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# M25-15

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Math Expert
Joined: 02 Sep 2009
Posts: 49438

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16 Sep 2014, 01:23
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25% (medium)

Question Stats:

64% (00:44) correct 36% (00:46) wrong based on 316 sessions

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Which of the following fractions is the largest?

A. $$\frac{3252}{3257}$$
B. $$\frac{3456}{3461}$$
C. $$\frac{3591}{3596}$$
D. $$\frac{3346}{3351}$$
E. $$\frac{3453}{3458}$$

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Joined: 02 Sep 2009
Posts: 49438

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16 Sep 2014, 01:23
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Official Solution:

Which of the following fractions is the largest?

A. $$\frac{3252}{3257}$$
B. $$\frac{3456}{3461}$$
C. $$\frac{3591}{3596}$$
D. $$\frac{3346}{3351}$$
E. $$\frac{3453}{3458}$$

In each fraction, the denominator is greater than the numerator by 5. Consider:
$$\frac{3252}{3257}=1-\frac{5}{3257}$$
$$\frac{3456}{3461}=1-\frac{5}{3461}$$
$$\frac{3591}{3596}=1-\frac{5}{3596}$$
$$\frac{3346}{3351}=1-\frac{5}{3351}$$
$$\frac{3453}{3458}=1-\frac{5}{3458}$$

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Joined: 07 Dec 2009
Posts: 97
GMAT Date: 12-03-2014

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13 Dec 2014, 13:44
1
Hi Bunuel,

Is there a Particular way to approach this kind of a question ?

Thanks
Manager
Joined: 14 Jul 2014
Posts: 93

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29 Dec 2014, 00:21
2
bhatiavai wrote:
Hi Bunuel,

Is there a Particular way to approach this kind of a question ?

Thanks

I think the foll is the approach that Bunuel has used. I used the same

Larger No = 1 - Smaller No

Using the above method, compare all the fractions:

You'll see that 5/3596 is the smallest fraction -- Same Numerator, Greatest Denominator.

Hence the Largest no. = 1 - Smallest fraction

Ans: C
Manager
Joined: 28 Dec 2013
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04 Nov 2015, 15:56
I think this the explanation isn't clear enough, please elaborate. Please let me know in further detail how we solve, is it because the right answer has the largest denominator? Also where does the 1 come from?
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Joined: 02 Jul 2015
Posts: 106
Schools: ISB '18
GMAT 1: 680 Q49 V33

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07 Dec 2015, 06:16
sagnik242 wrote:
I think this the explanation isn't clear enough, please elaborate. Please let me know in further detail how we solve, is it because the right answer has the largest denominator? Also where does the 1 come from?

Hi

If the numerator remains the same, then larger the denominator, lesser is the value of the fraction (as there is an inverse relationship between the two).

Consider this; x= a-b
Keeping a constant, larger the value of b, smaller is the value of x and vice versa.

Combining the above two concepts we get

x(answer of the our question)= 1- fraction
As numerator 5 is constant, larger denominator will give lower value fraction.
Hence one with the highest denominator will have the highest value.
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14 Jun 2016, 10:15
1
I think that this isnt the right approach. The straight math thing 1- Smallest Number.
As long as all of the fractions have something in common: denominator- numerator=5
we will select the fraction with the largest number as a numerator which is clearly C.

That's a 20 sec question.
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Intern
Joined: 26 May 2016
Posts: 22
GMAT 1: 640 Q49 V30

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02 May 2017, 05:00
1
Bunuel wrote:
Which of the following fractions is the largest?

A. $$\frac{3252}{3257}$$
B. $$\frac{3456}{3461}$$
C. $$\frac{3591}{3596}$$
D. $$\frac{3346}{3351}$$
E. $$\frac{3453}{3458}$$

consider 1/6 = 1/(1+5) = little over 0.1
2/7 = 2/(2+5) = little over 0.2
3/8 = 3/(3+5) = little over 0.3

i.e. the one with the greatest numerator is the largest. hence C is the answer.
Intern
Joined: 30 Oct 2016
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25 May 2017, 20:05
My approach was

The pattern is x/(x+5), to find the largest.
If we invert its (x+5)/x, and inverted value should be smallest
i,e 1 + 5/x should be smallest, in that case x should be highest , the highest value in numerator is C
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Joined: 22 Aug 2013
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25 May 2017, 21:48
1
Well, if we have a number of proper positive fractions (numerator < denominator), such that difference between the numerator and denominator for each of them be the same:- then, the one with the highest numerator will have the highest value.

Eg, lets consider 5 positive proper fractions:

a/(a+x), b/(b+x), c/(c+x), d/(d+x), e/(e+x)

where x is obviously a positive number.

Now, out of all the numerators, if a<b<c<d<e, Then:

definitely: a/(a+x) < b/(b+x) < c/(c+x) < d/(d+x) < e/(e+x)

Applying the same to our question, we can see that each option is a positive proper fraction where difference between numerator and denominator is 5.
So the one with highest numerator will have the highest value.

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Joined: 23 May 2018
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18 Jun 2018, 07:07
This one was pretty easy.
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Joined: 20 Apr 2018
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Concentration: Technology, Nonprofit
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18 Jun 2018, 08:41
All the numbers fit the function, f(x) = x/x+5
If you think about it, this is a function which approaches 1 as x increases and tends to infinity. This is an increasing function (for x > -1), so for a higher value of x, f(x) will be higher. Option C has the highest value of x. Hence, C.
Manager
Joined: 25 Jul 2017
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18 Jun 2018, 23:09
Bunuel wrote:
Which of the following fractions is the largest?

A. $$\frac{3252}{3257}$$
B. $$\frac{3456}{3461}$$
C. $$\frac{3591}{3596}$$
D. $$\frac{3346}{3351}$$
E. $$\frac{3453}{3458}$$

It's a basically 10 Sec question.
If you see, the difference between numerator & denominator is 5 for all.
So any number which has the largest numerator must be the largest one.
3591 is the largest numerator among 5.
C is the answer (A 10 sec question)
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Joined: 09 Aug 2017
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25 Jun 2018, 07:34
3252/3257 is proper fraction and adding positive integer K in numerator and denominator will shift the fraction towards 1. In C highest value of K= 339 is added. so C is most closest to 1 and, hence, highest value fraction.

Please give kudos if you like my explanation.
Re: M25-15 &nbs [#permalink] 25 Jun 2018, 07:34
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# M25-15

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