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M25-15

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M25-15 [#permalink]

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New post 16 Sep 2014, 00:23
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Question Stats:

58% (00:48) correct 42% (00:45) wrong based on 170 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. \(\frac{3453}{3458}\)
[Reveal] Spoiler: OA

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Re M25-15 [#permalink]

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New post 16 Sep 2014, 00:23
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:
\(\frac{3252}{3257}=1-\frac{5}{3257}\)
\(\frac{3456}{3461}=1-\frac{5}{3461}\)
\(\frac{3591}{3596}=1-\frac{5}{3596}\)
\(\frac{3346}{3351}=1-\frac{5}{3351}\)
\(\frac{3453}{3458}=1-\frac{5}{3458}\)

Hence the answer is C.


Answer: C
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Re: M25-15 [#permalink]

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New post 13 Dec 2014, 12:44
Hi Bunuel,

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

Thanks
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Re: M25-15 [#permalink]

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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
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Re M25-15 [#permalink]

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New post 04 Nov 2015, 14:56
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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Re: M25-15 [#permalink]

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New post 07 Dec 2015, 05:16
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

I'll try to help you out on this one.
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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Re: M25-15 [#permalink]

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New post 14 Jun 2016, 09:15
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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Re: M25-15 [#permalink]

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New post 02 May 2017, 04:00
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.
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Re: M25-15 [#permalink]

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New post 25 May 2017, 19:05
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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Re: M25-15 [#permalink]

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New post 25 May 2017, 20:48
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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.

Hence C is the answer
Re: M25-15   [#permalink] 25 May 2017, 20:48
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