aug 2016, 20:28
EBITDA wrote:
Which of the following fractions is the largest?

A) 5/6
B) 11/14
C) 12/15
D) 17/21
E) 29/35

Could you please explain what is the fastest way of solving this problem?

Thank you.

another way is by taking LCM of denominators(2*3*5*7)
(a) 175 (as lcm is 2*3*5*7 where 2*3 part is already in denominator just multiply 5*7 to numerator) ,similarly
(b) 165
(c)168
(d)170
(e)174

clearly (a) is largest..

Ans A

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Re: Which of the following fractions is the largest? [#permalink]

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New post 07 Aug 2016, 01:40
Rohit8865,

I also used your method. I wonder, however, if it is the fastest way to tackle this problem.

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Re: Which of the following fractions is the largest? [#permalink]

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New post 07 Aug 2016, 10:09
EBITDA wrote:
Rohit8865,

I also used your method. I wonder, however, if it is the fastest way to tackle this problem.

i find multiplication faster than divisiblity and more accurate and confident to answer
i would also love to know any faster method ,if any....

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Re: Which of the following fractions is the largest? [#permalink]

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New post 02 Aug 2017, 00:49
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cross multiplying numerator and denominator with putting sign according to numerator

5/6>11/14, bec 5*14>11*6
5/6>12/15, bec 5*15>12*6
5/6>17/21, bec 5*21>17*6
5/6>29/35, bec 5*35>29*6

A

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Re: Which of the following fractions is the largest? [#permalink]

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New post 02 Aug 2017, 05:18
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the fastest way IMO is- to compare each with others such as
5/6 and 11/14 = 5*14>11*6
5/6 and 12/15 = 5*15>6*12
5/6 and 17/21= 5*21>17*6
5/6 and 29/35= 5*35>6*29

hence 5/6 is the greatest

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Re: Which of the following fractions is the largest? [#permalink]

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New post 03 Sep 2017, 10:55
Convert the fractions to percentages and then compare.
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Re: Which of the following fractions is the largest? [#permalink]

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New post 04 Nov 2017, 22:17
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I want to share a simpler approach.
Rule : out of 2 fractions F1 & F2, F1 is greater if (1/F1) is smaller or vice versa.
In this Question
F1 = 5/6, 1/F1 = 6/5 =1.2
F2 = 11/14, 1/F2 = 14/11 >1.2
F3 = 12/15 , 1/F3 = 15/12 >1.2
F4= 17/21, 1/F4 = 21/17 >1.2
F5 = 29/35, 1/F5 = 35/29 >1.2

Since 1/F1 is smallest, F1 is greatest.

PS: similarly to find the lowest fraction, 1/fraction shall be highest.

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Re: Which of the following fractions is the largest? [#permalink]

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New post 10 Nov 2017, 20:39
This approach I find very interesting and very lucid to apply...
frndrobinster wrote:
I want to share a simpler approach.
Rule : out of 2 fractions F1 & F2, F1 is greater if (1/F1) is smaller or vice versa.
In this Question
F1 = 5/6, 1/F1 = 6/5 =1.2
F2 = 11/14, 1/F2 = 14/11 >1.2
F3 = 12/15 , 1/F3 = 15/12 >1.2
F4= 17/21, 1/F4 = 21/17 >1.2
F5 = 29/35, 1/F5 = 35/29 >1.2

Since 1/F1 is smallest, F1 is greatest.

PS: similarly to find the lowest fraction, 1/fraction shall be highest.

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Re: Which of the following fractions is the largest?   [#permalink] 10 Nov 2017, 20:39
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Which of the following fractions is the largest?

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