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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
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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 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
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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

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

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New post 29 Oct 2017, 11:53
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Bunuel wrote:
Which of the following fractions is the largest?

A. 5/6

B. 11/14

C. 12/15

D. 17/21

E. 29/35


LCM of denominators of all the fractions i.e LCM of 6, 14, 15, 21, 35 = 210

As a next stem we need to make all denominators equal to the LCM

A. \(\frac{5}{6} => \frac{5}{6}*\frac{35}{35}=\frac{175}{210}\)

B. \(\frac{11}{14} =>\frac{11}{14}*\frac{15}{15}=\frac{165}{210}\)

C. \(\frac{12}{15} =>\frac{12}{15}*\frac{14}{14}=\frac{168}{210}\)

D. \(\frac{17}{21} =>\frac{17}{21}*\frac{10}{10}=\frac{170}{210}\)

E. \(\frac{29}{35} => \frac{29}{35}*\frac{6}{6}=\frac{174}{210}\)

Clearly option A is the greatest

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

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New post 30 Oct 2017, 08:28
Bunuel wrote:
Which of the following fractions is the largest?

A. 5/6

B. 11/14

C. 12/15

D. 17/21

E. 29/35


In order to compare fractions, take LCM of all denominators, 6,14,15,21,35.
LCM=210
A) \(\frac{5}{6}\) = \(\frac{5*35}{6*35}\)=\(\frac{175}{210}\)
B) \(\frac{11}{14}\) = \(\frac{11*15}{14*15}\)=\(\frac{165}{210}\)
C) \(\frac{12}{15}\)= \(\frac{12*14}{15*14}\)= \(\frac{166}{210}\)
D) \(\frac{17}{21}\) = \(\frac{17*10}{21*10}\) = \(\frac{170}{210}\)
E) \(\frac{29}{35}\) = \(\frac{29*6}{35*6}\)= \(\frac{174}{210}\)

We see that A is the largest.
Answer A
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Which of the following fractions is the largest?  [#permalink]

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New post 30 Oct 2017, 08:48
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Bunuel wrote:
Which of the following fractions is the largest?

A. 5/6

B. 11/14

C. 12/15

D. 17/21

E. 29/35


hi..

the fractions are such that you can do away with LCM and thus some sort of calculations..

Remember - when we add SIMILAR quantity to BOTH numerator and denominator the resulting number is BIGGER
example \(1/2 <\frac{1+1}{2+1}<\frac{1+3}{2+3}\)

now lets see the choices..

Compare B and C as both have a difference of 3 in numerator and denominator.. 11/14 and 12/15 \(\frac{12}{15}= \frac{11+1}{14+1}\), so 12/15 is bigger
Now \(\frac{5}{6}= \frac{5*3}{6*3}=\frac{15}{18}\)... similarly 15/18>12/15
so A is the greatest in A,B and C..

lets check A with D and E...

D 17/21..... difference of 4 in numerator and denominator, so multiply 5/6 with 4/4.... \(\frac{5*4}{6*4}=\frac{20}{24}=\frac{17+3}{21+3}>\frac{17}{21}\).... so A is greater

compare with E.
E 29/35...... \(\frac{5}{6} = \frac{30}{36}=\frac{29+1}{35+1}>\frac{29}{35}\)
so A is greater

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

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New post 01 Nov 2017, 06:35
Check the difference between the numerator and denominator.

Fraction with least difference with be the highest fraction.
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Re: Which of the following fractions is the largest?  [#permalink]

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New post 01 Nov 2017, 07:36
nehasri wrote:
Check the difference between the numerator and denominator.

Fraction with least difference with be the highest fraction.

Hi nehasri,

This logic will not be useful when the difference between numerator and denominator will be the same for different fractions
E.g. 1/2 & 2/3

In this question also if option E had been 30/35 which is 6/7 then the approach would have to be changed

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

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New post 14 May 2019, 10:05
A simple and fast way is to determine quickly an approximate value of each an every fractions: 5/6=0.8, which won't be reached by any of the other fractions which are all below 0.8, either 0.7 or 0.6! Hope this helped you, however I definitely suck at quant...
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Re: Which of the following fractions is the largest?   [#permalink] 14 May 2019, 10:05
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