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# D01-07

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Math Expert
Joined: 02 Sep 2009
Posts: 43804

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15 Sep 2014, 23:11
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Difficulty:

25% (medium)

Question Stats:

64% (00:38) correct 36% (00:33) wrong based on 90 sessions

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Which of the following numbers is the greatest?

A. $$\frac{1876452}{1876455}$$
B. $$\frac{1883446}{1883449}$$
C. $$\frac{1883453}{1883456}$$
D. $$\frac{1883456}{1883459}$$
E. $$\frac{1883491}{1883494}$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43804

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15 Sep 2014, 23:11
Expert's post
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Official Solution:

Which of the following numbers is the greatest?

A. $$\frac{1876452}{1876455}$$
B. $$\frac{1883446}{1883449}$$
C. $$\frac{1883453}{1883456}$$
D. $$\frac{1883456}{1883459}$$
E. $$\frac{1883491}{1883494}$$

You have to notice that the difference between a numerator and denominator of any fraction equals 3. Thus, the greater the numerator/denominator, the greater the fraction. In this case, the greatest numerator is in the fifth fraction.

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Intern
Joined: 16 May 2015
Posts: 43

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05 Sep 2015, 00:48
1
KUDOS
can someone explain why is that so ? thanks
Manager
Joined: 31 Jul 2014
Posts: 143
GMAT 1: 630 Q48 V29

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28 Sep 2015, 03:02
1
KUDOS
Bunuel wrote:
Official Solution:

Which of the following numbers is the greatest?

A. $$\frac{1876452}{1876455}$$
B. $$\frac{1883446}{1883449}$$
C. $$\frac{1883453}{1883456}$$
D. $$\frac{1883456}{1883459}$$
E. $$\frac{1883491}{1883494}$$

You have to notice that the difference between a numerator and denominator of any fraction equals 3. Thus, the greater the numerator/denominator, the greater the fraction. In this case, the greatest numerator is in the fifth fraction.

Hi
If differnce in numerator and denominator is fixed then we have to just look at numerator?

Thanks
Intern
Joined: 22 Nov 2014
Posts: 32

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30 Oct 2015, 05:21
Each can be written as x/x+1.. test numbers x=2 x/x+1 =2/3, .666 x=3, x/x+1 =3/4=.75>.66 so as x increases value of fraction increases
Current Student
Joined: 30 Sep 2015
Posts: 90
Location: Singapore
Concentration: Operations, Technology
GMAT 1: 690 Q48 V37
GMAT 2: 740 Q50 V40
WE: Supply Chain Management (Manufacturing)

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24 Nov 2015, 19:36
3
KUDOS
1
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1876452/1876455 = (1876455 - 3)/1876455 = 1 - 3/1876455
1883491/1883494 = (1883494 - 3)/1883494 = 1 - 3/1883494

All the fractions can be written as 1 - 3/(Some number)
The largest denominator would make the number highest
Manager
Joined: 05 Jul 2015
Posts: 107
GMAT 1: 600 Q33 V40
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19 Feb 2016, 12:11
I had to quickly test the theory being asked with other numbers to remind myself.

1/2 is smaller than 2/3 is smaller than 5/6 is smaller than 50/51. So since the different between the numerator and denominator is always 3, E is the biggest number and thus the closest number to 1.
Intern
Joined: 06 Aug 2015
Posts: 46
Concentration: General Management, Entrepreneurship
GMAT Date: 10-30-2016
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24 May 2016, 04:56
Straight forward E)

Use Componendo and dividendo theorem.
If A/B = C/D = > (A+B)/(A-B) = (C+D)/(C-D) by Componendo and dividendo.

You will achieve at the right answer in seconds.
Intern
Joined: 26 Jul 2015
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10 Jul 2016, 08:22
HARRY113 : Can you please explain how to solve this question in seconds? please provide an example using the property that you mentioned.
Intern
Joined: 06 Aug 2015
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10 Jul 2016, 10:12
1
KUDOS
Hi,

With the above rule in mind, try hitting the options.
Apply it to any 2 options you like.
You can conclude that, sum of numerator and denominator matters.{ ( A + B ) from above and ( A - B ) is always 3 }
Henceforth, the option with largest numerator and denominator will be our answer.

Hope you understood!

Cheers,
Harry
Hit kudos if you like this approach!

Sent from my Lenovo A3500-HV using GMAT Club Forum mobile app
Intern
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Location: United States (WV)
Concentration: Social Entrepreneurship, Sustainability
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WE: Project Management (Non-Profit and Government)

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02 Aug 2016, 17:09
1
KUDOS
GMAT lists things in order from least to greatest...would they unintentionally do that for a question similar to this? haha
Intern
Joined: 26 Jan 2014
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Concentration: Operations, Entrepreneurship
GMAT Date: 05-02-2014
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06 Aug 2016, 19:32
1
KUDOS
Rule to follow here is :
Largest no. = 1 - smallest fraction (which is nothing but a fraction with highest denominator)
Intern
Joined: 11 Nov 2016
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25 Nov 2016, 05:34
Thanks for this solution. Very enlightening.
Intern
Joined: 25 May 2017
Posts: 27
GMAT 1: 620 Q48 V27

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15 Sep 2017, 04:02
If a fraction p/q < 1 then the faction p+n/q+n (where n is a positive intger) will always be greater than p/q.

To express this mathematically,

p+n/q+n > p/q , if p/q<1 & n>1

Now all the options in the question can be expressed as 1876452+n/1876455+n

Option E has the biggest value for n and will be the greatest fraction.

Intern
Joined: 25 Aug 2017
Posts: 34

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05 Oct 2017, 13:31
Wait, am I missing something here?

Example: 1/3 > 1/4; 1/3 is the largest number.
Intern
Joined: 11 Oct 2017
Posts: 11

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26 Dec 2017, 23:11
a simpler way to understand this is -
In all the given fractions, the numerator is 3 more than the denominator. therefore, all these fractions can be written in this form - (D - 3) / D. Where D is the denominator.
Now, this equation can be changed to (D/D) - (3/D). Basically split the numerator.
This now becomes - 1 - (3/D)
From the options, the one with the biggest denominator, will yield the smallest value for 3/D and thus the smallest value to be deducted from 1, subsequently yielding the largest value.

Intern
Joined: 22 Jan 2018
Posts: 2

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03 Feb 2018, 15:22
Also using limits theory:

lim (n/(n+3)) = 1 when n = infinity
lim (n/(n+3)) = 0 when n = 0

Then the bigger the "n" the bigger the fraction.

Cheers!
Re: D01-07   [#permalink] 03 Feb 2018, 15:22
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# D01-07

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