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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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16 Sep 2014, 00:11
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. Answer: E
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Re: D0107
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05 Sep 2015, 01:48
can someone explain why is that so ? thanks



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Re: D0107
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28 Sep 2015, 04:02
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.
Answer: E Hi If differnce in numerator and denominator is fixed then we have to just look at numerator? Thanks



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Re: D0107
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30 Oct 2015, 06:21
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



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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



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Re: D0107
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19 Feb 2016, 13:11
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.



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Re: D0107
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24 May 2016, 05:56
Straight forward E)
Use Componendo and dividendo theorem. If A/B = C/D = > (A+B)/(AB) = (C+D)/(CD) by Componendo and dividendo.
You will achieve at the right answer in seconds.



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Re: D0107
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10 Jul 2016, 09:22
HARRY113 : Can you please explain how to solve this question in seconds? please provide an example using the property that you mentioned.



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Re: D0107
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10 Jul 2016, 11:12
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 A3500HV using GMAT Club Forum mobile app



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02 Aug 2016, 18:09
GMAT lists things in order from least to greatest...would they unintentionally do that for a question similar to this? haha



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Re: D0107
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06 Aug 2016, 20:32
Rule to follow here is : Largest no. = 1  smallest fraction (which is nothing but a fraction with highest denominator)



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25 Nov 2016, 06:34
Thanks for this solution. Very enlightening.



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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.
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Re: D0107
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05 Oct 2017, 14:31
Wait, am I missing something here?
Example: 1/3 > 1/4; 1/3 is the largest number.



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Re: D0107
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27 Dec 2017, 00:11
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.
therefore, the answer is E



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Re: D0107
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03 Feb 2018, 16:22
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!



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Re: D0107
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26 Mar 2018, 18:28
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!



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Re: D0107
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26 Mar 2018, 21:01
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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Re: D0107
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20 Apr 2018, 05:43
property does nt hold true for 6/3 vs 12/9 chetan2u . where am i going wrong ?







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