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# M09-26

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Math Expert
Joined: 02 Sep 2009
Posts: 54376

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16 Sep 2014, 00:40
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Difficulty:

15% (low)

Question Stats:

81% (00:31) correct 19% (01:00) wrong based on 107 sessions

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Which of the following numbers is the largest?

A. $$\frac{11}{27}$$
B. $$\frac{5}{9}$$
C. $$\frac{1}{3}$$
D. $$\frac{25}{81}$$
E. $$\frac{3}{20}$$

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Math Expert
Joined: 02 Sep 2009
Posts: 54376

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16 Sep 2014, 00:40
1
Official Solution:

Which of the following numbers is the largest?

A. $$\frac{11}{27}$$
B. $$\frac{5}{9}$$
C. $$\frac{1}{3}$$
D. $$\frac{25}{81}$$
E. $$\frac{3}{20}$$

Only $$\frac{5}{9} \gt \frac{1}{2}$$

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Intern
Joined: 04 Mar 2015
Posts: 6

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31 Mar 2016, 06:04
Math Expert
Joined: 02 Sep 2009
Posts: 54376

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10 Apr 2016, 10:44

Don't know what more is there to add. It's easy to spot that all fractions but 5/9 are less than 1/2, therefore 5/9 is the largest. .
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Joined: 04 Mar 2015
Posts: 6

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10 Apr 2016, 23:44
Thanks
Intern
Joined: 29 Sep 2016
Posts: 16
Location: United States
Concentration: Finance, Economics
GPA: 3.01

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09 Nov 2016, 15:09
If it's hard to distinguish the magnitude of the fractions then here is my simple solution.

First look at the denominators A through C. 27, 9, 3. Obviously, the common denominator here is 27. Make the denominator 27 to compare the three fractions. A = 11/27, B = 15/27, C = 9/27. This alone eliminates A and C.

Compare B to D. B = 45/81, D = 25/81. Eliminate D.

Compare B to E. B = 25/40, E = 6/40.

Hope this helps.
Manager
Joined: 12 Jun 2016
Posts: 214
Location: India
WE: Sales (Telecommunications)

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08 Jul 2017, 08:52
1
Hi!

I may be a bit too late. But adding the details here, hope someone else will find it useful!

A. $$\frac{11}{27} = \frac{9}{27}+\frac{2}{27}$$ = A little over 0.33<----Helps to remember common reciprocals

B. $$\frac{5}{9} = 0.555$$ <----Helps to remember common reciprocals

C. $$\frac{1}{3} = 0.33$$

D. $$\frac{25}{81}$$. Note that $$\frac{25}{100} < \frac{25}{81} < \frac{25}{75}$$ = $$\frac{1}{4} < \frac{25}{81} < \frac{1}{3}$$. $$\frac{25}{81}$$ is between 0.25 and 0.33

E. $$\frac{3}{20} = \frac{2}{20} + \frac{1}{20}$$= a little over 0.1

Clearly B = 0.55 is the greatest.

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Re: M09-26   [#permalink] 08 Jul 2017, 08:52
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# M09-26

Moderators: chetan2u, Bunuel

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