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Math Expert V
Joined: 02 Sep 2009
Posts: 55609

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Difficulty:   25% (medium)

Question Stats: 66% (00:40) correct 34% (00:36) wrong based on 143 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. $$\frac{1883491}{1883494}$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 55609

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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
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can someone explain why is that so ? thanks
Manager  Joined: 31 Jul 2014
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GMAT 1: 630 Q48 V29 Show Tags

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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: 23 Nov 2014
Posts: 31

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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
Manager  Joined: 01 Oct 2015
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Location: Singapore
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GMAT 1: 690 Q48 V37 GMAT 2: 740 Q50 V40 WE: Supply Chain Management (Manufacturing)

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6
1
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
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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.
Manager  B
Joined: 06 Aug 2015
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Concentration: General Management, Entrepreneurship
GMAT Date: 10-30-2016
GRE 1: Q160 V135 GPA: 3.34
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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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HARRY113 : Can you please explain how to solve this question in seconds? please provide an example using the property that you mentioned.
Manager  B
Joined: 06 Aug 2015
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Concentration: General Management, Entrepreneurship
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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!

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Current Student Joined: 10 Jan 2016
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GMAT lists things in order from least to greatest...would they unintentionally do that for a question similar to this? haha
Intern  B
Joined: 26 Jan 2014
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GMAT Date: 05-02-2014
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1
Rule to follow here is :
Largest no. = 1 - smallest fraction (which is nothing but a fraction with highest denominator)
Intern  B
Joined: 12 Nov 2016
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Location: Nigeria
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Thanks for this solution. Very enlightening.
Intern  B
Joined: 26 May 2017
Posts: 25
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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  B
Joined: 25 Aug 2017
Posts: 32

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Wait, am I missing something here?

Example: 1/3 > 1/4; 1/3 is the largest number.
Intern  B
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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  B
Joined: 22 Jan 2018
Posts: 1

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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!
Senior Manager  P
Joined: 27 Dec 2016
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Bunuel chetan2u Hi Bunuel & Chetan, I was wondering does this concept apply to all similar problems? For example, if the difference were 4 amongst all of the answer choices or 5 instead of 3, would we be able to apply this same concept then as well? Please help! Thank You!
Math Expert V
Joined: 02 Sep 2009
Posts: 55609

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csaluja wrote:
Bunuel chetan2u Hi Bunuel & Chetan, I was wondering does this concept apply to all similar problems? For example, if the difference were 4 amongst all of the answer choices or 5 instead of 3, would we be able to apply this same concept then as well? Please help! Thank You!

Yes. You could easily check this yourself by picking simple fractions and comparing them.
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Intern  B
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property does nt hold true for 6/3 vs 12/9 chetan2u . where am i going wrong ? Re: D01-07   [#permalink] 20 Apr 2018, 05:43

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