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Which of the following fractions has the greatest value?

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by Anurag@Gurome » Mon Jul 09, 2012 8:39 am
gmatter2012 wrote:Which of the following fractions has the greatest value?
Let us try to make a common denominator equal to 10!, so that we can compare the terms by their numerators...
  • A. 3/8! = (3*9*10)/(8!*9*10) = (3*9*10)/10! = 270/10!
    B. 6(4!)/5(9!) = (6*4!*2)/(9!2*5) = (6*24*2)/10! = 288/10!
    C. 4(3!)/9! = (4*3!*10)/(9!*10) = (4*6*10)/10! = 240/10!
    D. 3/5(7!) = (3*2*8*9)/(7!*8*9*5*2) = (3*2*8*9)/10! = 432/10!
    E. 14/5(8!) = (14*2*9)/(8!*9*5*2) = (14*9*2)/10! = 252/10!
Option D is the greatest.

The correct answer is D.
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by eagleeye » Mon Jul 09, 2012 8:50 am
gmatter2012 wrote:Which of the following fractions has the greatest value?

A. 3/8!

B. 6(4!) / 5(9!)

C. 4(3!) / 9!

D. 3 / 5(7!)

E. 14 / 5(8!)
When comparing, do two things, compare the things with the same denominator, then convert everything to a common denominator and compare.

Pairing in groups can save us valuable time.

First compare A and E. We have 14/5 vs 3, 3 wins. Eliminate E.

Then compare B and C. 6/5*4! Vs( 4*3 != 4!). B wins, eliminate C.

Compare A and D. To compare we need 8! In both at the denominator.
D is (3/5)*(1/7!) = (3*8/5)/8! = (24/5)/(8!)
Now comparing A and D. 3 vs 24/5, 24/5 wins. Eliminate A.

Final comparison between B and D. Change D to 9! In denominator to compare with B.
D = (24/5)/8! = (24*9/5)/8!

Comparing B vs D. 6*4!/5 vs 24*9/5. Now 4! = 24, so we are comparing 6 vs 9. 9 wins. Eliminate B
leaving D as the final answer.
Hence D.
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by gmatter2012 » Mon Jul 09, 2012 9:34 am
Anurag@Gurome wrote: Let us try to make a common denominator equal to 10!, so that we can compare the terms by their numerators...
  • A. 3/8! = (3*9*10)/(8!*9*10) = (3*9*10)/10! = 270/10!
    B. 6(4!)/5(9!) = (6*4!*2)/(9!2*5) = (6*24*2)/10! = 288/10!
    C. 4(3!)/9! = (4*3!*10)/(9!*10) = (4*6*10)/10! = 240/10!
    D. 3/5(7!) = (3*2*8*9)/(7!*8*9*5*2) = (3*2*8*9)/10! = 432/10!
    E. 14/5(8!) = (14*2*9)/(8!*9*5*2) = (14*9*2)/10! = 252/10!
Option D is the greatest.

The correct answer is D.

Wonderful way , perfectly suits me , great !!Will go with this method. Many thanks
eagleeye wrote:
When comparing, do two things, compare the things with the same denominator, then convert everything to a common denominator and compare.

Pairing in groups can save us valuable time.

First compare A and E. We have 14/5 vs 3, 3 wins. Eliminate E.

Then compare B and C. 6/5*4! Vs( 4*3 != 4!). B wins, eliminate C.

Compare A and D. To compare we need 8! In both at the denominator.
D is (3/5)*(1/7!) = (3*8/5)/8! = (24/5)/(8!)
Now comparing A and D. 3 vs 24/5, 24/5 wins. Eliminate A......

@eagleeye: Thank you for sharing another approach !
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